Axiome

[Seldoon]

Je reviens sur Axiome, maintenant vu. Je ne retrouve plus vos discussions, je répète donc probablement des choses déjà dites, et je le fais dans un sujet séparé pour espérer mollement en retrouver une trace demain matin.

J’aime beaucoup ce personnage et beaucoup des scènes. J’ai quelques réserves ici et la. J’adore la mère, la lente découverte de sa mythomanie, la fin, le jeu qui s’établit rapidement entre le film et le spectateur : ment-il ? On se fait avoir ici et là, notamment sur la copine chanteuse lyrique. Mais la question se pose : est-elle vraiment chanteuse lyrique ? Elle est simplement envoyée là par ses parents et ne semble pas avoir de don ni d’intérêt particulier pour la discipline (ni en cours, ni en sortant du spectacle). Elle est déterminée à être dans la position ou posture d’une chanteuse lyrique.

Cette question de la détermination sociale reviendra plusieurs fois. Elle me semble profondément liée à la mythomanie de Julius. Si nous ne sommes que déterminations sociales alors nous ne sommes personne. Nous ne sommes que discours. Et alors tout est vrai. Je suis autant architecte que toi, autant croyant et athée que toi. J’aurais été toi si j’avais eu tes parents, j’aurais vu le type nu au passage piéton si j’avais été là à ta place. Or nous somme interchangeables, donc je suis toi, je l’ai vu, je suis croyant et athée, donc je suis architecte.
Julius est le trochet (c’est le nom, j’ai vérifié sur Wikipedia) de noisettes porté par le courant, comme il est porté à la fin par les fêtards sans l’avoir décidé. Sa mythomanie est une acceptation radicale de sa propre détermination. Si radicale qu’elle lui offre une vie de bifurcations.
Par deux fois dans ma vie j’ai rencontré des mythomanes : un partenaire professionnel pendant 6 mois, une fille pendant quelques heures dans un bar. J’ai beaucoup pensé à eux. Je raconterai quand le forum sera plus calme.

[Malice]

J’aime bien ton idée que Julius soit porté par le courant comme le troquet heu le le trochet.
En te lisant m’est revenu en tête le personnage principal de « Loin de Reuil », qui fréquemment au cours du récit « devient » les personnages qu’il voit ( sans être mythomane cela dit).
https://www.babelio.com/livres/Queneau-Loin-de-Rueil/27363

Au sujet de la chanteuse, à mes yeux elle en est une, mais contrairement à Julius elle résiste au personnage qu’elle doit incarner car le jeu n’est pas son fort, probablement? J’ai vu des opéras où le pb d’être un comédien en plus d’un chanteur se pose ( drame : on peut naître avec une voix miraculeuse mais ne pas parvenir à jouer…Par exemple j’ai vu une version des Noces de Figaro où Suzanne interprétée par Ying Fang m’a éblouie en tant que comédienne et chanteuse, tandis que son partenaire en comte Almaviva me semblait « forcer » toutes les émotions, ce qui était frustrant…)

[Malice]

J’ai hâte d’entendre tes récits de mythomanes; j’en ai un aussi, au sujet d’une ado rencontrée pendant une suite d’ atelier d’arts-plastiques et qui a raconté deux versions de sa vie au cours de deux sessions différentes, oubliant que j’étais témoin des deux histoires; dans l’une elle était populaire, organisait sans arrêt des soirées avec sa foule d’amis et était montée sur scène lors d’un concert de Lady Gaga; dans l’autre elle était martyrisée par son collège entier, ne sortait jamais de chez elle et n’avait aucun ami.

[Seldoon]

Sur Julius le trochet, ça me semble très souligné lors de la scène de fin. Il est littéralement porté par le groupe, et jette plusieurs coups d’œil vers chez Marie. On voit bien que son mouvement n’a rien à faire de son choix personnel, il avait le lait, il voulait rentrer chez Marie. Mais il suis le courant.
Tu as raison pour Marie la chanteuse, c’est bien son jeu qui est critiqué (et elle ne comprend pas). Alors que c’est justement la force de Julius.

[L’inconnu]

Intéressantes vos reflexions. Le trochet flottant puis s’arrêtant sur des branches m’a paru être une image de la structure du film. Julius jette un mensonge et laisse voir où ça le mène jusqu’à ce qu’il en arrive au bout, qu’il se fasse mettre à jour. Alors il quitte les personnes concernées pour ne pas être confronté ce qui lui est insupportable et recommence ailleurs. Mais lorsque sa copine comprend qu’il ment, elle ne le confronte pas comme le font les autres habituellement. On se dit qu’il va peut être pouvoir trouver un possible équilibre avec elle. Il a l’air d’avoir une hésitation. Rester ou pas ? Puis finalement rejette son trochet à l’eau en croisant le groupe. C’est comme ca qu’il vit.

[L’inconnu]

Je ne sais pas si les images de l’école à la fin sont des images réelles, auquel cas il ne ment pas sur son souvenir, ou si ce seraient des images mentales, qui montreraient qu’il vit réellement ses mensonges. Il a l’air de ne plus savoir qu’il a volé l’histoire de l’homme nu au feu rouge, comme s’il se faisait lui même piégé par ses histoires.

[Seldoon]

Pour moi il ne ment jamais. Il y croit toujours. Il a bien une partie de cerveau qui prend en charge la défense de ses histoires quand elles vont se faire dévoiler, mais lui vit au premier degré dans les mensonges.

[françois bégaudeau]

Sauf dans les mensonges « tactiques ». Par exemple quand il est coincé, au bar, le jour de l’expédition en bateau. Là il simule la crise d’épilepsie parce qu’il n’a plus d’autre solution
Ceci dit la crise est si bien simulée qu’on dirait qu’il l’a vraiment. Et l’a peut-etre vraiment.

[Charles]

Ah c’est marrant mais ça je ne l’ai jamais remis en question alors qu’effectivement on n’en trouve pas la trace après coup. Je me suis dit que c’était une somatisation, que son corps se défendait pour lui, malgré lui.

[Seldoon]

Oui mais même là il me semble se laisser porter. Il est mal, il tente de gagner du temps avant (il inspecte d’autres objets dans le magasin, il est incohérent puisqu’il s’achète pour lui même un gilet alors qu’il a dit qu’il en avait un sur le bateau…) mais je crois qu’il improvise totalement la crise.

[Schnoups]

La crise d’épilepsie est très bien vue, c’est comme s’il y avait un court circuit, la machine est en surchauffe et elle cale. Je crois que ce qui rend d’autant plus intéressant le personnage c’est qu’il sait bien qu’il ment, tout en ne le sachant plus vraiment par moment. Il simule une crise et la vie vraiment parce qu’il est coincé est c’est ce qu’il y a de pire pour lui. Face à sa mère il confesse ses mensonges mais ce petit manège dure depuis toujours entre eux, il a appris à le négocier – mot qu’il utilise pour parler du monde du travail dans lequel il ne veut pas être dominé, s’en échapper c’est reprendre le pouvoir. Deux passages très subtils sont intéressants à souligner, lorsqu’ils sont dans le moment critique de l’absence de gilets de sauvetage et que le collègue croyant trouve une solution, le magasin. Julius le regarde admiratif, satisfait, comme découvrant un nouvel ami. Alors qu’il aurait pu être contrarié de devoir retrouver plus tard une nouvelle manière de s’en sortir. Mais ce qui compte c’est effectivement le mouvement avant. Lorsqu’il fait ses repérages chez les architectes, il tente là d’impliquer l’archi sans que l’autre s’en rende compte, assez drôle cette façon jusqu’au boutiste qu’il a de continuer dans sa lancée. Lorsque l’employée vérifie l’information il se résigne à sortir, raté. Qu’il soit incapable ou extrêmement fébrile à convenir du fait qu’il mente ou à accepter d’être mis face à sa confusion (évocation des souvenirs avec la chanteuse) n’empêche pas qu’il ait l’attitude, les réactions, les bifurcations digne de quelqu’un qui sait qu’il doit se sortir d’un piège. Le blocage du personnage est comme ce court circuit avec deux forces qui s’affrontent et où aucune ne prend le dessus et il s’agit de passer au plan C. L’alternative peut être violente, contre lui-même (crise d’épilepsie) et contre les autres – scène géniale où il expose expose ses couilles à son couple de collègues, petite sidération histoire de temporiser.
Et on pense quand même à notre Jean-Claude Romand national, au moment où le voile commence à tomber, après 18 ans sur un même mensonge, il tue 5 personnes de sa famille.
Je veux bien entendre tes réserves ici et là Seldoon.

[Tony]

Eh oui Jean Claude Romand qui vit aujourd’hui dans un monastère et prie celui que certains désignent comme le plus grand des mythomanes.

[Fanny]

« Julius le regarde admiratif, satisfait, comme découvrant un nouvel ami. Alors qu’il aurait pu être contrarié »
Même là, comment être sûr qu’il ne soit pas en train de jouer la comédie (puisqu’il faut bien qu’il ait l’air content) ? Ou de se jouer une comédie intérieure ?
« Dans sa langue de bois catholique, je le trouvais, lui, réellement mystérieux. Au sens mathématique : indécidable.
Qu’il ne joue pas la comédie pour les autres, j’en suis sûr, mais est-ce que le menteur qui est en lui ne la joue pas ? Quand le Christ vient dans son cœur, quand la certitude d’être aimé malgré tout fait couler sur ses joues des larmes de joie, est-ce que ce n’est pas encore l’Adversaire qui le trompe ? » (Carrère)
J’aime bien ce côté indécidable.

[Schnoups]

Mais je ne dis pas qu’il n’y a pas d’indécidable chez lui. Est indécidable de savoir s’il est vraiment épileptique, s’il simule complètement, par contre on peut noter 1-qu’il y a eu crise et 2- au moment précis où son scénario bute sur une impasse. Savoir s’il ment ou pas lorsqu’il sourit en regardant son nouveau collègue ne m’intéresse pas. Ce qui est intéressant c’est qu’il le fait, et j’ai dit « de manière subtile » parce qu’à ce moment là il le fait pour lui-même, l’autre ne le regarde pas, les autres non plus.
Pour faire simple, on pourrait dire Fanny que toi aussi tu mens tout le temps. Rapidement la discussion tourne en rond. Ce qui est intéressant c’est comment c’est fait et à quel moment. Si tu mens tout le temps tu vas quand même sourire, râler, manger et pisser. On pourra même dans toutes tes actions et tes paroles observer un fonctionnement propre et en déduire certaines choses, sans occulter complètement les zones opaques, évidemment, sinon c’est pas drôle.
Pareil pour la machine à laver. ça me parait vachement plus intéressant de me dire qu’il a comme tout le monde une expérience pratique du monde. ça montre de manière encore une fois assez subtile et qui me plait beaucoup, que le gars est aussi rappelé au monde qu’il habite par des détails technique du quotidien. C’est bien pour ça qu’il est aussi déstabilisant et passionnant.

[Claire N]

Peut-être peut on ouvrir une troisième voie
Sur ce point précis : celui de la CNEP
Il s’agit d’authentiques «  crises «  mais bons épileptiques, avec une séméiologie bien a elles
Parfois déclenchées par un stimulus
Quelqu’un parlait ici de musique ( Ostros je crois)
J’aime bien l’idée
Et peut-être que là IL FAUT le croire

[nefa]

je ne connaissais pas ce trouble
je sens que je vais l’adorer
et du coup plutôt que :  » Il s’agit d’authentiques « crises « mais BONS épileptiques », peut-être :  » il s’agit d’authentiques crises mais NON épileptiques »
sinon j’ai pas compris le lien entre musique et CNEP
stimulus ?

[Malice]

Est-ce que les vraies fausses crises d’epilepsie existent? J’ai lu un article sur des personnes ayant eu des crises ressemblant en tous points à des crises d’epilepsie qui étaient par la suite interprétées comme des crises de grand stress. Claire tu es neurologue je crois, tu pourrais m’en dire plus?

[Demi Habile]

Phenom ´ enologie du Higgs aupr ´ es des collisionneurs hadroniques : `
du Modele Standard a la Supersym etrie. ´
R´esum´e
Cette these, conduite dans le contexte de la recherche du boson de Higgs, derniere pi`ece
manquante du m´ecanisme de brisure de la sym´etrie ´electrofaible et qui est une des plus importantes recherches aupr`es des collisionneurs hadroniques actuels, traite de la ph´enom´enologie
de ce boson a la fois dans le Modele Standard (SM) et dans son extension supersym´etrique
minimale (MSSM). Apres un r´esum´e de ce qui constitue le Modele Standard dans une premi`ere partie, nous pr´esenterons nos pr´edictions pour la section efficace inclusive de production
du boson de Higgs dans ses principaux canaux de production aupr`es des deux collisionneurs
hadroniques actuels que sont le Tevatron au Fermilab et le grand collisionneur de hadrons
(LHC) au CERN, en commen¸cant par le cas du Mod`ele Standard. Le principal r´esultat pr´esent´e est l’´etude la plus exhaustive possible des diff´erentes sources d’incertitudes th´eoriques
qui p`esent sur le calcul : les incertitudes d’´echelles vues comme une mesure de notre ignorance
des termes d’ordre sup´erieur dans un calcul perturbatif `a un ordre donn´e, les incertitudes reli´ees aux fonctions de distribution de partons dans le proton/l’anti–proton (PDF) ainsi que
les incertitudes reli´ees `a la valeur de la constante de couplage fort, et enfin les incertitudes
provenant de l’utilisation d’une th´eorie effective qui simplifie le calcul des ordres sup´erieurs
dans la section efficace de production. Dans un second temps nous ´etudierons les rapports
de branchement de la d´esint´egration du boson de Higgs en donnant ici aussi les incertitudes
th´eoriques qui p`esent sur le calcul. Nous poursuivrons par la combinaison des sections efficaces
de production avec le calcul portant sur la d´esint´egration du boson de Higgs, pour un canal
sp´ecifique, montrant quelles en sont les cons´equences int´eressantes sur l’incertitude th´eorique
totale. Ceci nous ameneraa un r´esultat significatif de la th`ese qui est la comparaison avec l’exp´erience et notamment les r´esultats des recherches du boson de Higgs au Tevatron. Nous irons
ensuite au-dela du Modele Standard dans une troisieme partie ou nous donnerons quelques
ingr´edients sur la supersym´etrie et sa mise en application dans le MSSM o`u nous avons cinq
bosons de Higgs, puis nous aborderons leur production et d´esint´egration en se focalisant sur
les deux canaux de production principaux par fusion de gluon et fusion de quarks b. Nous
pr´esenterons les r´esultats significatifs quant `a la comparaison avec aussi bien le Tevatron que
les r´esultats tr`es r´ecents d’ATLAS et CMS au LHC qui nous permettront d’analyser l’impact
de ces incertitudes sur l’espace des param`etres du MSSM, sans oublier de mentionner quelques
bruits de fond du signal des bosons de Higgs. Tout ceci va nous permettre de mettre en avant
le deuxieme r´esultat tres important de la th`ese, ouvrant une nouvelle voie de recherche pour
le boson de Higgs standard au LHC. La derni`ere partie sera consacr´ee aux perspectives de
ce travail et notamment donnera quelques r´esultats pr´eliminaires dans le cadre d’une ´etude
exclusive, d’un int´erˆet primordial pour les exp´erimentateurs.
Mots-clefs : Mod`ele Standard, Higgs, Supersym´etrie, Chromodynamique quantique, incertitudes th´eoriques.

Abstract
This thesis has been conducted in the context of one of the utmost important searches at
current hadron colliders, that is the search for the Higgs boson, the remnant of the electroweak
symmetry breaking. We wish to study the phenomenology of the Higgs boson in both the
Standard Model (SM) framework and its minimal Supersymmetric extension (MSSM). After
a review of the Standard Model in a first part and of the key reasons and ingredients for
the supersymmetry in general and the MSSM in particular in a third part, we will present the
calculation of the inclusive production cross sections of the Higgs boson in the main channels at
the two current hadron colliders that are the Fermilab Tevatron collider and the CERN Large
Hadron Collider (LHC), starting by the SM case in the second part and presenting the MSSM
results, where we have five Higgs bosons and focusing on the two main production channels that
are the gluon gluon fusion and the bottom quarks fusion, in the fourth part. The main output
of this calculation is the extensive study of the various theoretical uncertainties that affect the
predictions: the scale uncertainties which probe our ignorance of the higher–order terms in a
fixed order perturbative calculation, the parton distribution functions (PDF) uncertainties and
its related uncertainties from the value of the strong coupling constant, and the uncertainties
coming from the use of an effective field theory to simplify the hard calculation. We then
move on to the study of the Higgs decay branching ratios which are also affected by diverse
uncertainties. We will present the combination of the production cross sections and decay
branching fractions in some specific cases which will show interesting consequences on the
total theoretical uncertainties. We move on to present the results confronted to experiments
and show that the theoretical uncertainties have a significant impact on the inferred limits
either in the SM search for the Higgs boson or on the MSSM parameter space, including some
assessments about SM backgrounds to the Higgs production and how they are affected by
theoretical uncertainties. One significant result will also come out of the MSSM analysis and
open a novel strategy search for the Standard Higgs boson at the LHC. We finally present in
the last part some preliminary results of this study in the case of exclusive production which
is of utmost interest for the experimentalists.
Keywords : Standard Model, Higgs, Supersymmetry, QCD, theoretical uncertainties.

Remerciements
Trois ann´ees ont pass´e depuis que j’ai pouss´e pour la premi`ere fois les portes du Laboratoire de Physique Th´eorique d’Orsay, chaleureusement accueilli par son directeur Henk
Hilhorst que je remercie beaucoup. Trois ann´ees d’une activit´e intense, aussi bien dans
mes recherches scientifiques au LPT et au CERN, dans le groupe de physique th´eorique,
ou j’ai pass´e quelques moisa partir de la seconde ann´ee, que dans mes activit´es hors
recherche au sein de l’universit´e Paris-Sud 11. J’ai appris beaucoup et rencontr´e un certain nombre de personnes dont je vais me rappeler pour longtemps, si je ne les ´enum`ere
pas ici qu’elles veuillent bien me pardonner cela ne signifie pas que je les ai pour autant
oubli´ees.
Tout ceci n’aurait pu se faire sans les encouragements, les conseils et les discussions passionn´ees avec Abdelhak Djouadi, mon directeur de th`ese qui a guid´e ainsi mes
premiers pas de professionnel dans ma carri`ere de physicien th´eoricien des particules
´el´ementaires. Je l’en remercie profond´ement et j’esp`ere qu’il aura appr´eci´e notre collaboration autant que moi, aussi bien lors de notre travail qu’en dehors.
Je voudrais aussi remercier Rohini Godbole avec qui j’ai collabor´e sur la passionnante
physique du Higgs au Tevatron. Je ne peux non plus oublier Ana Teixeira pour son
soutien constant et les nombreuses discussions passionnantes aussi bien scientifiques que
personnelles que nous avons eues ensemble. Ma premi`ere ann´ee en tant que doctorant
lui doit beaucoup.
Je remercie aussi tous les membres de mon jury de th`ese et en particulier mes deux
rapporteurs qui m’ont certainement maudit d’avoir ´ecrit autant, non seulement pour le
temps qu’ils auront pris pour assister a ma soutenance et lire ma these, mais aussi pour
toutes leurs judicieuses remarques et questions.
Aussi bien le LPT que le CERN se sont r´ev´el´es des lieux tr`es enrichissants pour
le d´ebut de ma carri`ere scientifique. Je voudrais profiter tout d’abord de ces quelques
mots pour remercier les ´equipes administratives des deux laboratoires pour leur aide au
jour le jour, toujours avec le sourire, et pour toute leur aide dans mes divers voyages
scientifiques. Je remercie aussi tous les chercheurs de ces deux laboratoires pour toutes les
discussions que j’ai eues et qui m’ont beaucoup appris. Je pense tout particuli`erement
a Asmˆaa Abada eta Gr´egory Moreau d’un cˆot´e, `a G´eraldine Servant et Christophe
Grojean qui m’a invit´e `a venir au CERN, de l’autre. Je ne peux bien sur pas oublier les
doctorants et jeunes docteurs du groupe de physique th´eorique du CERN, Sandeepan
Gupta, Pantelis Tziveloglou et tous les autres, ainsi que L´ea Gauthier, doctorante au
CEA, que j’ai rencontr´ee au CERN : les magnifiques randonn´ees autour de Gen`eve
que nous avons faites ont ´et´e salutaires. Enfin je remercie aussi tous mes camarades
doctorants et jeunes docteurs du SINJE `a Orsay pour tous les merveilleux moments que
nous avons pass´es et toutes les discussions passionn´ees et passionnnantes, je ne vous cite
pas tous mais le cœur y est. Je pense quand mˆeme tout particulierementa mes camarades
ayant partag´e mon bureau et bien plus, Adrien Besse et C´edric Weiland, mais aussi `a
Guillaume Toucas, Blaise Gout´eraux et Andreas Goudelis. J´er´emie Quevillon qui va
prendre ma succession aupres de mon directeur de these n’est pas non plus oubli´e. Mes
amis de Toulouse eux aussi sont loin d’avoir ´et´e oubli´es et ont fortement contribu´e non
seulement a rendre exceptionnel mon stage de Master 2 mais aussi ma premiere ann´ee
de these, de loin en loin : mercia Ludovic Arnaud, Gaspard Bousquet, Arnaud Ralko,
Cl´ement Touya, Fabien Trousselet, mais aussi mes deux tuteurs Nicolas Destainville et
Manoel Manghi.
Je ne peux terminer sans exprimer ma profonde gratitude a ma famille eta mes amis
de longue date, qui se reconnaˆıtront. Anne, Charles, Elise, Gaetan, Lionel, Mathieu,
Matthieu, Patrick, Pierre, Rayna, Sophie, Yiting et tous ceux que je n’ai pas cit´es mais
qui sont dans mes pens´ees, ces mots sont pour vous ! Le mot de la fin revient `a ma
fianc´ee, Camille : sans ton profond amour et ton soutien constant, ces trois derni`eres
ann´ees auraient ´et´e bien diff´erentes, et certainement pas aussi f´econdes. Merci pour tout.
Acknowledgments
Three years have now passed since my first steps in the Laboratoire de Physique
Th´eorique at Orsay, where I have been warmly welcomed by its director Henk Hilhorst
that I thank a lot. They have been very intense, both in the laboratory and at the CERN
Theory Group in Geneva, where I spent some months starting from the second year. I
have learnt much, either within these labs or outside, encountered many people that I
will remember for a long time. If some of you are not cited in these acknowledgments,
please be kind with me: that does not mean I have forgotten you.
This would have never been possible without the constant encouragement, advices
and fruitful discussions with Dr. Abdelhak Djouadi, my thesis advisor, who guided my
first steps in theoretical particle physics research. I hope he got as much great time as
I had working with him and more than that.
I also would like to thank Pr. Rohini Godbole whom I worked with from time to
time on Higgs physics at the Tevatron. I cannot also forget Dr. Ana Teixeira for her
constant support and all the great discussions on various topics we had together. My
first year as a PhD candidate was scientifically exciting thanks to her.
I am very grateful to all the members in the jury for my defence, for the time they
would took and the useful comments. In particular I would like to thank my two referees
who certainly have cursed me for the length of the thesis.
The LPT environnement as well as the CERN Theory Group have been proven to be
very fruitful environnements for the beginning of my career. I then would like to thank
the administrative staff from both laboratories for their constant help in day–to–day life
and support when I had to travel for various workshops, conferences or seminars. I would
like to thank all the members of these two groups for the very passionate discussions
we had and where I have learnt a lot. I dedicate special thanks to Asmˆaa Abada and
Gr´egory Moreau on the one side, G´eraldine Servant and also Christophe Grojean, who
invited me to come by, on the other side. I cannot forget the PhD candidates and
post-doctoral researchers from the CERN Theory Group, Sandeepan Gupta, Pantelis
Tziveloglou and all the others, not to forget L´ea Gauthier, who is a PhD candidate
at the CEA and was at CERN at that time: the hiking we did in the Jura and Alps
around Geneva were great. I also would like to thank all my SINJE fellows at the
LPT, with whom I had so many great time and passionate discussions; you are not all
cited but I do not forget you. I dedicate special thanks to my office (and more than
office) friends Adrien Besse and C´edric Weiland, and also to Blaise Gout´eraux, Andreas
Goudelis and Guillaume Toucas. The next PhD candidate, J´er´emie Quevillon, who will
follow my path, is also thanked for the discussions we had. I finally cannot forget my
friends from Toulouse, where I did my Master 2 internship and whom I collaborated with
during my first PhD thesis year from time to time: many thanks to Ludovic Arnaud,
Gaspard Bousquet, Arnaud Ralko, Cl´ement Touya, Fabien Trousselet, and also to my
two internship advisors Nicolas Destainville and Manoel Manghi.
I now end this aknowledgments by expressing my deep gratitude and love to my family and long–time friends who will recognize themselves. Anne, Charles, Elise, Gaetan,
Lionel, Mathieu, Matthieu, Patrick, Pierre, Rayna, Sophie, Yiting and all the others,
these words are for you! The last word is for Camille, my fiancee: without your deep
love and constant support these three years would have been without doubts completely
different and not as fruitful.

Contents
Introduction 1
I A brief review of the Standard Model of particle physics 5
1 Symmetry principles and the zoology of the Standard Model 6
1.1 A brief history of the Standard Model . . . . . . . . . . . . . . . . . . . 6
1.2 Gauge symmetries, quarks and leptons . . . . . . . . . . . . . . . . . . . 12
2 The Brout–Englert–Higgs mechanism 16
2.1 Why do we need the electroweak symmetry breaking? . . . . . . . . . . . 16
2.2 The spontaneous electroweak symmetry breaking . . . . . . . . . . . . . 19
II SM Higgs production and decay at hadron colliders 27
3 Where can the SM Higgs boson be hiding? 29
3.1 Theoretical bounds on the Higgs mass . . . . . . . . . . . . . . . . . . . 29
3.2 Experimental bounds on the Higgs mass . . . . . . . . . . . . . . . . . . 36
4 Higgs production at the Tevatron 43
4.1 The main production channels . . . . . . . . . . . . . . . . . . . . . . . 47
4.2 Scale variation and higher order terms . . . . . . . . . . . . . . . . . . . 58
4.3 The PDF puzzle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.4 EFT and its uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.5 Combination and total uncertainty . . . . . . . . . . . . . . . . . . . . . 81
4.6 Summary and outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
4.A Appendix: analytical expressions for µR–NNLO terms in gg → H . . . . 90
5 Higgs production at the LHC 92
5.1 The main channel at the lHC . . . . . . . . . . . . . . . . . . . . . . . . 93
5.2 The scale uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
5.3 The PDF+αS uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . 98
5.4 EFT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
5.5 Total uncertainy at 7 TeV . . . . . . . . . . . . . . . . . . . . . . . . . . 106
5.6 LHC results at different center–of–mass energies . . . . . . . . . . . . . 110
5.7 Summary and outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
6 Higgs decay and the implications for Higgs searches 116
6.1 Important channels for experimental search . . . . . . . . . . . . . . . . 116
6.2 Uncertainties on the branching ratios . . . . . . . . . . . . . . . . . . . . 121
6.3 Combination at the Tevatron . . . . . . . . . . . . . . . . . . . . . . . . 125
6.4 Combination at the LHC . . . . . . . . . . . . . . . . . . . . . . . . . . 128
6.5 The Tevatron exclusion limit . . . . . . . . . . . . . . . . . . . . . . . . 129
6.6 Summary of the results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
III The Minimal Supersymmetric extension of the Standard
Model 137
7 Why Supersymmetry is appealing 138
7.1 The hierarchy problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
7.2 Coupling constants convergence at high energies . . . . . . . . . . . . . 140
7.3 SUSY and Dark Matter searches . . . . . . . . . . . . . . . . . . . . . . 142
8 Formal SUSY aspects 145
8.1 SUSY Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
8.2 Superspace, superfields and superpotential . . . . . . . . . . . . . . . . . 149
8.3 Soft SUSY breaking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
9 The Minimal Supersymmetric Standard Model 156
9.1 Fields content: Higgs and SUSY sectors of the MSSM . . . . . . . . . . 156
9.2 The Higgs sector and the number of Higgs doublets . . . . . . . . . . . . 161
9.3 The MSSM is not the end of the story . . . . . . . . . . . . . . . . . . . 168
IV MSSM Higgs(es) production and decay 171
10 The MSSM Higgs sector at hadron colliders 173
10.1 SUSY corrections to Higgs couplings to fermions . . . . . . . . . . . . . 173
10.2 Model independence of the results . . . . . . . . . . . . . . . . . . . . . 177
11 MSSM Higgs production at the Tevatron 180
11.1 Gluon–gluon fusion and bottom quarks fusion . . . . . . . . . . . . . . . 181
11.2 The scale uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
11.3 The PDF and αS uncertainties . . . . . . . . . . . . . . . . . . . . . . . 186
11.4 The b–quark mass uncertainty . . . . . . . . . . . . . . . . . . . . . . . 187
11.5 Summary and combination of the different sources of uncertainties . . . . 190
12 MSSM Higgs production at the LHC 192
12.1 Gluon–gluon fusion and bottom quarks fusion channels . . . . . . . . . . 192
12.2 The scale uncertainty at the lHC . . . . . . . . . . . . . . . . . . . . . . 194
12.3 The PDF and αS uncertainties at the lHC . . . . . . . . . . . . . . . . . 195
12.4 The b–quark mass issue . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
12.5 Combination and total uncertainty . . . . . . . . . . . . . . . . . . . . . 198
12.6 The case of the charged Higgs production in association with top quark
at the LHC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
13 Higgs→ τ τ channel and limits on the MSSM parameter space 209
13.1 The main MSSM Higgs branching ratios . . . . . . . . . . . . . . . . . . 209
13.2 Combination of production cross section and Higgs→ τ τ decay . . . . . 212
13.3 Impact of the theoretical uncertainties on the limits on the MSSM parameter space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
13.4 Consequences on the SM H → τ τ search at the LHC . . . . . . . . . . . 224
13.5 Summary and outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226
V Perspectives 229
14 Exclusive study of the gluon–gluon fusion channel 230
14.1 Exclusive SM Higgs production . . . . . . . . . . . . . . . . . . . . . . . 231
14.2 SM Backgrounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234
Conclusion 236
A Appendix : Synopsis 240
A.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240
A.2 Production et d´esint´egration du boson de Higgs du Mod`ele Standard . . 244
A.3 Le Mod`ele Standard Supersym´etrique Minimal (MSSM) . . . . . . . . . . 252
A.4 Production et d´esint´egration des bosons de Higgs supersym´etriques . . . 256
A.5 Perspectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261
References 263
List of Figures
1 Feynman diagrams at the Born level for the process e
+e
− → W+W− . . 17
2 Higgs potential in the case of a real scalar field, depending on the sign of
the mass term . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3 Higgs potential in the case of the SM . . . . . . . . . . . . . . . . . . . . 21
4 Tree–level SM Higgs boson couplings to gauge bosons and fermions . . . 25
5 One–loop SM Higgs boson couplings to the photons and the gluons . . . 25
6 Feynman diagrams up to one–loop correction for the Higgs self–coupling 34
7 Theoretical bounds on the Higgs mass in function of the scale of new
physics beyond the SM . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
8 Electroweak precision data . . . . . . . . . . . . . . . . . . . . . . . . . . 39
9 Indirect constraints on the SM Higgs boson mass . . . . . . . . . . . . . 40
10 95%CL exclusion limit on the SM Higgs boson mass at the LEP collider . 41
11 95%CL exclusion limit on the SM Higgs boson mass at the Tevatron collider 43
12 Feynman diagrams of the four main SM Higgs production channel . . . . 49
13 Some Feynman diagrams for NLO SM gg → H production . . . . . . . . 50
14 Some Feynman diagrams for NNLO SM gg → H production . . . . . . . 51
15 NLO QCD corrections to pp¯ → V
∗
. . . . . . . . . . . . . . . . . . . . . 55
16 NNLO QCD corrections to pp¯ → V
∗
. . . . . . . . . . . . . . . . . . . . 56
17 Total cross sections for Higgs production at the Tevatron in the four main
channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
18 Scale variation in the gg → H process at the Tevatron . . . . . . . . . . 62
19 Scale variation in the pp¯ → W H process at the Tevatron . . . . . . . . . 67
20 Comparison between different PDFs sets in gg → H at the Tevatron
using CTEQ/ABKM/MSTW PDF sets for 90%CL uncertainties and
MSTW/ABKM/HERA/JR for central predictions comparison . . . . . . 70
21 Comparison between MSTW PDFs set and ABKM PDFs set predictions
in gg → H channel at the Tevatron as for the uncertainties related to
PDF+∆αs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
22 The total PDF, PDF+∆expαs and PDF+∆exp+thαs uncertainties in gg →
H at the Tevatron using the MSTW PDFs set. . . . . . . . . . . . . . . . 75
23 Central predictions for NNLO pp¯ → W H at the Tevatron using the
MSTW, CTEQ and ABKM PDFs sets, together with their 90% CL PDF
uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
24 Comparison between MSTW PDFs set and ABKM PDFs set predictions
in pp¯ → W H channel at the Tevatron as for the uncertainties related to
PDF+∆αs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
25 b–loop uncertainty in gg → H at the Tevatron . . . . . . . . . . . . . . . 79
26 EW uncertainties in gg → H at the Tevatron . . . . . . . . . . . . . . . . 81
27 Production cross sections for gg → H at the Tevatron together with the
total theoretical uncertainties . . . . . . . . . . . . . . . . . . . . . . . . 85
28 Production cross sections for pp¯ → W H and pp¯ → ZH at the Tevatron
together with the total theoretical uncertainties . . . . . . . . . . . . . . 88
29 Total cross sections for SM Higgs production at the lHC . . . . . . . . . 95
30 Scale uncertainty at the lHC in gg → H at NNLO . . . . . . . . . . . . . 98
31 PDF and ∆exp,thαs uncertainties in gg → H at the lHC . . . . . . . . . . 99
32 Comparison between the predictions given by the four NNLO PDF sets
for gg → H at the lHC . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
33 Uncertainties due to EFT in the top quark and bottom quark loops of
gg → H at NNLO at the lHC . . . . . . . . . . . . . . . . . . . . . . . . 104
34 Total uncertainty due to the EFT approach in gg → H at NNLO at the
lHC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
35 Central prediction with its total uncertainty for gg → H at NNLO at the
lHC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
36 Central predictions for gg → H at NNLO at the lHC with √
s = 8, 9, 10
TeV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
37 Scale and total EFT uncertainties in gg → H at the LHC with √
s = 14
TeV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
38 PDF+∆exp,thαs uncertainties and the comparison between the 4 NNLO
PDF sets in gg → H at the LHC with √
s = 14 TeV . . . . . . . . . . . . 113
39 Central prediction and total uncertainty in gg → H at NNLO at the LHC
with √
s = 14 TeV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
40 SM Higgs decay channels on the interesting Higgs mass range . . . . . . 117
41 The Higgs decays branching ratios together with the total uncertainty
bands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
42 The production cross section times branching ratio for SM pp¯ → W H →
W b¯b and gg → H → W+W− at the Tevatron together with the total
uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
43 The production cross section times branching ratio for SM gg → H →
W+W− at the lHC together with the total uncertainty . . . . . . . . . . 129
44 The SM Higgs boson production cross section gg → H at the Tevatron
together with the total uncertainty using 4 different ways of adding the
theoretical uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
45 The CDF/D0 95%CL limit on the SM Higgs boson mass confronted to
our theoretical expectations in a naive approach. . . . . . . . . . . . . . . 132
46 The luminosity needed by the CDF experiment to recover their current
claimed sensitivity when compared to our theoretical expectations for the
uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
47 One–loop corrections to the Higgs boson mass within the SM . . . . . . . 139
48 One–loop corrections to gauge couplings . . . . . . . . . . . . . . . . . . 141
49 SU(3)c × SU(2)L × U(1)Y gauge couplings running from the weak scale
up to the GUT scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
50 Possible proton decay in SUSY theories without R–parity conservation . 143
51 The constrained NMSSM parameter space . . . . . . . . . . . . . . . . . 170
52 The impact of main one–loop SUSY corrections to the Φb
¯b coupling in
the MSSM at hadron colliders . . . . . . . . . . . . . . . . . . . . . . . . 178
53 Feynman diagrams for the bottom quark fusion process in the MSSM . . 184
54 The NLO gg → A and NNLO b
¯b→A cross sections at the Tevatron with
tan β = 30 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
55 Scale uncertainty in the gg → Φ and b
¯b → Φ processes at the Tevatron . 186
56 PDF+∆exp,thαs uncertainty in the gg → Φ and bb → Φ processes at the
Tevatron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
57 The comparison between the MSTW, ABKM and JR prediction for the
NNLO bottom quark fusion cross section at the Tevatron . . . . . . . . . 187
58 Specific b–quark mass uncertainties in the gg → Φ and b
¯b → Φ processes
at the Tevatron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
59 The gg → A and b
¯b → A cross sections at the Tevatron together with
their different sources of uncertainty and the total uncertainties . . . . . 191
60 The gg → Φ and b
¯b → Φ at the LHC for different center–of–mass energies 194
61 Scale uncertainty in the gg → Φ and b
¯b → Φ processes at the lHC . . . . 195
62 PDF+∆αs uncertainty in the gg → Φ and bb → Φ processes at the lHC . 196
63 Comparison between the different PDFs sets in the gg → Φ and b
¯b → Φ
processes at the lHC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
64 Specific b–quark mass uncertainties in the gg → Φ and b
¯b → Φ processes
at the lHC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
65 The gg → Φ and b
¯b → Φ cross sections at the lHC together with their
different sources of uncertainty and the total uncertainties . . . . . . . . 199
66 LO σ(gb → tL,RH−) cross section and polarization asymmetry at the lHC
in the MSSM in two benchmark scenarios as a function of tan β . . . . . 205
67 Scale and PDF dependence on top–charged Higgs asymmetry at the lHC 206
68 The impact of the NLO SUSY corrections on the top–charged Higgs asymmetry at the LHC with √
s = 14 TeV . . . . . . . . . . . . . . . . . . . . 208
69 CP–odd A boson production in the pp¯ → A → τ
+τ
− channel at the
Tevatron together with the total uncertainty . . . . . . . . . . . . . . . . 215
70 The total uncertainties on the MSSM Higgs production in the gg → Φ
and b
¯b → Φ channels at the lHC including the impact of the Φ → τ
+τ
−
branching fraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
71 CP–odd A boson production in the pp → A → τ
+τ
− channel at the lHC
together with the total uncertainty . . . . . . . . . . . . . . . . . . . . . 219
72 The 95%CL limits on the MSSM parameter space using our theoretical
uncertainties confronted to the Tevatron results . . . . . . . . . . . . . . 221
73 The 95%CL limits on the MSSM parameter space using our theoretical
uncertainties confronted to the lHC results . . . . . . . . . . . . . . . . . 222
74 Expectations at higher luminosity at the lHC for the 95%CL limits on
the MSSM parameter space using our theoretical calculation . . . . . . . 223
75 The MSSM Higgs analysis applied to the SM H → τ
+τ
− search channel
compared to the ATLAS H → γγ limits . . . . . . . . . . . . . . . . . . 226
76 Potentiel de Higgs dans le cas d’un champ scalaire r´eel selon le signe du
terme de masse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242
77 Incertitude d’´echelle dans le processus gg → H au Tevatron . . . . . . . . 246
78 Comparaison entre les pr´edictions des diff´erentes collaborations de PDFs
pour le canal gg → H au NNLO en QCD . . . . . . . . . . . . . . . . . . 247
79 Incertitude PDF+∆αs dans les canaux de production gg → H et pp¯ →
HW au Tevatron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248
80 Sections efficaces de production inclusives des canaux gg → H et pp¯ →
HV au Tevatron ainsi que les incertitudes th´eoriques totales associ´ees . . 249
81 Sections efficaces de production inclusives du canal gg → H au LHC `a 7
et 14 TeV ainsi que les incertitudes th´eoriques totales associ´ees . . . . . . 250
82 Luminosit´e n´ecessaire `a l’exp´erience CDF afin qu’elle obtienne la sensibilit´e qu’elle pr´etend avoir actuellement, en tenant compte de nos incertitudes th´eoriques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251
83 Les sections efficaces de production inclusives du boson de Higgs A du
MSSM au Tevatron dans les canaux gg → A et b
¯b → A accompagn´ees
des incertitudes th´eoriques . . . . . . . . . . . . . . . . . . . . . . . . . . 258
84 Les sections efficaces de production inclusives du boson de Higgs Φ du
MSSM au lHC dans les canaux gg → Φ et b
¯b → Φ accompagn´ees des
incertitudes th´eoriques . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258
85 Les limites a 95% de niveau de confiance sur l’espace des parametres du
MSSM en tenant compte de nos incertitudes th´eoriques confront´ees aux
donn´ees du Tevatron et du lHC . . . . . . . . . . . . . . . . . . . . . . . 260
86 L’analyse MSSM des bosons de Higgs neutres appliqu´ee au canal de
recherche H → τ
+τ
− du Mod`ele Standard, compar´ee aux r´esultats
obtenus par ATLAS dans le canal H → γγ . . . . . . . . . . . . . . . . . 261

List of Tables
1 The fermionic content of the Standard Model . . . . . . . . . . . . . . . 13
2 The NNLO total Higgs production cross sections in the gg → H process
at the Tevatron together with the detailed theoretical uncertainties as
well as the total uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . 84
3 The NNLO total cross section for Higgs–strahlung processes at the Tevatron together with the detailed theoretical uncertainties and the total
uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
4 The total Higgs production cross sections in the four main production
channels at the lHC with √
s = 7 TeV . . . . . . . . . . . . . . . . . . . . 96
5 The NNLO total Higgs production cross sections in the gg → H process
at the lHC with √
s = 7 TeV together with the associated theoretical
uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
6 The NNLO total production cross section in the gg → H channel at the
LHC with √
s = 8, 9, 10 TeV . . . . . . . . . . . . . . . . . . . . . . . . . 112
7 The NNLO total Higgs production cross section in the gg → H process
at the LHC with √
s = 14 TeV together with the associated theoretical
uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
8 The SM Higgs decay branching ratios in the b
¯b and WW modes for representatives Higgs masses together with the different sources of uncertainties as well as the total uncertainty. . . . . . . . . . . . . . . . . . . . . . 124
9 The SM Higgs decay branching ratios together with the total uncertainty
for the most important decay channels . . . . . . . . . . . . . . . . . . . 126
10 The superparticles and Higgs content of the MSSM before EWSB . . . . 157
11 The neutralinos, charginos and Higgs content of the MSSM after EWSB . 158
12 The main MSSM CP–odd like Higgs bosons decay branching fractions
together with their uncertainties . . . . . . . . . . . . . . . . . . . . . . . 211
13 The central predictions in the MSSM gg → Φ channel at the Tevatron
together with the detailed uncertainties and the impact of the Φ → τ
+τ
−
branching fraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
14 The central predictions in the MSSM b
¯b → Φ channel at the Tevatron
together with the detailed uncertainties and the impact of the Φ → τ
+τ
−
branching fraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
15 The central predictions in the MSSM gg → Φ channel at the lHC together with the detailed uncertainties and the impact of the Φ → τ
+τ
−
branching fraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
16 The central predictions in the MSSM b
¯b → Φ channel at the lHC together with the detailed uncertainties and the impact of the Φ → τ
+τ
−
branching fraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218
17 CMS cuts used in the SM exclusive study gg → H → WW → νν at
the lHC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231
18 Results for the gg → H+jet cross sections with MH = 160 GeV at the
lHC with HNNLO and MCFM programs . . . . . . . . . . . . . . . . . . 232
19 Uncertainties on the exclusive production gg → H → WW → νν with
MH = 160 GeV at the lHC with HNNLO program . . . . . . . . . . . . . . 233
20 Uncertainties on the exclusive production gg → H → WW → νν with
MH = 160 GeV at the lHC with MCFM program . . . . . . . . . . . . . . . 234
21 Central values and uncertainties for the H → WW SM backgrounds
exclusive cross sections at the lHC . . . . . . . . . . . . . . . . . . . . . . 235
22 Contenu fermionique du Mod`ele Standard . . . . . . . . . . . . . . . . . 241
23 Les superparticules et champs de Higgs du MSSM avant brisure ´electrofaible254
Liste des publications
Cette page donne la liste de tous mes articles concernant le travail r´ealis´e depuis 3 ans.
This page lists all the papers that I have written for 3 years in the context of my PhD
work.
Articles publi´es (published papers) :
Predictions for Higgs production at the Tevatron and the associated uncertainties,
J. B. et A. Djouadi, JHEP 10 (2010) 064;
Higgs production at the lHC, J. B. et A. Djouadi, JHEP 03 (2011) 055;
The Tevatron Higgs exclusion limits and theoretical uncertainties: A Critical appraisal, J. B., A. Djouadi, S. Ferrag et R. M. Godbole, Phys.Lett.B699 (2011) 368-371;
erratum Phys.Lett.B702 (2011) 105-106;
Revisiting the constraints on the Supersymmetric Higgs sector at the Tevatron, J. B.
et A. Djouadi, Phys.Lett.B699 (2011) 372-376;
The left-right asymmetry of the top quarks in associated top–charged Higgs bosons at
the LHC as a probe of the parameter tan β, J.B et al., Phys.Lett.B705 (2011) 212-216.
Articles non–publi´es (unpublished papers) :
Implications of the ATLAS and CMS searches in the channel pp → Higgs → τ
+τ
−
for the MSSM and SM Higgs bosons, J. B. et A. Djouadi, arXiv:1103.6247 [hep-ph]
(soumis `a Phys.Lett.B);
Clarifications on the impact of theoretical uncertainties on the Tevatron Higgs exclusion limits, J. B., A. Djouadi et R. M. Godbole, arXiv:1107.0281 [hep-ph].
Rapport de collaboration (review collaboration report) :
Handbook of LHC Higgs Cross Sections: 1. Inclusive Observables, LHC Higgs Cross
Section Working Group, S. Dittmaier et al., arXiv:1101:0593 [hep-ph].
Comptes–rendus de conf´erences (proceedings) :
Higgs production at the Tevatron: Predictions and uncertainties, J. B., ICHEP 2010,
Paris (France), PoS ICHEP2010 (2010) 048;
The Supersymmetric Higgs bounds at the Tevatron and the LHC, J.B., XLVIe
Rencontres de Moriond, EW interactions and unified theory, La Thuile (Italie),
arXiv:1105.1085 [hep-ph].

Cette these est d´edi´eea mon pere eta mes deux grand-p`eres, disparus bien
trop tˆot.

(From http://abstrusegoose.com/118)
Et maintenant, apprends les v´erit´es qui me restent `a te d´ecouvrir,
Tu vas entendre de plus claires r´ev´elations.
Je n’ignore pas l’obscurit´e de mon sujet ;
Lucr`ece, dans De rerum natura, v. 902-943 livre I
Les amoureux fervents et les savants aust`eres
Aiment ´egalement, dans leur mˆure saison,
Les chats puissants et doux, orgueil de la maison,
Qui comme eux sont frileux et comme eux s´edentaires.
Charles Baudelaire, dans Les Fleurs du Mal

Introduction 1
Introduction
In this thesis, we wish to present some predictions for the Higgs boson(s) study at the
two largest hadron colliders currently in activity: the Fermilab Tevatron collider and
the CERN Large Hadron Collider (LHC). Our focus will be on the inclusive production
cross sections and the decay branching fractions, first in the Standard Model which in
itself is the topic of part I and then in its minimal supersymmetric extension which is
the topic of part III.
The study of the fundamental mechanisms of Nature at the elementary level has a
long story and has known many milestones in the past sixty years. Physicists have built
a theory, nowadays known as the Standard Model, to describe the elementary particles
and their interactions, that are those of the strong, weak and electromagnetic, the two
last being unified in a single electroweak interaction. It relies on the elegant concept
of gauge symmetry within a quantum field theory framework and has known many
experimental successes: despite decades of effort to surpass this model it is still the one
that describes accurately nearly all the known phenomena1
. One of its key concepts
is the spontaneous breakdown of electroweak symmetry: indeed in order to give mass
to the weak bosons that mediate the weak interaction, a scalar field is introduced in
the theory whose vacuum breaks the electroweak symmetry and gives mass to the weak
bosons. In fact it also gives masses to the fermions and one piece of this mechanism
remains to be discovered: the Higgs boson, the “Holy Grail” of the Standard Model. Its
discovery is one of the main goal of current high energy colliders.
It is then of utmost importance to give theoretical predictions for the production
cross sections and decay branching fractions of the Higgs boson at current colliders to
serve as a guideline for experiments. However, the hadronic colliders are known to be
very difficult experimental environments because of the huge hadronic, that is Quantum
ChromoDynamics (QCD), activity. This is also true on a theoretical side, which means
that an accurate description of all possible sources of theoretical uncertainties is needed:
this is precisely the main output of this thesis. We shall mention that in the very final
stage of this thesis new results have been presented in the HEP–EPS 2011 conference;
our work is to be read in the light of the results that were available before these newest
experimental output which will be briefly commented in the conclusion.
Part I is entirely devoted to a review of the Standard Model. In section 1 we will draw
a short history of the Standard Model and list its main milestones of the past sixty years,
followed by a description of its main concepts. We will go into more details about the
Higgs mechanism, which spontaneously breaks electroweak symmetry, in section 2: we
will review some reasons to believe that either the Higgs mechanism itself or something
which looks like the Higgs mechanism is needed, and then how the Higgs boson emerges
1We leave aside the neutrino mass issue.
2 Introduction
from the electroweak symmetry breaking and what are its couplings to fermions and
bosons of the Standard Model.
Part II is the core of the Standard Model study of this thesis. Indeed the Higgs
boson remains to be discovered and is one of the major research programs at current
high energy colliders. The old CERN Large Electron Positron (LEP) collider has put
some bounds on the possible value of the Higgs boson mass, which is above 114.4 GeV in
the Standard Model at 95%CL. We will review in section 3 the current experimental and
theoretical bounds on the Higgs mass. We then give our predictions for the Standard
Model Higgs boson inclusive production cross section at the Tevatron in the two main
production channels that are the gluon–gluon fusion and the Higgs–strahlung processes,
giving all the possible sources of theoretical uncertainties: the scale uncertainty viewed
as an estimation of the unknown higher–order terms in the perturbative calculation;
the parton distribution functions (PDFs) uncertainties related to the non–perturbative
QCD processes within the proton, and its related strong coupling constant issue; the
uncertainty coming from the use of an effective theory approach to simplify the hard
calculation in the gluon–gluon fusion process. We will specifically address the issue of
the combination of all the uncertainties in section 4.5. We will then move on to the
same study at the LHC, concentrating on its current run at a 7 TeV center–of–mass
energy that we will name as the lHC for littler Hadron Collider; we will still give some
predictions for the designed LHC at 14 TeV. We will finish this part II by the Higgs
boson decay branching fractions predictions in section 6, together with a detailed study
of the uncertainties that affect these predictions. It will be followed by the combination
of the production cross sections and decay branching fractions into a single prediction,
first at the Tevatron in section 6.3 and then at the lHC in section 6.4. We will then
study the impact of our uncertainties on the Tevatron Higgs searches in section 6.5 and
in particular put into question the Tevatron exclusion limits that are debated within the
community.
Even if the Standard Model is a nice theory with great experimental successes, it
suffers from some problems, both on the theoretical and experimental sides. It is known
for example that the Higgs boson mass is not predicted by the Standard Model, and
even not protected: higher order corrections in the perturbative calculation of the Higgs
boson mass have the tendency to drive the mass up to the highest acceptable scale of the
theory which means that we need a highly fine–tuning of the parameters to cancel such
driving. It is known as the naturalness problem of the Standard Model. They are several
ways to solve such a problem, and one of them is particularly elegant and relies on a new
symmetry between bosons and fermions: supersymmetry. This theoretical concept, born
in the 1970s, has many consequences when applied to the Standard Model of particle
physics and is actively searched at current high energy colliders. This will be the topic
of part III in which we will review some of the reasons that drive the theorists to go
Introduction 3
beyond the Standard Model and in particular what makes supersymmetry interesting
in this view in section 7, then move on to the description of the mathematical aspects
of supersymmetry in section 8. We will finish this part III by a very short review of
the minimal supersymmetric extension of the Standard Model, called the MSSM, in
section 9. We will in particular focus on the Higgs sector of the theory and show that
the MSSM needs two Higgs doublets to break the electroweak symmetry breaking and
has thus a rich Higgs sector as five Higgs boson instead of a single one are present in
the spectrum: two neutral CP–even, one CP–odd and two charged Higgs bosons.
After this review of supersymmetry and the MSSM we will reproduce in part IV the
same outlines that have been developed in part II in the Standard Model case. We will
first review the neutral Higgs sector at hadron colliders in section 10 and show that we
can have a quite model–independent description for our predictions in the sense that
they will hardly depend on most of the (huge) parameters of the MSSM but two of
them, the mass of the CP–odd Higgs boson A and the ratio tan β between the vacuum
expectation values of the two Higgs doublets. We will then give in section 11 our
theoretical predictions for the neutral Higgs bosons inclusive production cross section at
the Tevatron in the two main production channels that are the gluon–gluon fusion and
the bottom quark fusions, the bottom quark playing a very important role in the MSSM
at hadron colliders. We will reproduce the same study at the lHC in section 12 before
giving the implications of our study on the [MA,tan β] parameter space in section 13.
We will first give in this last section our predictions for the main MSSM decay branching
fractions and in particular the di–tau branching fraction that is of utmost importance
for experimental searches. We we will then compare our predictions together with their
uncertainties to the experimental results obtained at the Tevatron and at the lHC that
has now been running for more than a year at 7 TeV and given impressive results. We
will see that the theoretical uncertainties have a significant impact on the Tevatron
results, less severe at the lHC. We will finish section 13 by a very important outcome of
our work: the possibility of using the MSSM neutral Higgs bosons searches in the di–
tau channel for the Standard Model Higgs boson in the gluon–gluon fusion production
channel followed by the di–tau decay channel in the low Higgs boson mass range 115–140
GeV.
Finally, we will give an outlook and draw some conclusions in part V together with
some perspectives for future work. These rest on the next step on the road of the
experiments, that is an exclusive study of the Higgs bosons production channels. We
shall give some early results in section 14 on the Standard Model Higgs boson at the
lHC in the gg → H → WW → νν search channel together with an exclusive study of
the main Standard Model backgrounds. This is also the current roadmap of the Higgs
bosons theoretical community and this work is done in the framework of a collaboration
on this topic.

5
Part I
A brief review of the Standard
Model of particle physics
Summary
1 Symmetry principles and the zoology of the Standard Model 6
1.1 A brief history of the Standard Model . . . . . . . . . . . . . . . . . 6
1.2 Gauge symmetries, quarks and leptons . . . . . . . . . . . . . . . . 12
2 The Brout–Englert–Higgs mechanism 16
2.1 Why do we need the electroweak symmetry breaking? . . . . . . . . 16
2.1.1 The unitarity puzzle . . . . . . . . . . . . . . . . . . . . . . . 16
2.1.2 Masses and gauge invariance . . . . . . . . . . . . . . . . . . 18
2.2 The spontaneous electroweak symmetry breaking . . . . . . . . . . . 19
2.2.1 Weak bosons masses and electroweak breaking . . . . . . . . 20
2.2.2 SM Higgs boson couplings . . . . . . . . . . . . . . . . . . . 24
6 Symmetry principles and the zoology of the Standard Model
1 Symmetry principles and the zoology of the Standard Model
The Standard Model (SM) of particle physics is the current description of the fundamental constituents of our universe together with the interactions that occur between them.
The SM was born in its current form in the seventies, after nearly twenty years of many
experiments and theoretical reflexions on how to build a somewhat simple and elegant
model to describe accurately the experimental results on the one hand and to make powerful predictions in order to have a falsifiable theory on the other hand. Its frameworks
are relativistic quantum field theory and group theory to classify the different interactions. It also needs the key concept of spontaneous (electroweak) symmetry breaking in
order to account for the masses of the different fields in the theory, the (weak) bosons
as well as the matter fermions. Other reasons also push for such a theoretical concept
and will be presented in the next sections.
We will in this section present a short review of the major historical points in the
birth of the SM, and present its theoretical fundations. The focus on the electroweak
symmetry breaking, in particular its minimal realization through the Brout–Englert–
Higgs mechanism, will be discussed in the next section.
1.1 A brief history of the Standard Model
This subsection will sketch the different historical steps that have lead to the current
form of the theory that describes the elementary particles and their interactions among
each other, called the Standard Model (SM). This model has a very rich history over
more than fifty years of the XXth century, not to mention all the diverse and fruitful
efforts made before to attain this level of description of the elementary world. We will
only select some (of the) outstanding events, both from the theoretical and experimental
sides, to present the twisted path leading to the current Standard Model of particle
physics.
The birth of modern QED
The first attempt to decribe electromagnetic phenomena in the framework of special
relativity together with quantum mechanics can be traced back in the 1920s. In particular Dirac was the first to describe the quantization of the electromagnetic fields as
an ensemble of harmonic oscillators, and introduced the famous creation–annihilation
operators [1]. In 1932 came Fermi with a first description of quantum electrodynamics [2], but physicists were blocked by the infinite results that did arise in the calculations
beyond the first order in perturbation theory.
1.1 – A brief history of the Standard Model 7
Years after, the difficulty was solved by Bethe in 1947 [3] with the concept of renormalization, that is the true physical quantities are not the bare parameters of the theory,
and thus the infinite that arise are absorbed in the physical quantities, leaving finite results in the end. This leads to the modern Quantum ElectroDynamics (QED) with the
key concept of gauge symmetry and renormalization, that was formulated by Feynman,
Schwinger and Tomonaga [4–6] in the years 1950s and awarded by a Nobel prize in 1965.
This is the first quantum field theory available and has been the root of all the SM ideas
for the key concepts of gauge symmetry and renormalizability.
P violation and V − A weak theory
It was long considered in physics that the parity symmetry was conserved: if we
repeated an experiment with the experimental apparatus mirror reversed, the results
would be the same as for the initial set–up. This assessment is true for any experiment
involving electromagnetism or strong interaction, but that is not the case for weak
interaction.
It was first proposed by Yang and Lee in 1956 that the weak interaction might indeed
not respect P–symmetry [7]. This was observed in 1957 by Chien-Shiung Wu (“Madam
Wu”) in the beta desintegration of cobalt 60 atoms [8]. Yang and Lee were then awarded
the 1957 Nobel prize for their theoretical developments on this concept.
Up until that period, the weak interaction, that shapes the decay of unstable nucleii,
was described by the Fermi theory in which the fermions interact through a four–particles
vertex. The discovery of the P–violation lead to the construction of an effective V − A
theory where the tensor structure of the thory is correct and does respect the charge and
parity violations. This V − A theory was later on replaced by the electroweak theory,
see below.
The quark description
In the first half of the XXth century the pattern of elementary particles was simple: the
electron (and its antiparticle the positron, postulated by Dirac in 1931 and discovered
in 1932 by Anderson), the proton and the neutron were the only known elementary
particles at that time. The neutrino, first postulated by Pauli in its famous letter in
1930 to save the energy–momentum conservation in beta decay reactions2 was discovered
only in 1956.
Experimental particle physicists discovered numerous new particles (the “hadrons”)
in the 1950s and 1960s after the discovery of the pion in 1947, predicted by Yukawa in
1935, thus casting some doubts on the elementary nature both of the “older” particles
2The original name was “neutron” for neutral particle. Chadwick discovered in 1932 what would be
the neutron, thus Fermi proposed the name “neutrino” meaning “little neutral one” in italian.
8 Symmetry principles and the zoology of the Standard Model
such as the neutron and the proton and on the new zoo discovered. Gell–Man and Zweig
proposed in 1964 a model of constituant particles of these hadrons and mesons that
could explain the pattern seen by experimentalists, using only a limited number of new
constituant particles: the quarks [9,10]. They introduce the SU(3) flavor symmetry with
the three up, down and strange quarks. One year later the charm quark was proposed to
improve the description of weak interactions between quarks, and in 1969 deep inelastic
scattering experiments at the Stanford Linear Accelerator Center (SLAC) discovered
point–like objects within the proton [11], an experimental proof of the compositeness of
the hadrons. It is interesting to note that the term used for these new point–like objects
was “parton”, proposed by Feynman, as the community was not entirely convinced that
they were indeed the Gell–Mann’s quarks. Nowadays “parton” is still a word used in
particle physics to name the different constituants of the hadrons (the quarks, antiquarks
and gluons, the later being the bosons of the strong interaction).
The (nearly) final word on the quark model was given in 1974 when the J/Ψ meson
was discovered [12, 13] and thus proved the existence of the charm quark, which was
proposed by Glashow, Iliopoulos and Maiani in the GIM mechanism [14] in 1970 to explain the universality of weak interaction in the quark sector, preventing flavor changing
neutral currents. The heaviest quark, that is the top quark, was finally discovered in
1995 at the Fermilab Tevatron collider [15, 16].
CP violation and the concept of generation
To explain both the universality and the u ←→ d transitions in weak interactions,
Cabibbo introduced in 1963 what is known as the Cabibbo angle [17] and was used
to write in the mass eigenstates basis the weak eigenstate for the down quark d. A
year later, Cronin and his collaborators discovered that not only C and P symmetries
are broken by weak interactions, but also the combined CP symmetry [18], studing the
K0K
0
oscillations: the probability of oscillating from K0
state into K
0
state is different
from that of the K
0
→ K0
, indicating that T time reversal symmetry is violated. As
the combined CPT is assumed to be conserved, this means that CP is violated.
As mentioned a few lines above, the GIM mechanism introduced a fourth quark, the
charm quark c. It then restores universality in the weak coupling for the quarks, as we
have now two weak eigenstates
|d
0
i = cos θc|di + sin θc|si
|s
0
i = − sin θc|di + cos θc|si (1.1)
coupled to respectively the u quark and the c quark. We thus have two generations
in the quark sector, the first one is the (u, d) doublet and the second one is the (c, s)
1.1 – A brief history of the Standard Model 9
doublet. However, as explained in 1973 by Kobayashi and Maskawa extending the work
initiated by Cabibbo, this is not sufficient to explain the CP violation observed by the
1964 experiment. Only with three generations could be introduced some CP violating
effects through a phase angle, and thus extending the Cabbibo angle to what is known
as the Cabibbo–Kobayashi–Maskawa (CKM) matrix [19]. Kobayashi and Maskawa were
awarded the 2008 Nobel prize for this result3
.
Yang–Mills theory and spontaneous symmetry breaking
We have seen a few lines above that the Fermi theory describing the weak interactions
had been refined by the V − A picture to take into account the P violation. Still the
V − A theory was known to be an effective theory as the theory was not renormalizable
and did not allow for calculations beyond the first order in perturbation theory. The only
gauge theory that was available at that time was QED, an abelian gauge theory, which
obviously is not the right description of weak processes as it describes only light–matter
interactions.
The first step toward the solution was set–up in 1954, when Yang and Mills developed a formulation of non–abelian gauge theories [20] in order to provide (initially) an
explanation for the strong interaction at the hadron level (that we call nuclear interaction). Unfortunately the theory was not a success at first, as the gauge bosons must
remain massless to preserve the symmetry of the theory, thus meaning that the weak
interaction should be long–range; experimentally that is not the case.
The key result to solve this contradiction and then still use the elegant description of
gauge theory is given in 1964 by Brout, Englert, Higgs, Guralnik, Hagen and Kibble after
some important work on the concept of symmetry breaking from Nambu and Goldstone:
the spontaneously gauge symmetry breaking [21–24] described by the Brout–Englert–
Higgs mechanism. This will be presented in the following in details, but we can already
remind the reader that the most important result is that it allows for the use of a
Yang–Mills theory together with a description of massive gauge bosons for any gauge
theory.
Interlude: from nuclear force to strong interaction
Before arriving to the final electroweak description that constitutes the heart of the
SM, we recall the road leading to the description of the strong interaction between the
quarks.
As stated above, Yang–Mills theory in 1954 was the first attempt to describe the
interaction between the hadrons, that we call nuclear interaction, in a gauge formulation.
3Unfortunately the Nobel committee failed to recognize the important pionnering work from
Cabibbo.
10 Symmetry principles and the zoology of the Standard Model
After the introduction of the quark model by Gell–Mann in 1964 (see above) and the
discovery of the quarks in 1969 (see above), it has been proposed that the quarks must
have a new quantum charge, called color, to accomodate for the Pauli exclusion principle
within some baryons [25]. This was experimentally observed in the SLAC experiments
in 1969 which discovered point–like objects within the nucleon, as discussed earlier.
With the help of the discovery of asymptotic freedom [26, 27] in 1973 by Wilczek,
Gross and Politzer (who share the 2004 Nobel prize for this result), that states that at
very high energy quarks are free, and with a SU(3) gauge Yang–Mills theory, Quantum
ChromoDynamics (QCD) was firmly established in the 1970s as being the theory of
the strong interactions, with the gluons as the gauge bosons. Evidence of gluons was
discovered in three jet events at PETRA in 1979 [28], giving further credits to QCD.
The nuclear interaction between the hadrons is then a residual force originating from
the strong interaction between quarks (and gluons). However, as the strong coupling
is indeed very strong at large distance (that is the confinement), preventing from the
use of perturbation theory, an analytical description of the strong interaction within the
hadrons at low energies is still to be found. This problem is now studied within the
framework of lattice gauge theories which give spectacular results.
The weak neutral currents and the path to electroweak theory
As stated above it was known that the V − A theory for the weak interaction was
an effective theory, with difficulties calculating beyond the first order in perturbation
theory. With the advent of Yang–Mills theory and the Brout–Englert–Higgs mechanism,
describing the weak interaction with a gauge theory and in the same time allowing for
massive weak bosons as dictated by the experiments, the weak interaction being a short
distance interaction, it would be possible to account for a renormalizable description of
the weak interaction.
During the 1960s there were many attempts to carry on this roadmap, trying lots of
different gauge groups to account for the QED on the one hand, the weak interaction
on the other hand, as both interactions play a role for lepton particles such as the
electron. The gauge theory that did emerge was the SU(2) × U(1) model where the
weak and electromagnetic interactions are unified in a single gauge theory description4
,
with contributions notabely from Glashow [29], Salam [30] and Weinberg [31]. This
model together with the Brout–Englert–Higgs mechanism predicts in particular that
there should be a neutral weak boson Z
0
to be discovered and thus neutral currents.
4
It is actually not a complete unified theory as the algebra describing the electroweak interaction is a
product of two Lie algebras. Nevertheless as the decription of the weak and electromagnetic interactions
are intimely connected through the pattern of the electroweak symmetry breaking, see below, this can
be viewed as at least a partial unification.

[Claire N]

Oui
On les appelle CNEP ( crises nons épileptiques psychogènes)
Avant on les appelait pseudo crise ( je te laisse imaginer les ravages de ce vocable)
Ça bosse et ça bouge sur le sujet depuis quelques années
On retrouve souvent des violences, traumatismes psychiques , abus
La ou ça se corse c’est que les épileptiques peuvent en faire

[Malice]

Je n’avais pas vu ta réponse entre deux trollages, merci pour tes précisions!

[nefa]

trochet mettant l’accent sur le fait qu’on a à faire à une structure assemblant plusieurs éléments et bogue à une enveloppe

[Seldoon]

Exactement, j’ai compté 4 bogues mais j’ai pu me tromper.

[Carton de Lait]

Putain de solo de basse quand meme

.

.

(ok je me casse)

[Fanny]

Et comme le trochet Julius a plusieurs faces. Il présente aux autres de préférence celle qui ne suit pas le courant (aristo vs prolo, croyant vs athée etc).

[Seldoon]

Mes anecdotes de mythomanes. Le premier mythomane était un allemand d’une cinquantaine d’année du nom de Michael P. À l’époque, j’avais entre 20 et 25 ans et travaillais – en stage – avec mon père sur un jeu en ligne pour enfants depuis disparu. Le jeu existait en France, on voulait le lancer dans plusieurs pays d’Europe et on cherchait donc dans chaque pays un partenaire local pour s’occuper des relations presse et du SAV.
Michael était le mari d’une amie d’amie de la famille. Il habitait à Strasbourg avec sa femme, avait deux sociétés (en Allemagne et en France) spécialisée en marketing digital. On l’a rencontré, il semblait parfait pour le job. On a travaillé avec lui pendant 6 mois avant la sortie allemande du jeu. Comme la sortie prenait du retard (de notre côté), il était un peu payé à ne rien faire. Il devait simplement vérifier quelques traductions qu’on lui envoyait, et préparer un plan média (principalement presse). Franchement pas grand chose, et rien de difficile même sans rien n’y connaître.
Or il ne le faisait pas. Ou si peu. C’était moi qui m’occupais de tous les partenaires internationaux, donc j’avais hérité de ce type du double de mon âge qui me baladait et évitait de me mettre en contact avec ses employés. On a mis en place une routine pour être sûr qu’il avance régulièrement, avec point hebdomadaire au téléphone… Il annulait ces points au dernier moment, les repoussait au maximum chaque semaine. Et continuait de n’envoyer que 20 mots vérifiés tous les mois, et des listes de 3 noms de journaux.
On a voulu annuler le contrat, et c’est ce jour là qu’il m’a annoncé une grave maladie. Un cancer. C’est à cause de sa faible santé et des nombreux examens qu’il avait manqué de fiabilité ces derniers temps. Il ne lui restait plus que deux ans à vivre. Il avait bien réfléchi à ce qu’il voulait faire de ces deux dernières années, il avait donc annulé tous ses contrats sauf deux. « We’re gonna make something of this game ! ». Impossible de rompre dans ces conditions, il a gagné deux semaines. Il a continué à ne rien foutre. On l’a alors viré au cours d’un appel chargé en émotion, il a pleuré au téléphone (sans résister), on avait tous les larmes aux yeux. On se sentait très mal de lui faire ça à ce moment là mais on ne pouvait continuer et lui à l’évidence non plus.

Un an plus tard, sans nouvelles, mon père demande au cours d’un diner des nouvelles de Michael à A. (l’amie qui nous avait mis en contact). « Michael ? Mais il va très bien, pourquoi ? » A. est perturbée. Elle est très proche de la femme de Michael, elle le saurait s’il avait un cancer. Un mois plus tard, mon père insiste, A. lui apprend que :

1. Michael est à l’hôpital. Psychiatrique. Il mentait à tout le monde, sa femme comprise, depuis 10 ans. Il n’avait pas de société en Allemagne. Pas d’appartement de fonction (il disparaissait pourtant plusieurs nuits par semaine) malgré les photos qu’il lui avait montrées. Mais elle l’aimait, elle lui pardonnait, elle l’aiderait à remonter la pente à condition qu’il se soigne.
2. Il disait depuis 1 an à sa femme et sa femme à A. qu’on ne le payait plus alors qu’il continuait de bosser. Il était très gêné par la situation. Et A. aussi, d’apprendre que nous étions des arnaqueurs. C’est pourquoi elle ne nous en parlait pas.

Et j’insiste : tout ce qu’on lui demandait de faire jusqu’à présent était faisable par presque n’importe qui dont la langue maternelle était l’allemand. Il a grillé 10 ans de mensonges à ses proches parce qu’il n’arrivait pas à bosser 1h par semaine. Il y avait un blocage quelque part, avant le mensonge.

[Malice]

Merci pour ton récit, je me demande comment ça se passe pour lui et sa femme ( est-ce qu’il a réussi à se « soigner », est-ce que son couple a survécu…)

[Seldoon]

Je n’ai pas de nouvelles. Il a un profil LinkedIn relativement à jour, c’est tout ce que je sais.

[Seldoon]

La deuxième histoire a eu lieu il y a quelques années dans un bar que j’aimais beaucoup : le Tambour. Il ne fermait pas de la nuit, on y trouvait toutes sortes de personnalités, de toutes classes sociales, de pas mal de pays. Notamment quelques dérangés, comme, un autre soir, un vieil homme très élégant, noeud papillon et tout, qui a passé des heures à parler de voyages à une chaise vide – et en sortant le grand jeu, s’excusant d’aller aux toilettes, « pardon je t’ai interrompue » en revenant, etc. Plus dérangé encore : la dernière fois que j’y suis allé (le lieu a fermé définitivement un mois plus tard) j’y ai discuté rapidement avec Vincent Malausa. L’anecdote en question ne concerne aucun de ces deux types mais une jeune fille. Je venais, pour la seule fois de ma vie, de me « battre » (je ne rentre pas dans les détails, j’insiste juste sur les guillemets) avec un mec bourré. Ce mec avait voulu chourer mon chapeau pour m’emmerder et était sorti perdant de l’interaction. Une fille, qui dinait avec ses amis et son mec à la table d’à côté, nous a alors rejoint. Elle m’a félicité pour la façon dont j’avais traité le crétin bourré, en me faisant clairement du rentre dedans, en étant passionnée et étrangement… congruente ? parfaitement adaptée ? À tout ce que je racontais. Bref elle semblait être LA personne la plus intimement proche de tout ce qu’on pouvait dire – d’abord moi, puis mon pote E. et moi. Et progressivement, comme elle s’avançait trop sur chaque sujet, on commence à découvrir des incohérences. Mais elle s’arrangeait toujours pour nager dans un nuage de flou qui rendait ces incohérences louches mais on ne pouvait jamais les lui mettre sous le nez. Oui oui elle connaissait très bien Versailles, elle y allait très souvent avec un ami il y a quelques années. Quel coin ? Près de Versailles Chantiers. Je ne sais plus pourquoi j’évoque les « croyants » à Versailles, et la voilà catholique. On parle de l’église à côté de Chantiers, ah bah c’est là qu’elle allait justement. Je note que c’est un temple protestant, et la voilà protestante. Même cirque sur tous les sujets (incohérence et proximité intime). Le tout avec son mec qui fulmine à la table d’à côté, puis va fumer dehors. Comme je suis assis dos contre la vitre, il est en fait 20cm derrière moi, à fumer rageusement. Je lui fais signe de venir s’assoir avec nous pour désamorcer toute jalousie, pour arrêter cette séduction particulièrement désagréable. Il refuse.
Un vieil arabe bourré vient s’assoir avec nous, et pendant que la fille continue à nous mentir sur tous les sujets du monde, physiquement, les deux se rapprochent. Il ne dit rien, mais il sait ce qu’il fait, et elle l’encourage. Cuisse contre cuisse, elle lui caresse les mains tout en nous fixant. Le copain est toujours dans mon dos. On ne sait plus trop où se mettre. Au bout d’un moment, le vieux se fait trop entreprenant, elle l’arrête en jouant l’effarouchée, « ce n’était que de la tendresse ». Il s’énerve violemment, se fait foutre dehors. Elle nous prend à témoin, E. plus courageux que moi lui dit qu’elle l’avait quand même bien encouragé, qu’elle avait tous les droits de le repousser mais que c’était un peu gonflé de jouer la surprise. Elle s’offusque, crise de larmes, part dehors pour une heure ou deux. Je la perds de vue, elle repartira plus tard avec son copain.

[Juliette B]

Merci Seldoon. Beau récit, chaque incidente au début – drôle leur répétition, comme dans Le petit Nicolas – donne sacrément envie d’aller aussi y voir de plus près. Ca densifie d’emblée cette petite frustration qu’aucune ne sera développée..
La principale, la fille, est forte, parce qu’on voit autant le n’importe quoi de son récit évolutif que son innocence vertigineuse à y croire.
J’ai aussi pensé en te lisant que tu avais expérimenté un truc fréquemment vécu par les femmes, que tu t’étais coulé dedans.
Et ta tentative ratée de désamorçage de la jalousie de l’autre derrière la fenêtre m’a fait rire. On voit le film.

[Claire N]

Merci Seldoon
Ta deuxième histoire m’a un peu glacée
Je n’ai pu m’empêcher de penser à une amie victime d’inceste toute petite , qui n’a pas été crue d’ailleurs
Elle peut parfois se comporter comme cela

[Malice]

Le principe du « moi aussi » où la personne semble ne pas supporter d’être absente des histoires qu’on lui raconte…ça me donne toujours l’impression que le ou la menteur(se) se sent exclu(e) de la vie des autres : ce qui arrive en dehors de moi n’a pas le droit d’exister.

[Claire N]

Oui alors si on retourne j’existe plus si cela arrive en dehors de moi ? J’arrive pas à trancher si c’est un mini ou un gros ego –

[Malice]

Les deux mon général
L’ego est si petit qu’il se gonfle et devient gros

[Claire N]

Oui je vois, un peu comme une baudruche ;
Un orgueil qui tient sur du vent
– si on les pique ils s’effondrent
Et probablement recommencent laborieusement à se pomper pour y survivre
Une sacrée triste ornière

[Malice]

Mais la comparaison avec la baudruche s’arrête là, du moins si je me base sur mon expérience des menteurs car leur système fait qu’ils mourraient plutôt que de se laisser dégonfler.
Le train retombe toujours sur toutes ses roues même s’il a provisoirement déraillé, à cause d’une confrontation…C’est le pouvoir infini du menteur, il pourra toujours créer de nouvelles justifications à ses mensonges, et il est aidé en cela par le fait que les humains sont toujours en quête de ces justifications ( il n’y a bien que dans l’art qu’on se satisfait de ne pas tout comprendre).
Louie CK avait fait une éloge du mensonge dans un sketch, en disant que c’était un pouvoir fabuleux et quasi irrésistible, mais je ne sais plus dans quel spectacle…

[Seldoon]

De mémoire il y expliquait qu’il était très difficile de dire à ses enfants de ne pas mentir, car le mensonge était la solution à tous leurs problèmes.

[Malice]

Voilà! Et c’est tellement vrai

[Juliette B]

C’est vrai Claire, ça me fait penser en te lisant à tous ces enfants placés, qui n’ont pas été crus ou n’ont pas pu parler, au moment où ils les vivaient, des abus dont ils étaient l’objet, et qui après mythonent sans cesse la réalité, accusant jour après jour des innocents des crimes autrefois vécus par eux.

[Claire N]

Oui c’est vrai
Je me dis que c’est sûrement très compliqué
D’avoir des relations d’amour chaste ( au sens du respect absolu de sa propre intégrité et de celle de l’autre) lorsqu’on a vécu de telles atrocités et finalement peu de références dans la vie
Avec mon amie je passe par «  au dessus du mensonge «  , jamais d’ironie, et inutile de la confronter, sinon paradoxalement c’est elle qui perd confiance

[Malice]

Et comment tu gères une amitié si compliquée ( si ce n’est pas indiscret)?

[Claire N]

On se voit relativement peu je pense que cela ma permet une certaine «  patience «  et disponibilités lorsqu’on se rencontre
Et en pratique je parle peu ; elle parle beaucoup ça s’équilibre ; elle a d’autres qualités elle est rayonnante quand elle raconte ses histoires, sensible et rigolote

[Malice]

Elle ment non stop ou elle exagère seulement et ponctuellement des événements?
Je me demande aussi comment tu fais pour ne pas ressentir de malaise quand tu entends des mensonges ( personnellement je n’arrive pas à cacher ma gêne, rester concentrée ou impliquée dans la conversation quand j’entends des choses douteuses)…

[Claire N]

Non pas tout le temps, les dernières fois c’était plutôt effectivement des justifications , l’histoire de sa non présentation a des examens était peu être la plus n’importe quoi.
Comment je fais je sais pas trop mais je crois que d’une certaine façon j’évite de le prendre personnellement ; en l’espèce il y a crainte de jugement j’imagine j’évite d’en rajouter

[Claire N]

Elle somatise aussi beaucoup mais ça c’est pas du mensonge dans ma religion ; il y a peut etre un lien cependant faudrait que j’y réfléchisse

[Malice]

Elle somatiserait parce-qu’elle est empêchée dire des choses justes ( ou j’ai mal compris)?

[Claire N]

Ça me paraît en tout cas une définition intéressante de la somatisation ce que tu viens de proposer là

[Malice]

Je ne suis pas du tout sûre de ne pas être en train de tenir des propos de pmu de la psychiatrie! Tout ce que je sais sur la somatisation c’est que des fois dans ma vie j’ai eu mal au dos ou la migraine quand je ne pouvais pas dire que des choses/des gens me pétaient les couilles/me remplissaient d’un chagrin infini; Alice Miller me l’a confirmé mais en ce qui concerne les mythos je ne m’avancerais pas.

[Claire N]

Peut-être que toi tu avais et mal et conscience que des gens de petaient les couilles
Dans son cas a elle on va dire que seul l’aspect physique est porté à sa connaissance ; c’est plus de l’ordre du trouble fonctionnel ou anciennement nomme trouble converssif – le « passe- passe « semble total
Pour la migraine le stress, les changements de rythme, hormonaux, aliments sont des facteurs «  à égalité «  dans leur déclenchement ; le processus migraineux est de plus très organique
Ce qui est encore plus troublant dans ce jeux d’intrication c’est que des imagerie fonctionnelles d’un trouble conversif – une paralysie du membre inférieur par exemple – montrent un hypofonctionnemt du cortex moteur correspondant
Cela est passionnant, je m’écarte du sujet, mais tu mesures bien l’impact d’une émotion sur l’organe

[Mao]

La vie est une farce, un jeu absurde. Julius en prend acte. Il refuse de se reconnaître un rôle figé et déterminé. Il est alors un acteur qui joue la situation jusqu’au bout pour voir où ça le mène. Il improvise constamment. Une idée, une situation chasse l’autre. Il est parfois à l’origine du dispositif et se fait alors metteur en scène. Sans être un mythomane invétéré, il m’est souvent arrivé de dire d’énormes conneries pour voir jusqu’où les gens sont prêts à marcher. Je crois que c’est aussi comme ça que fonctionne l’humour pince sans rire. On balance des horreurs et on voit ceux qui vous prennent au premier degré.

[Malice]

Je me suis dit aussi que Julius devait trouver un certain plaisir dans les « défis » de ses mensonges; toute la séquence de la randonnée est chargée d’un suspense où je pensais : il a peur, mais c’est peut-être la peur de qui à la fois redoute et prend plaisir au danger. Julius serait un artiste de cirque, un funambule, son côté bateleur très charmant irait dans ce sens.

[L’inconnu]

De même que la science est comme la religion une croyance, de même toute conversation avec quelqu’un est de l’ordre de la croyance également, on a a priori aucune preuve que la personne en face de nous nous raconte une vérité, elle peut bien tout inventer, des récits comme des opinions, mais le fait est qu’on est porté en général à la croire (à moins que la personne ait l’air faux, qu’elle joue mal). De ce point de vue le mensonge est égal à la vérité, il crée de la vérité chez celui qui le reçoit comme le fait la religion, alors pourquoi ne pas mentir puisque ce n’est pas mentir. C’est ce qu’illustre la dernière scène. Il rejoue la confession de l’homme croyant (gageons qu’il dit vrai) à d’autres pour le même résultat. Sauf quand les mensonges butent sur des faits – je n’ai pas de bateau – il ne reste plus qu’à fuir.
Je ne savais pas que les mythomanes pouvaient croire réellement à leurs mensonges. Mais pour reprendre les mots de Santé Magazine :
« La mythomanie est une tendance pathologique à travestir ou réinventer la réalité sans en avoir conscience. »
« le mythomane a besoin de croire en ses mensonges pour vivre, même s’il sait, au fond de lui, que ce n’est pas vrai. » Peut-être qu’il sait que ce n’est pas vrai seulement par intermittence. De ce point de vue on peut penser que même la crise d’épilepsie est vraie, somatique comme dit plus haut, même si je trouve ça bien plus drôle qu’il la joue.
Une idée quand même du pourquoi de ces plans d’école abandonnée à la fin ? Pourquoi montrer l’école aujourd’hui plutôt qu’à l’époque ?

[Demi Habile]

Phenom ´ enologie du Higgs aupr ´ es des collisionneurs hadroniques : `
du Modele Standard a la Supersym etrie. ´
R´esum´e
Cette these, conduite dans le contexte de la recherche du boson de Higgs, derniere pi`ece
manquante du m´ecanisme de brisure de la sym´etrie ´electrofaible et qui est une des plus importantes recherches aupr`es des collisionneurs hadroniques actuels, traite de la ph´enom´enologie
de ce boson a la fois dans le Modele Standard (SM) et dans son extension supersym´etrique
minimale (MSSM). Apres un r´esum´e de ce qui constitue le Modele Standard dans une premi`ere partie, nous pr´esenterons nos pr´edictions pour la section efficace inclusive de production
du boson de Higgs dans ses principaux canaux de production aupr`es des deux collisionneurs
hadroniques actuels que sont le Tevatron au Fermilab et le grand collisionneur de hadrons
(LHC) au CERN, en commen¸cant par le cas du Mod`ele Standard. Le principal r´esultat pr´esent´e est l’´etude la plus exhaustive possible des diff´erentes sources d’incertitudes th´eoriques
qui p`esent sur le calcul : les incertitudes d’´echelles vues comme une mesure de notre ignorance
des termes d’ordre sup´erieur dans un calcul perturbatif `a un ordre donn´e, les incertitudes reli´ees aux fonctions de distribution de partons dans le proton/l’anti–proton (PDF) ainsi que
les incertitudes reli´ees `a la valeur de la constante de couplage fort, et enfin les incertitudes
provenant de l’utilisation d’une th´eorie effective qui simplifie le calcul des ordres sup´erieurs
dans la section efficace de production. Dans un second temps nous ´etudierons les rapports
de branchement de la d´esint´egration du boson de Higgs en donnant ici aussi les incertitudes
th´eoriques qui p`esent sur le calcul. Nous poursuivrons par la combinaison des sections efficaces
de production avec le calcul portant sur la d´esint´egration du boson de Higgs, pour un canal
sp´ecifique, montrant quelles en sont les cons´equences int´eressantes sur l’incertitude th´eorique
totale. Ceci nous ameneraa un r´esultat significatif de la th`ese qui est la comparaison avec l’exp´erience et notamment les r´esultats des recherches du boson de Higgs au Tevatron. Nous irons
ensuite au-dela du Modele Standard dans une troisieme partie ou nous donnerons quelques
ingr´edients sur la supersym´etrie et sa mise en application dans le MSSM o`u nous avons cinq
bosons de Higgs, puis nous aborderons leur production et d´esint´egration en se focalisant sur
les deux canaux de production principaux par fusion de gluon et fusion de quarks b. Nous
pr´esenterons les r´esultats significatifs quant `a la comparaison avec aussi bien le Tevatron que
les r´esultats tr`es r´ecents d’ATLAS et CMS au LHC qui nous permettront d’analyser l’impact
de ces incertitudes sur l’espace des param`etres du MSSM, sans oublier de mentionner quelques
bruits de fond du signal des bosons de Higgs. Tout ceci va nous permettre de mettre en avant
le deuxieme r´esultat tres important de la th`ese, ouvrant une nouvelle voie de recherche pour
le boson de Higgs standard au LHC. La derni`ere partie sera consacr´ee aux perspectives de
ce travail et notamment donnera quelques r´esultats pr´eliminaires dans le cadre d’une ´etude
exclusive, d’un int´erˆet primordial pour les exp´erimentateurs.
Mots-clefs : Mod`ele Standard, Higgs, Supersym´etrie, Chromodynamique quantique, incertitudes th´eoriques.

Abstract
This thesis has been conducted in the context of one of the utmost important searches at
current hadron colliders, that is the search for the Higgs boson, the remnant of the electroweak
symmetry breaking. We wish to study the phenomenology of the Higgs boson in both the
Standard Model (SM) framework and its minimal Supersymmetric extension (MSSM). After
a review of the Standard Model in a first part and of the key reasons and ingredients for
the supersymmetry in general and the MSSM in particular in a third part, we will present the
calculation of the inclusive production cross sections of the Higgs boson in the main channels at
the two current hadron colliders that are the Fermilab Tevatron collider and the CERN Large
Hadron Collider (LHC), starting by the SM case in the second part and presenting the MSSM
results, where we have five Higgs bosons and focusing on the two main production channels that
are the gluon gluon fusion and the bottom quarks fusion, in the fourth part. The main output
of this calculation is the extensive study of the various theoretical uncertainties that affect the
predictions: the scale uncertainties which probe our ignorance of the higher–order terms in a
fixed order perturbative calculation, the parton distribution functions (PDF) uncertainties and
its related uncertainties from the value of the strong coupling constant, and the uncertainties
coming from the use of an effective field theory to simplify the hard calculation. We then
move on to the study of the Higgs decay branching ratios which are also affected by diverse
uncertainties. We will present the combination of the production cross sections and decay
branching fractions in some specific cases which will show interesting consequences on the
total theoretical uncertainties. We move on to present the results confronted to experiments
and show that the theoretical uncertainties have a significant impact on the inferred limits
either in the SM search for the Higgs boson or on the MSSM parameter space, including some
assessments about SM backgrounds to the Higgs production and how they are affected by
theoretical uncertainties. One significant result will also come out of the MSSM analysis and
open a novel strategy search for the Standard Higgs boson at the LHC. We finally present in
the last part some preliminary results of this study in the case of exclusive production which
is of utmost interest for the experimentalists.
Keywords : Standard Model, Higgs, Supersymmetry, QCD, theoretical uncertainties.

Remerciements
Trois ann´ees ont pass´e depuis que j’ai pouss´e pour la premi`ere fois les portes du Laboratoire de Physique Th´eorique d’Orsay, chaleureusement accueilli par son directeur Henk
Hilhorst que je remercie beaucoup. Trois ann´ees d’une activit´e intense, aussi bien dans
mes recherches scientifiques au LPT et au CERN, dans le groupe de physique th´eorique,
ou j’ai pass´e quelques moisa partir de la seconde ann´ee, que dans mes activit´es hors
recherche au sein de l’universit´e Paris-Sud 11. J’ai appris beaucoup et rencontr´e un certain nombre de personnes dont je vais me rappeler pour longtemps, si je ne les ´enum`ere
pas ici qu’elles veuillent bien me pardonner cela ne signifie pas que je les ai pour autant
oubli´ees.
Tout ceci n’aurait pu se faire sans les encouragements, les conseils et les discussions passionn´ees avec Abdelhak Djouadi, mon directeur de th`ese qui a guid´e ainsi mes
premiers pas de professionnel dans ma carri`ere de physicien th´eoricien des particules
´el´ementaires. Je l’en remercie profond´ement et j’esp`ere qu’il aura appr´eci´e notre collaboration autant que moi, aussi bien lors de notre travail qu’en dehors.
Je voudrais aussi remercier Rohini Godbole avec qui j’ai collabor´e sur la passionnante
physique du Higgs au Tevatron. Je ne peux non plus oublier Ana Teixeira pour son
soutien constant et les nombreuses discussions passionnantes aussi bien scientifiques que
personnelles que nous avons eues ensemble. Ma premi`ere ann´ee en tant que doctorant
lui doit beaucoup.
Je remercie aussi tous les membres de mon jury de th`ese et en particulier mes deux
rapporteurs qui m’ont certainement maudit d’avoir ´ecrit autant, non seulement pour le
temps qu’ils auront pris pour assister a ma soutenance et lire ma these, mais aussi pour
toutes leurs judicieuses remarques et questions.
Aussi bien le LPT que le CERN se sont r´ev´el´es des lieux tr`es enrichissants pour
le d´ebut de ma carri`ere scientifique. Je voudrais profiter tout d’abord de ces quelques
mots pour remercier les ´equipes administratives des deux laboratoires pour leur aide au
jour le jour, toujours avec le sourire, et pour toute leur aide dans mes divers voyages
scientifiques. Je remercie aussi tous les chercheurs de ces deux laboratoires pour toutes les
discussions que j’ai eues et qui m’ont beaucoup appris. Je pense tout particuli`erement
a Asmˆaa Abada eta Gr´egory Moreau d’un cˆot´e, `a G´eraldine Servant et Christophe
Grojean qui m’a invit´e `a venir au CERN, de l’autre. Je ne peux bien sur pas oublier les
doctorants et jeunes docteurs du groupe de physique th´eorique du CERN, Sandeepan
Gupta, Pantelis Tziveloglou et tous les autres, ainsi que L´ea Gauthier, doctorante au
CEA, que j’ai rencontr´ee au CERN : les magnifiques randonn´ees autour de Gen`eve
que nous avons faites ont ´et´e salutaires. Enfin je remercie aussi tous mes camarades
doctorants et jeunes docteurs du SINJE `a Orsay pour tous les merveilleux moments que
nous avons pass´es et toutes les discussions passionn´ees et passionnnantes, je ne vous cite
pas tous mais le cœur y est. Je pense quand mˆeme tout particulierementa mes camarades
ayant partag´e mon bureau et bien plus, Adrien Besse et C´edric Weiland, mais aussi `a
Guillaume Toucas, Blaise Gout´eraux et Andreas Goudelis. J´er´emie Quevillon qui va
prendre ma succession aupres de mon directeur de these n’est pas non plus oubli´e. Mes
amis de Toulouse eux aussi sont loin d’avoir ´et´e oubli´es et ont fortement contribu´e non
seulement a rendre exceptionnel mon stage de Master 2 mais aussi ma premiere ann´ee
de these, de loin en loin : mercia Ludovic Arnaud, Gaspard Bousquet, Arnaud Ralko,
Cl´ement Touya, Fabien Trousselet, mais aussi mes deux tuteurs Nicolas Destainville et
Manoel Manghi.
Je ne peux terminer sans exprimer ma profonde gratitude a ma famille eta mes amis
de longue date, qui se reconnaˆıtront. Anne, Charles, Elise, Gaetan, Lionel, Mathieu,
Matthieu, Patrick, Pierre, Rayna, Sophie, Yiting et tous ceux que je n’ai pas cit´es mais
qui sont dans mes pens´ees, ces mots sont pour vous ! Le mot de la fin revient `a ma
fianc´ee, Camille : sans ton profond amour et ton soutien constant, ces trois derni`eres
ann´ees auraient ´et´e bien diff´erentes, et certainement pas aussi f´econdes. Merci pour tout.
Acknowledgments
Three years have now passed since my first steps in the Laboratoire de Physique
Th´eorique at Orsay, where I have been warmly welcomed by its director Henk Hilhorst
that I thank a lot. They have been very intense, both in the laboratory and at the CERN
Theory Group in Geneva, where I spent some months starting from the second year. I
have learnt much, either within these labs or outside, encountered many people that I
will remember for a long time. If some of you are not cited in these acknowledgments,
please be kind with me: that does not mean I have forgotten you.
This would have never been possible without the constant encouragement, advices
and fruitful discussions with Dr. Abdelhak Djouadi, my thesis advisor, who guided my
first steps in theoretical particle physics research. I hope he got as much great time as
I had working with him and more than that.
I also would like to thank Pr. Rohini Godbole whom I worked with from time to
time on Higgs physics at the Tevatron. I cannot also forget Dr. Ana Teixeira for her
constant support and all the great discussions on various topics we had together. My
first year as a PhD candidate was scientifically exciting thanks to her.
I am very grateful to all the members in the jury for my defence, for the time they
would took and the useful comments. In particular I would like to thank my two referees
who certainly have cursed me for the length of the thesis.
The LPT environnement as well as the CERN Theory Group have been proven to be
very fruitful environnements for the beginning of my career. I then would like to thank
the administrative staff from both laboratories for their constant help in day–to–day life
and support when I had to travel for various workshops, conferences or seminars. I would
like to thank all the members of these two groups for the very passionate discussions
we had and where I have learnt a lot. I dedicate special thanks to Asmˆaa Abada and
Gr´egory Moreau on the one side, G´eraldine Servant and also Christophe Grojean, who
invited me to come by, on the other side. I cannot forget the PhD candidates and
post-doctoral researchers from the CERN Theory Group, Sandeepan Gupta, Pantelis
Tziveloglou and all the others, not to forget L´ea Gauthier, who is a PhD candidate
at the CEA and was at CERN at that time: the hiking we did in the Jura and Alps
around Geneva were great. I also would like to thank all my SINJE fellows at the
LPT, with whom I had so many great time and passionate discussions; you are not all
cited but I do not forget you. I dedicate special thanks to my office (and more than
office) friends Adrien Besse and C´edric Weiland, and also to Blaise Gout´eraux, Andreas
Goudelis and Guillaume Toucas. The next PhD candidate, J´er´emie Quevillon, who will
follow my path, is also thanked for the discussions we had. I finally cannot forget my
friends from Toulouse, where I did my Master 2 internship and whom I collaborated with
during my first PhD thesis year from time to time: many thanks to Ludovic Arnaud,
Gaspard Bousquet, Arnaud Ralko, Cl´ement Touya, Fabien Trousselet, and also to my
two internship advisors Nicolas Destainville and Manoel Manghi.
I now end this aknowledgments by expressing my deep gratitude and love to my family and long–time friends who will recognize themselves. Anne, Charles, Elise, Gaetan,
Lionel, Mathieu, Matthieu, Patrick, Pierre, Rayna, Sophie, Yiting and all the others,
these words are for you! The last word is for Camille, my fiancee: without your deep
love and constant support these three years would have been without doubts completely
different and not as fruitful.

Contents
Introduction 1
I A brief review of the Standard Model of particle physics 5
1 Symmetry principles and the zoology of the Standard Model 6
1.1 A brief history of the Standard Model . . . . . . . . . . . . . . . . . . . 6
1.2 Gauge symmetries, quarks and leptons . . . . . . . . . . . . . . . . . . . 12
2 The Brout–Englert–Higgs mechanism 16
2.1 Why do we need the electroweak symmetry breaking? . . . . . . . . . . . 16
2.2 The spontaneous electroweak symmetry breaking . . . . . . . . . . . . . 19
II SM Higgs production and decay at hadron colliders 27
3 Where can the SM Higgs boson be hiding? 29
3.1 Theoretical bounds on the Higgs mass . . . . . . . . . . . . . . . . . . . 29
3.2 Experimental bounds on the Higgs mass . . . . . . . . . . . . . . . . . . 36
4 Higgs production at the Tevatron 43
4.1 The main production channels . . . . . . . . . . . . . . . . . . . . . . . 47
4.2 Scale variation and higher order terms . . . . . . . . . . . . . . . . . . . 58
4.3 The PDF puzzle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.4 EFT and its uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.5 Combination and total uncertainty . . . . . . . . . . . . . . . . . . . . . 81
4.6 Summary and outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
4.A Appendix: analytical expressions for µR–NNLO terms in gg → H . . . . 90
5 Higgs production at the LHC 92
5.1 The main channel at the lHC . . . . . . . . . . . . . . . . . . . . . . . . 93
5.2 The scale uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
5.3 The PDF+αS uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . 98
5.4 EFT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
5.5 Total uncertainy at 7 TeV . . . . . . . . . . . . . . . . . . . . . . . . . . 106
5.6 LHC results at different center–of–mass energies . . . . . . . . . . . . . 110
5.7 Summary and outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
6 Higgs decay and the implications for Higgs searches 116
6.1 Important channels for experimental search . . . . . . . . . . . . . . . . 116
6.2 Uncertainties on the branching ratios . . . . . . . . . . . . . . . . . . . . 121
6.3 Combination at the Tevatron . . . . . . . . . . . . . . . . . . . . . . . . 125
6.4 Combination at the LHC . . . . . . . . . . . . . . . . . . . . . . . . . . 128
6.5 The Tevatron exclusion limit . . . . . . . . . . . . . . . . . . . . . . . . 129
6.6 Summary of the results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
III The Minimal Supersymmetric extension of the Standard
Model 137
7 Why Supersymmetry is appealing 138
7.1 The hierarchy problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
7.2 Coupling constants convergence at high energies . . . . . . . . . . . . . 140
7.3 SUSY and Dark Matter searches . . . . . . . . . . . . . . . . . . . . . . 142
8 Formal SUSY aspects 145
8.1 SUSY Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
8.2 Superspace, superfields and superpotential . . . . . . . . . . . . . . . . . 149
8.3 Soft SUSY breaking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
9 The Minimal Supersymmetric Standard Model 156
9.1 Fields content: Higgs and SUSY sectors of the MSSM . . . . . . . . . . 156
9.2 The Higgs sector and the number of Higgs doublets . . . . . . . . . . . . 161
9.3 The MSSM is not the end of the story . . . . . . . . . . . . . . . . . . . 168
IV MSSM Higgs(es) production and decay 171
10 The MSSM Higgs sector at hadron colliders 173
10.1 SUSY corrections to Higgs couplings to fermions . . . . . . . . . . . . . 173
10.2 Model independence of the results . . . . . . . . . . . . . . . . . . . . . 177
11 MSSM Higgs production at the Tevatron 180
11.1 Gluon–gluon fusion and bottom quarks fusion . . . . . . . . . . . . . . . 181
11.2 The scale uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
11.3 The PDF and αS uncertainties . . . . . . . . . . . . . . . . . . . . . . . 186
11.4 The b–quark mass uncertainty . . . . . . . . . . . . . . . . . . . . . . . 187
11.5 Summary and combination of the different sources of uncertainties . . . . 190
12 MSSM Higgs production at the LHC 192
12.1 Gluon–gluon fusion and bottom quarks fusion channels . . . . . . . . . . 192
12.2 The scale uncertainty at the lHC . . . . . . . . . . . . . . . . . . . . . . 194
12.3 The PDF and αS uncertainties at the lHC . . . . . . . . . . . . . . . . . 195
12.4 The b–quark mass issue . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
12.5 Combination and total uncertainty . . . . . . . . . . . . . . . . . . . . . 198
12.6 The case of the charged Higgs production in association with top quark
at the LHC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
13 Higgs→ τ τ channel and limits on the MSSM parameter space 209
13.1 The main MSSM Higgs branching ratios . . . . . . . . . . . . . . . . . . 209
13.2 Combination of production cross section and Higgs→ τ τ decay . . . . . 212
13.3 Impact of the theoretical uncertainties on the limits on the MSSM parameter space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
13.4 Consequences on the SM H → τ τ search at the LHC . . . . . . . . . . . 224
13.5 Summary and outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226
V Perspectives 229
14 Exclusive study of the gluon–gluon fusion channel 230
14.1 Exclusive SM Higgs production . . . . . . . . . . . . . . . . . . . . . . . 231
14.2 SM Backgrounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234
Conclusion 236
A Appendix : Synopsis 240
A.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240
A.2 Production et d´esint´egration du boson de Higgs du Mod`ele Standard . . 244
A.3 Le Mod`ele Standard Supersym´etrique Minimal (MSSM) . . . . . . . . . . 252
A.4 Production et d´esint´egration des bosons de Higgs supersym´etriques . . . 256
A.5 Perspectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261
References 263
List of Figures
1 Feynman diagrams at the Born level for the process e
+e
− → W+W− . . 17
2 Higgs potential in the case of a real scalar field, depending on the sign of
the mass term . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3 Higgs potential in the case of the SM . . . . . . . . . . . . . . . . . . . . 21
4 Tree–level SM Higgs boson couplings to gauge bosons and fermions . . . 25
5 One–loop SM Higgs boson couplings to the photons and the gluons . . . 25
6 Feynman diagrams up to one–loop correction for the Higgs self–coupling 34
7 Theoretical bounds on the Higgs mass in function of the scale of new
physics beyond the SM . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
8 Electroweak precision data . . . . . . . . . . . . . . . . . . . . . . . . . . 39
9 Indirect constraints on the SM Higgs boson mass . . . . . . . . . . . . . 40
10 95%CL exclusion limit on the SM Higgs boson mass at the LEP collider . 41
11 95%CL exclusion limit on the SM Higgs boson mass at the Tevatron collider 43
12 Feynman diagrams of the four main SM Higgs production channel . . . . 49
13 Some Feynman diagrams for NLO SM gg → H production . . . . . . . . 50
14 Some Feynman diagrams for NNLO SM gg → H production . . . . . . . 51
15 NLO QCD corrections to pp¯ → V
∗
. . . . . . . . . . . . . . . . . . . . . 55
16 NNLO QCD corrections to pp¯ → V
∗
. . . . . . . . . . . . . . . . . . . . 56
17 Total cross sections for Higgs production at the Tevatron in the four main
channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
18 Scale variation in the gg → H process at the Tevatron . . . . . . . . . . 62
19 Scale variation in the pp¯ → W H process at the Tevatron . . . . . . . . . 67
20 Comparison between different PDFs sets in gg → H at the Tevatron
using CTEQ/ABKM/MSTW PDF sets for 90%CL uncertainties and
MSTW/ABKM/HERA/JR for central predictions comparison . . . . . . 70
21 Comparison between MSTW PDFs set and ABKM PDFs set predictions
in gg → H channel at the Tevatron as for the uncertainties related to
PDF+∆αs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
22 The total PDF, PDF+∆expαs and PDF+∆exp+thαs uncertainties in gg →
H at the Tevatron using the MSTW PDFs set. . . . . . . . . . . . . . . . 75
23 Central predictions for NNLO pp¯ → W H at the Tevatron using the
MSTW, CTEQ and ABKM PDFs sets, together with their 90% CL PDF
uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
24 Comparison between MSTW PDFs set and ABKM PDFs set predictions
in pp¯ → W H channel at the Tevatron as for the uncertainties related to
PDF+∆αs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
25 b–loop uncertainty in gg → H at the Tevatron . . . . . . . . . . . . . . . 79
26 EW uncertainties in gg → H at the Tevatron . . . . . . . . . . . . . . . . 81
27 Production cross sections for gg → H at the Tevatron together with the
total theoretical uncertainties . . . . . . . . . . . . . . . . . . . . . . . . 85
28 Production cross sections for pp¯ → W H and pp¯ → ZH at the Tevatron
together with the total theoretical uncertainties . . . . . . . . . . . . . . 88
29 Total cross sections for SM Higgs production at the lHC . . . . . . . . . 95
30 Scale uncertainty at the lHC in gg → H at NNLO . . . . . . . . . . . . . 98
31 PDF and ∆exp,thαs uncertainties in gg → H at the lHC . . . . . . . . . . 99
32 Comparison between the predictions given by the four NNLO PDF sets
for gg → H at the lHC . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
33 Uncertainties due to EFT in the top quark and bottom quark loops of
gg → H at NNLO at the lHC . . . . . . . . . . . . . . . . . . . . . . . . 104
34 Total uncertainty due to the EFT approach in gg → H at NNLO at the
lHC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
35 Central prediction with its total uncertainty for gg → H at NNLO at the
lHC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
36 Central predictions for gg → H at NNLO at the lHC with √
s = 8, 9, 10
TeV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
37 Scale and total EFT uncertainties in gg → H at the LHC with √
s = 14
TeV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
38 PDF+∆exp,thαs uncertainties and the comparison between the 4 NNLO
PDF sets in gg → H at the LHC with √
s = 14 TeV . . . . . . . . . . . . 113
39 Central prediction and total uncertainty in gg → H at NNLO at the LHC
with √
s = 14 TeV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
40 SM Higgs decay channels on the interesting Higgs mass range . . . . . . 117
41 The Higgs decays branching ratios together with the total uncertainty
bands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
42 The production cross section times branching ratio for SM pp¯ → W H →
W b¯b and gg → H → W+W− at the Tevatron together with the total
uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
43 The production cross section times branching ratio for SM gg → H →
W+W− at the lHC together with the total uncertainty . . . . . . . . . . 129
44 The SM Higgs boson production cross section gg → H at the Tevatron
together with the total uncertainty using 4 different ways of adding the
theoretical uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
45 The CDF/D0 95%CL limit on the SM Higgs boson mass confronted to
our theoretical expectations in a naive approach. . . . . . . . . . . . . . . 132
46 The luminosity needed by the CDF experiment to recover their current
claimed sensitivity when compared to our theoretical expectations for the
uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
47 One–loop corrections to the Higgs boson mass within the SM . . . . . . . 139
48 One–loop corrections to gauge couplings . . . . . . . . . . . . . . . . . . 141
49 SU(3)c × SU(2)L × U(1)Y gauge couplings running from the weak scale
up to the GUT scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
50 Possible proton decay in SUSY theories without R–parity conservation . 143
51 The constrained NMSSM parameter space . . . . . . . . . . . . . . . . . 170
52 The impact of main one–loop SUSY corrections to the Φb
¯b coupling in
the MSSM at hadron colliders . . . . . . . . . . . . . . . . . . . . . . . . 178
53 Feynman diagrams for the bottom quark fusion process in the MSSM . . 184
54 The NLO gg → A and NNLO b
¯b→A cross sections at the Tevatron with
tan β = 30 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
55 Scale uncertainty in the gg → Φ and b
¯b → Φ processes at the Tevatron . 186
56 PDF+∆exp,thαs uncertainty in the gg → Φ and bb → Φ processes at the
Tevatron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
57 The comparison between the MSTW, ABKM and JR prediction for the
NNLO bottom quark fusion cross section at the Tevatron . . . . . . . . . 187
58 Specific b–quark mass uncertainties in the gg → Φ and b
¯b → Φ processes
at the Tevatron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
59 The gg → A and b
¯b → A cross sections at the Tevatron together with
their different sources of uncertainty and the total uncertainties . . . . . 191
60 The gg → Φ and b
¯b → Φ at the LHC for different center–of–mass energies 194
61 Scale uncertainty in the gg → Φ and b
¯b → Φ processes at the lHC . . . . 195
62 PDF+∆αs uncertainty in the gg → Φ and bb → Φ processes at the lHC . 196
63 Comparison between the different PDFs sets in the gg → Φ and b
¯b → Φ
processes at the lHC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
64 Specific b–quark mass uncertainties in the gg → Φ and b
¯b → Φ processes
at the lHC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
65 The gg → Φ and b
¯b → Φ cross sections at the lHC together with their
different sources of uncertainty and the total uncertainties . . . . . . . . 199
66 LO σ(gb → tL,RH−) cross section and polarization asymmetry at the lHC
in the MSSM in two benchmark scenarios as a function of tan β . . . . . 205
67 Scale and PDF dependence on top–charged Higgs asymmetry at the lHC 206
68 The impact of the NLO SUSY corrections on the top–charged Higgs asymmetry at the LHC with √
s = 14 TeV . . . . . . . . . . . . . . . . . . . . 208
69 CP–odd A boson production in the pp¯ → A → τ
+τ
− channel at the
Tevatron together with the total uncertainty . . . . . . . . . . . . . . . . 215
70 The total uncertainties on the MSSM Higgs production in the gg → Φ
and b
¯b → Φ channels at the lHC including the impact of the Φ → τ
+τ
−
branching fraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
71 CP–odd A boson production in the pp → A → τ
+τ
− channel at the lHC
together with the total uncertainty . . . . . . . . . . . . . . . . . . . . . 219
72 The 95%CL limits on the MSSM parameter space using our theoretical
uncertainties confronted to the Tevatron results . . . . . . . . . . . . . . 221
73 The 95%CL limits on the MSSM parameter space using our theoretical
uncertainties confronted to the lHC results . . . . . . . . . . . . . . . . . 222
74 Expectations at higher luminosity at the lHC for the 95%CL limits on
the MSSM parameter space using our theoretical calculation . . . . . . . 223
75 The MSSM Higgs analysis applied to the SM H → τ
+τ
− search channel
compared to the ATLAS H → γγ limits . . . . . . . . . . . . . . . . . . 226
76 Potentiel de Higgs dans le cas d’un champ scalaire r´eel selon le signe du
terme de masse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242
77 Incertitude d’´echelle dans le processus gg → H au Tevatron . . . . . . . . 246
78 Comparaison entre les pr´edictions des diff´erentes collaborations de PDFs
pour le canal gg → H au NNLO en QCD . . . . . . . . . . . . . . . . . . 247
79 Incertitude PDF+∆αs dans les canaux de production gg → H et pp¯ →
HW au Tevatron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248
80 Sections efficaces de production inclusives des canaux gg → H et pp¯ →
HV au Tevatron ainsi que les incertitudes th´eoriques totales associ´ees . . 249
81 Sections efficaces de production inclusives du canal gg → H au LHC `a 7
et 14 TeV ainsi que les incertitudes th´eoriques totales associ´ees . . . . . . 250
82 Luminosit´e n´ecessaire `a l’exp´erience CDF afin qu’elle obtienne la sensibilit´e qu’elle pr´etend avoir actuellement, en tenant compte de nos incertitudes th´eoriques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251
83 Les sections efficaces de production inclusives du boson de Higgs A du
MSSM au Tevatron dans les canaux gg → A et b
¯b → A accompagn´ees
des incertitudes th´eoriques . . . . . . . . . . . . . . . . . . . . . . . . . . 258
84 Les sections efficaces de production inclusives du boson de Higgs Φ du
MSSM au lHC dans les canaux gg → Φ et b
¯b → Φ accompagn´ees des
incertitudes th´eoriques . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258
85 Les limites a 95% de niveau de confiance sur l’espace des parametres du
MSSM en tenant compte de nos incertitudes th´eoriques confront´ees aux
donn´ees du Tevatron et du lHC . . . . . . . . . . . . . . . . . . . . . . . 260
86 L’analyse MSSM des bosons de Higgs neutres appliqu´ee au canal de
recherche H → τ
+τ
− du Mod`ele Standard, compar´ee aux r´esultats
obtenus par ATLAS dans le canal H → γγ . . . . . . . . . . . . . . . . . 261

List of Tables
1 The fermionic content of the Standard Model . . . . . . . . . . . . . . . 13
2 The NNLO total Higgs production cross sections in the gg → H process
at the Tevatron together with the detailed theoretical uncertainties as
well as the total uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . 84
3 The NNLO total cross section for Higgs–strahlung processes at the Tevatron together with the detailed theoretical uncertainties and the total
uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
4 The total Higgs production cross sections in the four main production
channels at the lHC with √
s = 7 TeV . . . . . . . . . . . . . . . . . . . . 96
5 The NNLO total Higgs production cross sections in the gg → H process
at the lHC with √
s = 7 TeV together with the associated theoretical
uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
6 The NNLO total production cross section in the gg → H channel at the
LHC with √
s = 8, 9, 10 TeV . . . . . . . . . . . . . . . . . . . . . . . . . 112
7 The NNLO total Higgs production cross section in the gg → H process
at the LHC with √
s = 14 TeV together with the associated theoretical
uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
8 The SM Higgs decay branching ratios in the b
¯b and WW modes for representatives Higgs masses together with the different sources of uncertainties as well as the total uncertainty. . . . . . . . . . . . . . . . . . . . . . 124
9 The SM Higgs decay branching ratios together with the total uncertainty
for the most important decay channels . . . . . . . . . . . . . . . . . . . 126
10 The superparticles and Higgs content of the MSSM before EWSB . . . . 157
11 The neutralinos, charginos and Higgs content of the MSSM after EWSB . 158
12 The main MSSM CP–odd like Higgs bosons decay branching fractions
together with their uncertainties . . . . . . . . . . . . . . . . . . . . . . . 211
13 The central predictions in the MSSM gg → Φ channel at the Tevatron
together with the detailed uncertainties and the impact of the Φ → τ
+τ
−
branching fraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
14 The central predictions in the MSSM b
¯b → Φ channel at the Tevatron
together with the detailed uncertainties and the impact of the Φ → τ
+τ
−
branching fraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
15 The central predictions in the MSSM gg → Φ channel at the lHC together with the detailed uncertainties and the impact of the Φ → τ
+τ
−
branching fraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
16 The central predictions in the MSSM b
¯b → Φ channel at the lHC together with the detailed uncertainties and the impact of the Φ → τ
+τ
−
branching fraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218
17 CMS cuts used in the SM exclusive study gg → H → WW → νν at
the lHC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231
18 Results for the gg → H+jet cross sections with MH = 160 GeV at the
lHC with HNNLO and MCFM programs . . . . . . . . . . . . . . . . . . 232
19 Uncertainties on the exclusive production gg → H → WW → νν with
MH = 160 GeV at the lHC with HNNLO program . . . . . . . . . . . . . . 233
20 Uncertainties on the exclusive production gg → H → WW → νν with
MH = 160 GeV at the lHC with MCFM program . . . . . . . . . . . . . . . 234
21 Central values and uncertainties for the H → WW SM backgrounds
exclusive cross sections at the lHC . . . . . . . . . . . . . . . . . . . . . . 235
22 Contenu fermionique du Mod`ele Standard . . . . . . . . . . . . . . . . . 241
23 Les superparticules et champs de Higgs du MSSM avant brisure ´electrofaible254
Liste des publications
Cette page donne la liste de tous mes articles concernant le travail r´ealis´e depuis 3 ans.
This page lists all the papers that I have written for 3 years in the context of my PhD
work.
Articles publi´es (published papers) :
Predictions for Higgs production at the Tevatron and the associated uncertainties,
J. B. et A. Djouadi, JHEP 10 (2010) 064;
Higgs production at the lHC, J. B. et A. Djouadi, JHEP 03 (2011) 055;
The Tevatron Higgs exclusion limits and theoretical uncertainties: A Critical appraisal, J. B., A. Djouadi, S. Ferrag et R. M. Godbole, Phys.Lett.B699 (2011) 368-371;
erratum Phys.Lett.B702 (2011) 105-106;
Revisiting the constraints on the Supersymmetric Higgs sector at the Tevatron, J. B.
et A. Djouadi, Phys.Lett.B699 (2011) 372-376;
The left-right asymmetry of the top quarks in associated top–charged Higgs bosons at
the LHC as a probe of the parameter tan β, J.B et al., Phys.Lett.B705 (2011) 212-216.
Articles non–publi´es (unpublished papers) :
Implications of the ATLAS and CMS searches in the channel pp → Higgs → τ
+τ
−
for the MSSM and SM Higgs bosons, J. B. et A. Djouadi, arXiv:1103.6247 [hep-ph]
(soumis `a Phys.Lett.B);
Clarifications on the impact of theoretical uncertainties on the Tevatron Higgs exclusion limits, J. B., A. Djouadi et R. M. Godbole, arXiv:1107.0281 [hep-ph].
Rapport de collaboration (review collaboration report) :
Handbook of LHC Higgs Cross Sections: 1. Inclusive Observables, LHC Higgs Cross
Section Working Group, S. Dittmaier et al., arXiv:1101:0593 [hep-ph].
Comptes–rendus de conf´erences (proceedings) :
Higgs production at the Tevatron: Predictions and uncertainties, J. B., ICHEP 2010,
Paris (France), PoS ICHEP2010 (2010) 048;
The Supersymmetric Higgs bounds at the Tevatron and the LHC, J.B., XLVIe
Rencontres de Moriond, EW interactions and unified theory, La Thuile (Italie),
arXiv:1105.1085 [hep-ph].

Cette these est d´edi´eea mon pere eta mes deux grand-p`eres, disparus bien
trop tˆot.

(From http://abstrusegoose.com/118)
Et maintenant, apprends les v´erit´es qui me restent `a te d´ecouvrir,
Tu vas entendre de plus claires r´ev´elations.
Je n’ignore pas l’obscurit´e de mon sujet ;
Lucr`ece, dans De rerum natura, v. 902-943 livre I
Les amoureux fervents et les savants aust`eres
Aiment ´egalement, dans leur mˆure saison,
Les chats puissants et doux, orgueil de la maison,
Qui comme eux sont frileux et comme eux s´edentaires.
Charles Baudelaire, dans Les Fleurs du Mal

Introduction 1
Introduction
In this thesis, we wish to present some predictions for the Higgs boson(s) study at the
two largest hadron colliders currently in activity: the Fermilab Tevatron collider and
the CERN Large Hadron Collider (LHC). Our focus will be on the inclusive production
cross sections and the decay branching fractions, first in the Standard Model which in
itself is the topic of part I and then in its minimal supersymmetric extension which is
the topic of part III.
The study of the fundamental mechanisms of Nature at the elementary level has a
long story and has known many milestones in the past sixty years. Physicists have built
a theory, nowadays known as the Standard Model, to describe the elementary particles
and their interactions, that are those of the strong, weak and electromagnetic, the two
last being unified in a single electroweak interaction. It relies on the elegant concept
of gauge symmetry within a quantum field theory framework and has known many
experimental successes: despite decades of effort to surpass this model it is still the one
that describes accurately nearly all the known phenomena1
. One of its key concepts
is the spontaneous breakdown of electroweak symmetry: indeed in order to give mass
to the weak bosons that mediate the weak interaction, a scalar field is introduced in
the theory whose vacuum breaks the electroweak symmetry and gives mass to the weak
bosons. In fact it also gives masses to the fermions and one piece of this mechanism
remains to be discovered: the Higgs boson, the “Holy Grail” of the Standard Model. Its
discovery is one of the main goal of current high energy colliders.
It is then of utmost importance to give theoretical predictions for the production
cross sections and decay branching fractions of the Higgs boson at current colliders to
serve as a guideline for experiments. However, the hadronic colliders are known to be
very difficult experimental environments because of the huge hadronic, that is Quantum
ChromoDynamics (QCD), activity. This is also true on a theoretical side, which means
that an accurate description of all possible sources of theoretical uncertainties is needed:
this is precisely the main output of this thesis. We shall mention that in the very final
stage of this thesis new results have been presented in the HEP–EPS 2011 conference;
our work is to be read in the light of the results that were available before these newest
experimental output which will be briefly commented in the conclusion.
Part I is entirely devoted to a review of the Standard Model. In section 1 we will draw
a short history of the Standard Model and list its main milestones of the past sixty years,
followed by a description of its main concepts. We will go into more details about the
Higgs mechanism, which spontaneously breaks electroweak symmetry, in section 2: we
will review some reasons to believe that either the Higgs mechanism itself or something
which looks like the Higgs mechanism is needed, and then how the Higgs boson emerges
1We leave aside the neutrino mass issue.
2 Introduction
from the electroweak symmetry breaking and what are its couplings to fermions and
bosons of the Standard Model.
Part II is the core of the Standard Model study of this thesis. Indeed the Higgs
boson remains to be discovered and is one of the major research programs at current
high energy colliders. The old CERN Large Electron Positron (LEP) collider has put
some bounds on the possible value of the Higgs boson mass, which is above 114.4 GeV in
the Standard Model at 95%CL. We will review in section 3 the current experimental and
theoretical bounds on the Higgs mass. We then give our predictions for the Standard
Model Higgs boson inclusive production cross section at the Tevatron in the two main
production channels that are the gluon–gluon fusion and the Higgs–strahlung processes,
giving all the possible sources of theoretical uncertainties: the scale uncertainty viewed
as an estimation of the unknown higher–order terms in the perturbative calculation;
the parton distribution functions (PDFs) uncertainties related to the non–perturbative
QCD processes within the proton, and its related strong coupling constant issue; the
uncertainty coming from the use of an effective theory approach to simplify the hard
calculation in the gluon–gluon fusion process. We will specifically address the issue of
the combination of all the uncertainties in section 4.5. We will then move on to the
same study at the LHC, concentrating on its current run at a 7 TeV center–of–mass
energy that we will name as the lHC for littler Hadron Collider; we will still give some
predictions for the designed LHC at 14 TeV. We will finish this part II by the Higgs
boson decay branching fractions predictions in section 6, together with a detailed study
of the uncertainties that affect these predictions. It will be followed by the combination
of the production cross sections and decay branching fractions into a single prediction,
first at the Tevatron in section 6.3 and then at the lHC in section 6.4. We will then
study the impact of our uncertainties on the Tevatron Higgs searches in section 6.5 and
in particular put into question the Tevatron exclusion limits that are debated within the
community.
Even if the Standard Model is a nice theory with great experimental successes, it
suffers from some problems, both on the theoretical and experimental sides. It is known
for example that the Higgs boson mass is not predicted by the Standard Model, and
even not protected: higher order corrections in the perturbative calculation of the Higgs
boson mass have the tendency to drive the mass up to the highest acceptable scale of the
theory which means that we need a highly fine–tuning of the parameters to cancel such
driving. It is known as the naturalness problem of the Standard Model. They are several
ways to solve such a problem, and one of them is particularly elegant and relies on a new
symmetry between bosons and fermions: supersymmetry. This theoretical concept, born
in the 1970s, has many consequences when applied to the Standard Model of particle
physics and is actively searched at current high energy colliders. This will be the topic
of part III in which we will review some of the reasons that drive the theorists to go
Introduction 3
beyond the Standard Model and in particular what makes supersymmetry interesting
in this view in section 7, then move on to the description of the mathematical aspects
of supersymmetry in section 8. We will finish this part III by a very short review of
the minimal supersymmetric extension of the Standard Model, called the MSSM, in
section 9. We will in particular focus on the Higgs sector of the theory and show that
the MSSM needs two Higgs doublets to break the electroweak symmetry breaking and
has thus a rich Higgs sector as five Higgs boson instead of a single one are present in
the spectrum: two neutral CP–even, one CP–odd and two charged Higgs bosons.
After this review of supersymmetry and the MSSM we will reproduce in part IV the
same outlines that have been developed in part II in the Standard Model case. We will
first review the neutral Higgs sector at hadron colliders in section 10 and show that we
can have a quite model–independent description for our predictions in the sense that
they will hardly depend on most of the (huge) parameters of the MSSM but two of
them, the mass of the CP–odd Higgs boson A and the ratio tan β between the vacuum
expectation values of the two Higgs doublets. We will then give in section 11 our
theoretical predictions for the neutral Higgs bosons inclusive production cross section at
the Tevatron in the two main production channels that are the gluon–gluon fusion and
the bottom quark fusions, the bottom quark playing a very important role in the MSSM
at hadron colliders. We will reproduce the same study at the lHC in section 12 before
giving the implications of our study on the [MA,tan β] parameter space in section 13.
We will first give in this last section our predictions for the main MSSM decay branching
fractions and in particular the di–tau branching fraction that is of utmost importance
for experimental searches. We we will then compare our predictions together with their
uncertainties to the experimental results obtained at the Tevatron and at the lHC that
has now been running for more than a year at 7 TeV and given impressive results. We
will see that the theoretical uncertainties have a significant impact on the Tevatron
results, less severe at the lHC. We will finish section 13 by a very important outcome of
our work: the possibility of using the MSSM neutral Higgs bosons searches in the di–
tau channel for the Standard Model Higgs boson in the gluon–gluon fusion production
channel followed by the di–tau decay channel in the low Higgs boson mass range 115–140
GeV.
Finally, we will give an outlook and draw some conclusions in part V together with
some perspectives for future work. These rest on the next step on the road of the
experiments, that is an exclusive study of the Higgs bosons production channels. We
shall give some early results in section 14 on the Standard Model Higgs boson at the
lHC in the gg → H → WW → νν search channel together with an exclusive study of
the main Standard Model backgrounds. This is also the current roadmap of the Higgs
bosons theoretical community and this work is done in the framework of a collaboration
on this topic.

5
Part I
A brief review of the Standard
Model of particle physics
Summary
1 Symmetry principles and the zoology of the Standard Model 6
1.1 A brief history of the Standard Model . . . . . . . . . . . . . . . . . 6
1.2 Gauge symmetries, quarks and leptons . . . . . . . . . . . . . . . . 12
2 The Brout–Englert–Higgs mechanism 16
2.1 Why do we need the electroweak symmetry breaking? . . . . . . . . 16
2.1.1 The unitarity puzzle . . . . . . . . . . . . . . . . . . . . . . . 16
2.1.2 Masses and gauge invariance . . . . . . . . . . . . . . . . . . 18
2.2 The spontaneous electroweak symmetry breaking . . . . . . . . . . . 19
2.2.1 Weak bosons masses and electroweak breaking . . . . . . . . 20
2.2.2 SM Higgs boson couplings . . . . . . . . . . . . . . . . . . . 24
6 Symmetry principles and the zoology of the Standard Model
1 Symmetry principles and the zoology of the Standard Model
The Standard Model (SM) of particle physics is the current description of the fundamental constituents of our universe together with the interactions that occur between them.
The SM was born in its current form in the seventies, after nearly twenty years of many
experiments and theoretical reflexions on how to build a somewhat simple and elegant
model to describe accurately the experimental results on the one hand and to make powerful predictions in order to have a falsifiable theory on the other hand. Its frameworks
are relativistic quantum field theory and group theory to classify the different interactions. It also needs the key concept of spontaneous (electroweak) symmetry breaking in
order to account for the masses of the different fields in the theory, the (weak) bosons
as well as the matter fermions. Other reasons also push for such a theoretical concept
and will be presented in the next sections.
We will in this section present a short review of the major historical points in the
birth of the SM, and present its theoretical fundations. The focus on the electroweak
symmetry breaking, in particular its minimal realization through the Brout–Englert–
Higgs mechanism, will be discussed in the next section.
1.1 A brief history of the Standard Model
This subsection will sketch the different historical steps that have lead to the current
form of the theory that describes the elementary particles and their interactions among
each other, called the Standard Model (SM). This model has a very rich history over
more than fifty years of the XXth century, not to mention all the diverse and fruitful
efforts made before to attain this level of description of the elementary world. We will
only select some (of the) outstanding events, both from the theoretical and experimental
sides, to present the twisted path leading to the current Standard Model of particle
physics.
The birth of modern QED
The first attempt to decribe electromagnetic phenomena in the framework of special
relativity together with quantum mechanics can be traced back in the 1920s. In particular Dirac was the first to describe the quantization of the electromagnetic fields as
an ensemble of harmonic oscillators, and introduced the famous creation–annihilation
operators [1]. In 1932 came Fermi with a first description of quantum electrodynamics [2], but physicists were blocked by the infinite results that did arise in the calculations
beyond the first order in perturbation theory.
1.1 – A brief history of the Standard Model 7
Years after, the difficulty was solved by Bethe in 1947 [3] with the concept of renormalization, that is the true physical quantities are not the bare parameters of the theory,
and thus the infinite that arise are absorbed in the physical quantities, leaving finite results in the end. This leads to the modern Quantum ElectroDynamics (QED) with the
key concept of gauge symmetry and renormalization, that was formulated by Feynman,
Schwinger and Tomonaga [4–6] in the years 1950s and awarded by a Nobel prize in 1965.
This is the first quantum field theory available and has been the root of all the SM ideas
for the key concepts of gauge symmetry and renormalizability.
P violation and V − A weak theory
It was long considered in physics that the parity symmetry was conserved: if we
repeated an experiment with the experimental apparatus mirror reversed, the results
would be the same as for the initial set–up. This assessment is true for any experiment
involving electromagnetism or strong interaction, but that is not the case for weak
interaction.
It was first proposed by Yang and Lee in 1956 that the weak interaction might indeed
not respect P–symmetry [7]. This was observed in 1957 by Chien-Shiung Wu (“Madam
Wu”) in the beta desintegration of cobalt 60 atoms [8]. Yang and Lee were then awarded
the 1957 Nobel prize for their theoretical developments on this concept.
Up until that period, the weak interaction, that shapes the decay of unstable nucleii,
was described by the Fermi theory in which the fermions interact through a four–particles
vertex. The discovery of the P–violation lead to the construction of an effective V − A
theory where the tensor structure of the thory is correct and does respect the charge and
parity violations. This V − A theory was later on replaced by the electroweak theory,
see below.
The quark description
In the first half of the XXth century the pattern of elementary particles was simple: the
electron (and its antiparticle the positron, postulated by Dirac in 1931 and discovered
in 1932 by Anderson), the proton and the neutron were the only known elementary
particles at that time. The neutrino, first postulated by Pauli in its famous letter in
1930 to save the energy–momentum conservation in beta decay reactions2 was discovered
only in 1956.
Experimental particle physicists discovered numerous new particles (the “hadrons”)
in the 1950s and 1960s after the discovery of the pion in 1947, predicted by Yukawa in
1935, thus casting some doubts on the elementary nature both of the “older” particles
2The original name was “neutron” for neutral particle. Chadwick discovered in 1932 what would be
the neutron, thus Fermi proposed the name “neutrino” meaning “little neutral one” in italian.
8 Symmetry principles and the zoology of the Standard Model
such as the neutron and the proton and on the new zoo discovered. Gell–Man and Zweig
proposed in 1964 a model of constituant particles of these hadrons and mesons that
could explain the pattern seen by experimentalists, using only a limited number of new
constituant particles: the quarks [9,10]. They introduce the SU(3) flavor symmetry with
the three up, down and strange quarks. One year later the charm quark was proposed to
improve the description of weak interactions between quarks, and in 1969 deep inelastic
scattering experiments at the Stanford Linear Accelerator Center (SLAC) discovered
point–like objects within the proton [11], an experimental proof of the compositeness of
the hadrons. It is interesting to note that the term used for these new point–like objects
was “parton”, proposed by Feynman, as the community was not entirely convinced that
they were indeed the Gell–Mann’s quarks. Nowadays “parton” is still a word used in
particle physics to name the different constituants of the hadrons (the quarks, antiquarks
and gluons, the later being the bosons of the strong interaction).
The (nearly) final word on the quark model was given in 1974 when the J/Ψ meson
was discovered [12, 13] and thus proved the existence of the charm quark, which was
proposed by Glashow, Iliopoulos and Maiani in the GIM mechanism [14] in 1970 to explain the universality of weak interaction in the quark sector, preventing flavor changing
neutral currents. The heaviest quark, that is the top quark, was finally discovered in
1995 at the Fermilab Tevatron collider [15, 16].
CP violation and the concept of generation
To explain both the universality and the u ←→ d transitions in weak interactions,
Cabibbo introduced in 1963 what is known as the Cabibbo angle [17] and was used
to write in the mass eigenstates basis the weak eigenstate for the down quark d. A
year later, Cronin and his collaborators discovered that not only C and P symmetries
are broken by weak interactions, but also the combined CP symmetry [18], studing the
K0K
0
oscillations: the probability of oscillating from K0
state into K
0
state is different
from that of the K
0
→ K0
, indicating that T time reversal symmetry is violated. As
the combined CPT is assumed to be conserved, this means that CP is violated.
As mentioned a few lines above, the GIM mechanism introduced a fourth quark, the
charm quark c. It then restores universality in the weak coupling for the quarks, as we
have now two weak eigenstates
|d
0
i = cos θc|di + sin θc|si
|s
0
i = − sin θc|di + cos θc|si (1.1)
coupled to respectively the u quark and the c quark. We thus have two generations
in the quark sector, the first one is the (u, d) doublet and the second one is the (c, s)
1.1 – A brief history of the Standard Model 9
doublet. However, as explained in 1973 by Kobayashi and Maskawa extending the work
initiated by Cabibbo, this is not sufficient to explain the CP violation observed by the
1964 experiment. Only with three generations could be introduced some CP violating
effects through a phase angle, and thus extending the Cabbibo angle to what is known
as the Cabibbo–Kobayashi–Maskawa (CKM) matrix [19]. Kobayashi and Maskawa were
awarded the 2008 Nobel prize for this result3
.
Yang–Mills theory and spontaneous symmetry breaking
We have seen a few lines above that the Fermi theory describing the weak interactions
had been refined by the V − A picture to take into account the P violation. Still the
V − A theory was known to be an effective theory as the theory was not renormalizable
and did not allow for calculations beyond the first order in perturbation theory. The only
gauge theory that was available at that time was QED, an abelian gauge theory, which
obviously is not the right description of weak processes as it describes only light–matter
interactions.
The first step toward the solution was set–up in 1954, when Yang and Mills developed a formulation of non–abelian gauge theories [20] in order to provide (initially) an
explanation for the strong interaction at the hadron level (that we call nuclear interaction). Unfortunately the theory was not a success at first, as the gauge bosons must
remain massless to preserve the symmetry of the theory, thus meaning that the weak
interaction should be long–range; experimentally that is not the case.
The key result to solve this contradiction and then still use the elegant description of
gauge theory is given in 1964 by Brout, Englert, Higgs, Guralnik, Hagen and Kibble after
some important work on the concept of symmetry breaking from Nambu and Goldstone:
the spontaneously gauge symmetry breaking [21–24] described by the Brout–Englert–
Higgs mechanism. This will be presented in the following in details, but we can already
remind the reader that the most important result is that it allows for the use of a
Yang–Mills theory together with a description of massive gauge bosons for any gauge
theory.
Interlude: from nuclear force to strong interaction
Before arriving to the final electroweak description that constitutes the heart of the
SM, we recall the road leading to the description of the strong interaction between the
quarks.
As stated above, Yang–Mills theory in 1954 was the first attempt to describe the
interaction between the hadrons, that we call nuclear interaction, in a gauge formulation.
3Unfortunately the Nobel committee failed to recognize the important pionnering work from
Cabibbo.
10 Symmetry principles and the zoology of the Standard Model
After the introduction of the quark model by Gell–Mann in 1964 (see above) and the
discovery of the quarks in 1969 (see above), it has been proposed that the quarks must
have a new quantum charge, called color, to accomodate for the Pauli exclusion principle
within some baryons [25]. This was experimentally observed in the SLAC experiments
in 1969 which discovered point–like objects within the nucleon, as discussed earlier.
With the help of the discovery of asymptotic freedom [26, 27] in 1973 by Wilczek,
Gross and Politzer (who share the 2004 Nobel prize for this result), that states that at
very high energy quarks are free, and with a SU(3) gauge Yang–Mills theory, Quantum
ChromoDynamics (QCD) was firmly established in the 1970s as being the theory of
the strong interactions, with the gluons as the gauge bosons. Evidence of gluons was
discovered in three jet events at PETRA in 1979 [28], giving further credits to QCD.
The nuclear interaction between the hadrons is then a residual force originating from
the strong interaction between quarks (and gluons). However, as the strong coupling
is indeed very strong at large distance (that is the confinement), preventing from the
use of perturbation theory, an analytical description of the strong interaction within the
hadrons at low energies is still to be found. This problem is now studied within the
framework of lattice gauge theories which give spectacular results.
The weak neutral currents and the path to electroweak theory
As stated above it was known that the V − A theory for the weak interaction was
an effective theory, with difficulties calculating beyond the first order in perturbation
theory. With the advent of Yang–Mills theory and the Brout–Englert–Higgs mechanism,
describing the weak interaction with a gauge theory and in the same time allowing for
massive weak bosons as dictated by the experiments, the weak interaction being a short
distance interaction, it would be possible to account for a renormalizable description of
the weak interaction.
During the 1960s there were many attempts to carry on this roadmap, trying lots of
different gauge groups to account for the QED on the one hand, the weak interaction
on the other hand, as both interactions play a role for lepton particles such as the
electron. The gauge theory that did emerge was the SU(2) × U(1) model where the
weak and electromagnetic interactions are unified in a single gauge theory description4
,
with contributions notabely from Glashow [29], Salam [30] and Weinberg [31]. This
model together with the Brout–Englert–Higgs mechanism predicts in particular that
there should be a neutral weak boson Z
0
to be discovered and neutral currents.
4
It is actually not a complete unified theory as the algebra describing the electroweak interaction is a
product of two Lie algebras. Nevertheless as the decription of the weak and electromagnetic interactions
are intimely connected through the pattern of the electroweak symmetry breaking, see below, this can
be viewed as at least a partial unification.

[Charles]

Pourquoi restes-tu sur le forum? Tout le monde t’est hostile (et réciproquement) et tu ne supportes pas que l’on te pousse à bout.

[Demi Habile]

Charles: C’est parce que tout le monde m’est hostile que je me torche le cul avec vos commentaires sur mon comportement. Et si tu veux me faire croire que tu supporterais qu’on te pousse à bout, c’est que tu te racontes trop d’histoires mon petit bourgeois.

[maelstrom]

Qu’elle est la raison originelle qui te pousse a polluer le forum ?

[maelstrom]

moi je n’y comprend rien un coup c’est deleatur un coup c’est toi

[Charles]

Demi-habile : n’étant pas masochiste, si on me poussait à bout je ne resterais pas dans cet environnement, environnement que j’aurais déjà quitté depuis longtemps en constatant que je n’aimais personne et que c’était réciproque. Comment expliquer ton comportement paradoxal?

[Demi Habile]

Charles: Tu penses que ça se passe comment si je signale le forum à la CNIL en faisant remarquer que François ne veut pas supprimer mes messages comme la loi l’exige?

[Charles]

Je pense que tout le monde s’en branle.

[Demi Habile]

Charles: Je doute que la CNIL s’en branle mon mignon.

[Demi Habile]

Charles: Et mon grand, si tu t’en branles de tout ça, arrête de me casser les couilles avec tes réflexions à deux balles, poursuis ta vie de ton côté pendant que je vis la mienne de l’autre au lieu de me faire chier avec tes réflexions à deux balles.

[Charles]

Justement j’aimerais bien que tu vives ta vie ailleurs qu’ici plutôt que de jouer à la petite frappe de cour de recré qui ne s’assume pas.

[Demi Habile]

Charles: T’as le sentiment que j’en ai quelque chose à foutre de ce que je peux vouloir?

[Demi Habile]

Charles: T’as le sentiment que j’en ai quelque chose à foutre de ce que tu peux vouloir?

[Demi Habile]

Charles: T’as le sentiment qu’on en a quelque chose à foutre de ce que tu peux vouloir?

[Demi Habile]

Charles: T’as le sentiment que j’en ai quelque chose à foutre de ce que vous pouvez vouloir?

[Demi Habile]

and also the definition of the unpolarized cross section to write
X
spins
Z
|M12→34|
2
(2π)
4
δ
4
(p1 + p2 − p3 − p4)
d
3p3
(2π)
32E3
d
3p4
(2π)
32E4
=
4F g1g2 σ12→34, (1.31)
where F ≡ [(p1 · p2)
2 − m2
1m2
2
]
1/2
and the spin factors g1, g2 come from the average
over initial spins. This way, the collision term (1.29) is written in a more compact form
g1
Z
C[f1]
d
3p1
(2π)
3
= −
Z
σvMøl (dn1dn2 − dn
eq
1 dn
eq
2
), (1.32)
where σ =
P
(all f)
σ12→f is the total annihilation cross section summed over all the
possible final states and vMøl ≡
F
E1E2
. The so called Møller velocity, vMøl, is defined in
such a way that the product vMøln1n2 is invariant under Lorentz transformations and,
in terms of particle velocities ~v1 and ~v2, it is given by the expression
vMøl =
h
~v2
1 − ~v2
2

2
− |~v1 × ~v2|
2
i1/2
. (1.33)
Due to symmetry considerations, the distributions in kinetic equilibrium are proportional to those in chemical equilibrium, with a proportionality factor independent of
the momentum. Therefore, the collision term (1.32), both before and after decoupling,
can be written in the form
g1
Z
C[f1]
d
3p1
(2π)
3
= −hσvMøli(n1n2 − n
eq
1 n
eq
2
), (1.34)
where the thermal averaged total annihilation cross section times the Møller velocity
has been defined by the expression
hσvMøli =
R
σvMøldn
eq
1 dn
eq
2
R
dn
eq
1 dn
eq
2
. (1.35)
We will come back to the thermal averaged cross section in the next subsection.
We are, now, able to write the full integrated Boltzmann equation, using the expressions (1.28), (1.34) that we have derived for the Liouville and the collision term,
respectively. In the simplified but interesting case of identical particles 1 and 2, the
Boltzmann equation is, finally, written as
n˙ + 3Hn = −hσvMøli(n
2 − n
2
eq). (1.36)
18 Dark Matter
However, instead of using n, it is more convenient to take the expansion of the universe
into account and calculate the number density per comoving volume Y , which can be
defined as the ratio of the number and entropy densities: Y ≡ n/s. The total entropy
density S = R3
s (R is the scale factor) remains constant, hence we can obtain a
differential equation for Y by dividing (1.36) by S. Before we write the final form
of the Boltzmann equation that it is used for the relic density calculations, we have
to change the variable that parametrizes the comoving density. In practice, the time
variable t is not convenient and the temperature of the Universe (actually the photon
temperature, since the photons were the last particles that went out of equilibrium) is
used instead. However, it proves even more useful to use as time variable the quantity
defined by x ≡ m/T with m the DM mass, so that Eq. (1.36) transforms into
dY
dx
=
1
3H
ds
dx
hσvMøli

Y
2 − Y
2
eq
. (1.37)
Last, using the Hubble parameter (1.2) for a radiation dominated Universe and the
expressions (1.20), (1.21) for the energy and entropy density, the Boltzmann equation
is written in its final form
dY
dx
= −
r
45GN
π
g
1/2
∗ m
x
2
hσvMøli

Y
2 − Y
2
eq
, (1.38)
where the effective degrees of freedom g
1/2
∗ have been defined by
g
1/2
∗ ≡
heff
g
1/2
eff

1 +
1
3
T
heff
dheff
dT

. (1.39)
The equilibrium density per comoving volume Yeq ≡ neq/s can be expressed as
Yeq(x) = 45g
4π
4
x
2K2(x)
heff(m/x)
, (1.40)
with K2 the modified Bessel function of second kind.
1.4.3 Thermal average of the annihilation cross section
We are going to derive a simple formula that one can use to calculate the thermal
average of the cross section times velocity, based again on the analysis of [38]. We will
use the assumption that equilibrium functions follow the Maxwell-Boltzmann distribution, instead of the actual Bose-Einstein or Fermi-Dirac. This is a well established
assumption if the freeze out occurs after T ≃ m/3 or for x >∼ 3, which is actually the
case for WIMPs. Under this assumption, the expression (1.35) gives, in the cosmic
comoving frame,
hσvMøli =
R
vMøle
−E1/T e
−E2/T d
3p1d
3p2
R
e
−E1/T e
−E2/T d
3p1d
3p2
. (1.4
1.4.3 Thermal average of the annihilation cross section 19
The volume element can be written as d3p1d
3p2 = 4πp1dE14πp2dE2
1
2
cos θ, with θ the
angle between ~p1 and ~p2. After changing the integration variables to E+, E−, s given
by
E+ = E1 + E2, E− = E1 − E2, s = 2m2 + 2E1E2 − 2p1p2 cos θ, (1.42)
(with s = −(p1 − p2)
2 one of the Mandelstam variables,) the volume element becomes
d
3p1d
3p2 = 2π
2E1E2dE+dE−ds and the initial integration region
{E1 > m, E2 > m, | cos θ| ≤ 1i
transforms into
|E−| ≤
1 −
4m2
s
1/2
(E
2
+ − s)
1/2
, E+ ≥
√
s, s ≥ 4m2
. (1.43)
After some algebraic calculations, it can be found that the quantity hσvMøliE1E2
depends only on s, specifically vMølE1E2 =
1
2
p
s(s − 4m2
). Hence, the numerator of the expression (1.41), which after changing the integration variables reads
2π
2
R
dE+
R
dE−
R
dsσvMølE1E2e
−E+/T , can be written, eventually, as
Z
vMøle
−E1/T e
−E2/T = 2π
2
Z ∞
4m2
dsσ(s − 4m2
)
Z
dE+e
−E+/T (E
2
+ − s)
1/2
. (1.44)
The integral over E+ can be written with the help of the modified Bessel function of
the first kind K1 as √
s T K1(
√
s/T). The denominator of (1.41) can be treated in a
similar way, so that the thermal average is, finally, given by the expression
hσvMøli =
1
8m4TK2
2
(x)
Z ∞
4m2
ds σ(s)(s − 4m2
)
√
s K1(
√
s/T). (1.45)
Eqs. (1.38)–(1.40) along with this last Eq. (1.45) are all we need in order to calculate
the relic density of a WIMP, if its total annihilation cross section in terms of the
Mandelstam variable s is known.
In many cases, in order to avoid the numerical integration in Eq. (1.45), an approximation for hσvMøli can be used. The thermal average is expanded in powers of x
−1
(or, equivalently, in powers of the squared WIMP velocity):
hσvMøli = a + bx−1 + . . . . (1.46)
(The coefficient a corresponds to the s-wave contribution to the cross section, the
coefficient b to the p-wave contribution, and so on.) This partial wave expansion gives
a quite good approximation, provided there are no s-channel resonances and thresholds
for the final states [39].
In [40], it was shown that, after expanding the integrands of Eq. (1.41) in powers
of x
−1
, all the integrations can be performed analytically. As we saw, the expression
20 Dark Matter
vMølE1E2 depends on momenta only through s. Therefore, one can form the Lorentz
invariant quantity
w(s) ≡ σ(s)vMølE1E2 =
1
2
σ(s)
p
s(s − 4m2
). (1.47)
The integration involves the Taylor expansion of this quantity w around s/4m2 = 1
and the general formula for the partial wave expansion of the thermal average is [40]
hσvMøli =
1
m2

w −
3
2
(2w − w
′
)x
−1 +
3
8
(16w − 8w
′ + 5w
′′)x
−2
−
5
16
(30w − 15w
′ + 3w
′′ − 7x
′′′)x
−3 + O(x
−4
)

s/4m2=1
, (1.48)
where primes denote derivatives with respect to s/4m2 and all quantities have to be
evaluated at s = 4m2
.
1.5 Direct Detection of DM
Since the beginning of 1980s, it has been realized that besides the numerous facts showing evidence for the existence of these new dark particles, it is also possible to detect
them directly. Already in 1985, two pioneering articles [41, 42] appeared, describing
the detection methods for WIMPs. Since WIMPs are expected to cluster gravitationally together with ordinary stars in the Milky Way halo, they would pass also through
Earth and, in principle, they can be detected through scattering with the nuclei in a
detector’s material. In practice, one has to measure the recoil energy deposited by this
scattering.
However, although one can deduce from rotation curves that DM dominates the
dark halo in the outer parts of our galaxy, it is not so obvious from direct measurements
whether there is any substantial amount of DM inside the solar radius R0 ≃ 8 kpc.
Using indirect methods (involving the determination of the gravitational potential,
through the measuring of the kinematics of stars, both near the mid-plane of the
galactic disk and at heights several times the disk thickness), it is almost certain
that the DM is also present in the solar system, with a local density ρ0 = (0.3 ±
0.1) GeV cm−3
[43].
This value for the local density implies that for a WIMP mass of order ∼ 100 GeV,
the local number density is n0 ∼ 10−3
cm−3
. It is also expected that the WIMPs
velocity is similar to the velocity with which the Sun orbits around the galactic center
(v0 ≃ 220 km s−1
), since they are both moving under the same gravitational potential.
These two quantities allow to estimate the order of magnitude of the incident flux
of WIMPs on the Earth: J0 = n0v0 ∼ 105
cm−2
s
−1
. This value is manifestly large,
but the very weak interactions of the DM particles with ordinary matter makes their
detection a difficult, although in principle feasible, task. In order to compensate for
the very low WIMP-nucleus scattering cross section, very large detectors are required.
1.5.1 Elastic scattering event rate 21
1.5.1 Elastic scattering event rate
In the following, we will confine ourselves to the elastic scattering with nuclei. Although
inelastic scattering of WIMPs off nuclei in a detector or off orbital electrons producing
an excited state is possible, the event rate of these processes is quite suppressed. In
contrast, during an elastic scattering the nucleus recoils as a whole.
The direct detection experiments measure the number of events per day and per
kilogram of the detector material, as a function of the amount of energy Q deposited
in the detector. This event rate would be given by R = nWIMP nnuclei σv in a simplified
model with WIMPs moving with a constant velocity v. The number density of WIMPs
is nWIMP = ρ0/mX and the number density of nuclei is just the ratio of the detector’s
mass over the nuclear mass mN .
For accurate calculations, one should take into account that the WIMPs move in the
halo not with a uniform velocity, but rather following a velocity distribution f(v). The
Earth’s motion in the solar system should be included into this distribution function.
The scattering cross section σ also depends on the velocity. Actually, the cross section
can be parametrized by a nuclear form factor F(Q) as
dσ =
σ
4m2
r
v
2
F
2
(Q)d|~q|
2
, (1.49)
where |~q|
2 = 2m2
r
v
2
(1 − cos θ) is the momentum transferred during the scattering,
mr =
mXmN
mX+mN
is the reduced mass of the WIMP – nucleus system and θ is the scattering
angle in the center of momentum frame. Therefore, one can write a general expression
for the differential event rate per unit detector mass as
dR =
ρ0
mX
1
mN
σF2
(Q)d|~q|
2
4m2
r
v
2
vf(v)dv. (1.50)
The energy deposited in the detector (transferred to the nucleus through one elastic
scattering) is
Q =
|~q|
2
2mN
=
m2
r
v
2
mN
(1 − cos θ). (1.51)
Therefore, the differential event rate over deposited energy can be written, using the
equations (1.50) and (1.51), as
dR
dQ
=
σρ0
√
πv0mXm2
r
F
2
(Q)T(Q), (1.52)
where, following [37], we have defined the dimensionless quantity T(Q) as
T(Q) ≡
√
π
2
v0
Z ∞
vmin
f(v)
v
dv, (1.53)
with the minimum velocity given by vmin =
qQmN
2m2
r
, obtained by Eq. (1.51). Finally,
the event rate R can be calculated by integrating (1.52) over the energy
R =
Z ∞
ET
dR
dQ
dQ. (1.54)
22 Dark Matter
The integration is performed for energies larger than the threshold energy ET of the
detector, below which it is insensitive to WIMP-nucleus recoils.
Using Eqs. (1.54) and (1.52), one can derive the scattering cross section from the
event rate. The experimental collaborations prefer to give their results already in terms
of the scattering cross section as a function of the WIMP mass. To be more precise,
the WIMP-nucleus total cross section consists of two parts: the spin-dependent (SD)
cross section and the spin-independent (SI) one. The former comes from axial current
couplings, whereas the latter comes from scalar-scalar and vector-vector couplings.
The SD cross section is much suppressed compared to the SI one in the case of heavy
nuclei targets and it vanishes if the nucleus contains an even number of nucleons, since
in this case the total nuclear spin is zero.
We see that two uncertainties enter the above calculation: the exact value of the
local density ρ0 and the exact form of the velocity distribution f(v). To these, one
has to include one more. The cross section σ that appears in the previous expressions
concerns the WIMP-nucleon cross section. The couplings of a WIMP with the various
quarks that constitute the nucleon are not the same and the WIMP-nucleon cross
section depends strongly on the exact quark content of the nucleon. To be more
precise, the largest uncertainty lies on the strange content of the nucleon, but we shall
return to this point when we will calculate the cross section in a specific particle theory,
the Next-to-Minimal Supersymmetric Standard Model, in Sec. 3.5.1.
1.5.2 Experimental status
The situation of the experimental results from direct DM searches is a bit confusing. The null observations in most of the experiments led them to set upper limits
on the WIMP-nucleon cross section. These bounds are quite stringent for the spinindependent cross section7
, especially in the regime of WIMP masses of the order of
100 GeV. However, some collaborations have already reported possible DM signals,
mainly in the low mass regime. The preferred regions of these experiments do not
coincide, while some of them have been already excluded by other experiments. The
present picture, for WIMP masses ranging from 5 to 1000 GeV, is summarized in Fig.
1.5, 1.6.
Fig. 1.5 mainly presents upper bounds coming from XENON100 [44]. XENON100
[46] is an experiment located at the Gran Sasso underground laboratory in Italy. It
contains in total 165 kg of liquid Xenon, with 65 kg acting as target mass and the
rest shielding the detector from background radiation. For these upper limits, 225
live days of data were used. The minimum value for the predicted upper bounds on
the cross section is 2 · 10−45 cm2
for WIMP mass ∼ 55 GeV (at 90% confidence level),
almost one order of magnitude lower than the previously released limits [47] by the
same collaboration, using 100 live days of data.
The stringent upper bounds up-to-date (at least for WIMP mass larger than about
7 GeV) come from the first results of the LUX experiment (see Fig. 1.6), after the first
7For the spin-dependent scattering, the exclusion limits are quite relaxed. Hence, we will focus on
the SI cross sections.
1.5.2 Experimental status 23
Figure 1.5: The XENON100 exclusion limit (thick blue line), along with the expected
sensitivity in green (1σ) and yellow (2σ) band. Other upper bounds are also shown as
well as detection claims. From [44].
85.3 live-days of its operation [45]. LUX [53] is a detector containing liquid Xenon, as
XENON100, but in larger quantity, with total mass 370 kg. Its operation started on
April 2013 with a goal to clearly detect or exclude WIMPs with a spin independent
cross section ∼ 2 · 10−46 cm2
.
In Fig. 1.5, except of the XENON100 bounds and other experimental limits on larger
WIMP-nucleon cross section, some detection claims also appear. These come from
DAMA [48,49], CoGeNT [50] and CRESST-II [51] experiments. The first positive result
came from DAMA [52], back in 2000. Since then, the experiment has accumulated 1.17
ton-yr of data over 13 years of operation. DAMA consists of 250 kg of radio pure NaI
scintillator and looks for the annual modulation of the WIMP flux in order to reduce
the influence of the background.
The annual modulation of the DM flux (see [54] for a recent review) is due to the
Earth’s orbital motion relative to the rotation of the galactic disk. The galactic disk
rotation through an essentially non-rotating DM halo, creates an effective DM wind in
the solar frame. During the earth’s heliocentric orbit, this wind reaches a maximum
when the Earth is moving fastest in the direction of the disk rotation (this happens
in the beginning of June) and a minimum when it is moving fastest in the opposite
direction (beginning of December).
DAMA claims an 8.9σ annual modulation with a minimum flux on May 26±7 days,
consistent with the expectation. Since the detector’s target consists of two different
nuclei and the experiment cannot distinguish between sodium and iodine recoils, there
24 Dark Matter
Figure 1.6: The LUX 90% confidence exclusion limit (blue line) with the 1σ range
(shaded area). The XENON100 upper bound is represented by the red line. The inset
shows also preferred regions by CoGeNT (shaded light red), CDMS II silicon detector
(shaded green), CRESST II (shaded yellow) and DAMA (shaded gray). From [45].
is no model independent way to determine the exact region in the cross section versus
WIMP mass plane to which the observed modulation corresponds. However, one can
assume two cases: one that the WIMP scattering off the sodium nucleus dominates the
recoil energy and the other with the iodine recoils dominating. The former corresponds
[55] to a light WIMP (∼ 10 GeV) and quite large scattering cross section and the latter
to a heavier WIMP (∼ 50 to 100 GeV) with smaller cross section (see Fig. 1.5).
The positive result of DAMA was followed many years later by the ones of CoGeNT
and CRESST-II, and more recently by the silicon detector of CDMS [56] (Fig. 1.7).
The discrepancy of the results raised a lot of debates among the experiments (for
example, [64–67]) and by some the positive results are regarded as controversial. On
the other hand, it also raised an effort to find a physical explanation behind this
inconsistency (see, for example, [68–71]).
1.6 Indirect Methods for DM Detection
The same annihilation processes that determined the DM relic abundance in the early
Universe also occur today in galactic regions where the DM concentration is higher.
This fact rises the possibility of detecting potential WIMP pair annihilations indirectly
through their imprints on the cosmic rays. Therefore, the indirect DM searches aim
at the detection of an excess over the known astrophysical background of charged
particles, photons or neutrinos.
Charged particles – electrons, protons and their antiparticles – may originate from
direct products (pair of SM particles) of WIMP annihilations, after their decay and
1.6 Indirect Methods for DM Detection 25
Figure 1.7: The blue contours represent preferred regions for a possible signal at 68%
and 90% C.L. using the silicon detector of CMDS [56]. The blue dotted line represents
the upper limit obtained by the same analysis and the blue solid line is the combined
limit with the silicon CDMS data set reported in [57]. Other limits also appear:
from the CMDS standard germanium detector (light and dark red dashed line, for
standard [58] and low threshold analysis [59], respectively), EDELWEISS [60] (dashed
orange), XENON10 [61] (dash-dotted green) and XENON100 [44] (long-dash-dotted
green). The filled regions identify possible signal regions associated with data from
CoGeNT [62] (dashed yellow, 90% C.L.), DAMA [49,55] (dotted tan, 99.7% C.L.) and
CRESST-II [51, 63] (dash-dotted pink, 95.45% C.L.) experiments. Taken from [56].
through the process of showering and hadronization. Although the exact shape of the
resulting spectrum would depend on the specific process, it is expected to show a steep
cutoff at the WIMP mass. Once produced in the DM halo, the charged particles have
to travel to the point of detection through the turbulent galactic field, which will cause
diffusion. Apart from that, a lot of processes disturb the propagation of the charged
particles, such as bremsstrahlung, inverse Compton scattering with CMB photons and
many others. Therefore, the uncertainties that enter the propagation of the charged
flux until it reaches the telescope are important (contrary to the case of photons and
neutrinos that propagate almost unperturbed through the galaxy).
As in the case of direct detection, the experimental status of charged particle detection concerning the DM is confusing. After some hints from HEAT [72] and AMS01 [73] (the former a far-infrared telescope in Antarctica, the latter a spectrometer,
prototype for AMS-02 mounted on the International Space Station [74]), the PAMELA
satellite observed [75, 76] a steep increase in the energy spectrum of positron fraction
e
+/(e
+ + e
−)
8
. Later FERMI satellite [77] and AMS-02 [78] confirmed the results up
8The searches for charged particles focus on the antiparticles in order to have a reduced background,
26 Dark Matter
Figure 1.8: A compilation of data of charged cosmic rays, together with plausible but
uncertain astrophysical backgrounds, taken from [79]. Left: Positron flux. Center:
Antiproton flux. Right: Sum of electrons and positrons.
to energies of ∼ 200 GeV. However, the excess of positrons is not followed by an excess
of antiprotons, whose flux seems to coincide with the predicted background [75]. In
Fig. 1.8, three plots summarizing the situation are shown [79].
The observed excess is very difficult to explain in terms of DM [79]. To begin with,
the annihilation cross section required to reproduce the excess is quite large, many
orders of magnitude larger than the thermal cross section. Moreover, an “ordinary”
WIMP with large annihilation cross section giving rise to charged leptons is expected
to give, additionally, a large number of antiprotons, a fact in contradiction with the
observations. Although a lot of work has been done to fit a DM particle to the observed
pattern, it is quite possible that the excesses come from a yet unknown astrophysical
source. We are not going to discuss further this matter, but we end with a comment.
If this excess is due to a source other than DM, then a possible DM positron excess
would be lost under this formidable background.
A last hint for DM came from the detection of highly energetic photons. However,
we will interrupt this discussion, since this signal and a possible explanation is the
subject of Ch. 4. There, we will also see the upper bounds on the annihilation cross
section being set due to the absence of excesses in diffuse γ radiation.
since they are much less abundant than the corresponding particles.
CHAPTER 2
PARTICLE PHYSICS
Since the DM comprises of particles, it should be explained by a general particle physics
theory. We start in the following section by describing the Standard Model (SM) of
particle physics. Although the SM describes so far the fundamental particles and their
interactions quite accurately, it cannot provide a DM candidate. Besides, the SM
suffers from some theoretical problems, which we discuss in Sec. 2.2. We will see that
these problems can be solved if one introduces a new symmetry, the supersymmetry,
which we describe in Sec. 2.3. We finish this chapter by briefly describing in Sec. 2.4 a
supersymmetric extension of the SM with the minimal additional particle content, the
Minimal Supersymmetric Standard Model (MSSM).
2.1 The Standard Model of Particle Physics
The Standard Model (SM) of particle physics1
consists of two well developed theories,
the quantum chromodynamics (QCD) and the electroweak (EW) theory. The former
describes the strong interactions among the quarks, whereas the latter describes the
electroweak interactions (the weak and electromagnetic interactions in a unified context) between fermions. The EW theory took its final form in the late 1960s by the
introduction by S. Weinberg [85] and A. Salam [86] of the Higgs mechanism that gives
masses to the SM particles, which followed the unification of electromagnetic and weak
interactions [87,88]. At the same time, the EW model preserves the gauge invariance,
making the theory renormalizable, as shown later by ’t Hooft [89]. On the other hand,
QCD obtained its final form some years later, after the confirmation of the existence
of quarks. Of course, the history of the SM is much longer and it can be traced back to
1920s with the formulation of a theoretical basis for a Quantum Field Theory (QFT).
Since then, the SM had many successes. The SM particle content was completed with
the discovery of the heaviest of the quarks, the top quark [90,91], in 1995 and, recently,
with the discovery of the Higgs boson [92, 93].
1There are many good textbooks on the SM and Quantum Field Theory, e.g. [80–84].
28 Particle Physics
The key concept within the SM, as in every QFT, is that of symmetries. Each
interaction respects a gauge symmetry, based on a Lie algebra. The strong interaction is
described by an SU(3)c symmetry, where the subscript c stands for color, the conserved
charge of strong interactions. The EW interactions, on the other hand, are based on
a SU(2)L × U(1)Y Lie algebra. Here, as we will subsequently see, L refers to the
left-handed fermions and Y is the hypercharge, the conserved charge under the U(1).
SU(2)L conserves a quantity known as weak isospin I. Therefore, the SM contains the
internal symmetries of the unitary product group
SU(2)L × U(1)Y × SU(3)c. (2.1)
2.1.1 The particle content of the SM
We mention for completeness that particles are divided into two main classes according
to the statistics they follow. The bosons are particles with integer spin and follow the
Bose-Einstein distribution, whereas fermions have half-integer spin and follow the
Dirac-Einstein statistics, obeying the Pauli exclusion principle. In the SM, all the
fermions have spin 1/2, whereas the bosons have spin 1 with only exception the Higgs
boson, which is a scalar (spin zero). We begin the description of the SM particles with
the fermions.
Each fermion is classified in irreducible representations of each individual Lie algebra, according to the conserved quantum numbers, i.e. the color C, the weak isospin
I and the hypercharge Y . A first classification of fermions can be done into leptons
and quarks, which transform differently under the SU(3)c. Leptons are singlets under
this transformation, while quarks act as triplets (the fundamental representation of
this group). The EW interactions violate maximally the parity symmetry and SU(2)L
acts only on states with negative chirality (left-handed). A Dirac spinor Ψ can be
decomposed into left and right chirality components using, respectively, the projection
operators PL =
1
2
(1 − γ5) and PR =
1
2
(1 + γ5):
ΨL = PLΨ and ΨR = PRΨ. (2.2)
Left-handed fermions have I = 1/2, with a third component of the isospin I3 = ±1/2.
Fermions with positive I3 are called up-type fermions and those with negative are
called down-type. These behave the same way under SU(2)L and form doublets with
one fermion of each type. On the other hand, right-handed fermions have I = 0 and
form singlets that do not undergo weak interactions. The hypercharge is written in
terms of the electric charge Q and the third component of the isospin I3 through the
Gell-Mann–Nishijima relation:
Q = I3 + Y/2. (2.3)
Therefore, left- and right-handed components transform differently under the U(1)Y ,
since they have different hypercharge.
The fermionic sector of the SM comprises three generations of fermions, transforming as spinors under Lorentz transformations. Each generation has the same structure.
For leptons, it is an SU(2)L doublet with components consisting of one left-handed
2.1.2 The SM Lagrangian 29
charged lepton and one neutrino (neutrinos are only left-handed in the SM), along
with a gauge singlet right-handed charged lepton. The quark doublet consists of an
up- (u) and a down-type (d) (left-handed) quark and the pattern is completed by the
two corresponding SU(2)L singlet right-handed quarks. We write these representations
as
Quarks: Q ≡

u
i
L
d
i
L
!
, ui
R, di
R Leptons: L ≡

ν
i
L
e
i
L
!
, ei
R, (2.4)
with i = 1, 2, 3 the generation index.
Having briefly described the fermionic sector, we turn to the bosonic sector of
the SM. It consists of the gauge bosons that mediate the interactions and the Higgs
boson that gives masses to the particles through a spontaneous symmetry breaking,
the electroweak symmetry breaking (EWSB) [94–98], which we shall describe in Sec.
2.1.3. Before the EWSB, these bosons are
• three Wa
µ
(a = 1, 2, 3) weak bosons, associated with the generators of SU(2)L,
• one neutral Bµ boson, associated with the generator of U(1)Y ,
• eight gluons Ga
µ
(a = 1, . . . , 8), associated with the generators of SU(3)c, and
• the complex scalar Higgs doublet Φ =
φ
+
φ
0
!
.
After the EWSB, the EW boson states mix and give the two W± bosons, the neutral
Z boson and the massless photon γ. From the symmetry breaking, one scalar degree of
freedom remains which is the famous (neutral) Higgs boson [97–99]. We will return to
the mixed physical states, after describing the Higgs mechanism for symmetry breaking.
A complete list of the SM particles (the physical states after EWSB) is shown in Table
2.1.
2.1.2 The SM Lagrangian
The gauge bosons are responsible for the mediation of the interactions and are associated with the generators of the corresponding symmetry. The EW gauge bosons Bµ
and Wa
µ
are associated, respectively, with the generator Y of the U(1)Y and the three
generators T
a
2
of the SU(2)L. The latter are defined as half of the Pauli matrices τ
a
(T
a
2 =
1
2
τ
a
) and they obey the algebra

T
a
2
, Tb
2

= iǫabcT
c
2
, (2.5)
where ǫ
abc is the fully antisymmetric Levi-Civita tensor. The eight gluons are associated
with an equal number of generators T
a
3
(Gell-Mann matrices) of SU(3)c and obey the
Lie algebra

T
a
3
, Tb
3

= if abcT
c
3
, with Tr
T
a
3 T
b
3

=
1
2
δ
ab
, (2.6)
30 Particle Physics
Name symbol mass charge (|e|) spin
Leptons
electron e 0.511 MeV −1 1/2
electron neutrino νe 0 (<2 eV) 0 1/2
muon µ 105.7 MeV −1 1/2
muon neutrino νµ 0 (<2 eV) 0 1/2
tau τ 1.777 GeV −1 1/2
tau neutrino ντ 0 (<2 eV) 0 1/2
Quarks
up u 2.7
+0.7
−0.5 MeV 2/3 1/2
down d 4.8
+0.7
−0.3 MeV −1/3 1/2
strange s (95 ± 5) MeV −1/3 1/2
charm c (1.275 ± 0.025) GeV 2/3 1/2
bottom b (4.18 ± 0.03) GeV −1/3 1/2
top t (173.5 ± 0.6 ± 0.8) GeV 2/3 1/2
Bosons
photon γ 0 (<10−18 eV) 0 (<10−35) 1
W boson W± (80.385 ± 0.015) GeV ±1 1
Z boson Z (91.1876 ± 0.0021) GeV 0 1
gluon g 0 (.O(1) MeV) 0 1
Higgs H
(125.3 ± 0.4 ± 0.5) GeV
0 0
(126.0 ± 0.4 ± 0.4) GeV
Table 2.1: The particle content of the SM. All values are those given in [100], except of
the Higgs mass that is taken from [92, 93] (up and down row, respectively), assuming
that the observed excess corresponds to the SM Higgs. The u, d and s quark masses
are estimates of so-called “current-quark masses” in a mass-independent subtraction
scheme as MS at a scale ∼ 2 GeV. The c and b quark masses are the running masses
in the MS scheme. The values in the parenthesis are the current experimental limits.
with f
abc the structure constants of the group.
Using the structure constants of the corresponding groups, we define the field
strengths for the gauge bosons as
Bµν ≡ ∂µBν − ∂νBµ, (2.7a)
Wµν ≡ ∂µWa
ν − ∂νWa
µ + g2ǫ
abcWb
µWc
ν
(2.7b)
and
G
a
µν ≡ ∂µG
a
ν − ∂νG
a
µ + g3f
abcG
b
µG
c
ν
. (2.7c)
2.1.2 The SM Lagrangian 31
We use the notation g1, g2 and g3 for the coupling constants of U(1)Y , SU(2)L and
SU(3)c, respectively. As in any Yang-Mills theory, the non-abelian gauge groups lead
to self-interactions, which is not the case for the abelian U(1)Y group.
Before we finally write the full Lagrangian, we have to introduce the covariant
derivative for fermions, which in a general form can be written as
DµΨ =
∂µ − ig1
1
2
Y Bµ − ig2T
a
2 Wa
µ − ig3T
a
3 G
a
µ

Ψ. (2.8)
This form has to be understood as that, depending on Ψ, only the relevant terms
apply, hence for SU(2)L singlet leptons only the two first terms inside the parenthesis
are relevant, for doublet leptons the three first terms and for the corresponding quark
singlets and doublets the last term also participates. We also have to notice that in
order to retain the gauge symmetry, mass terms are forbidden in the Lagrangian. For
example, the mass term mψψ¯ = m

ψ¯
LψR + ψ¯
RψL

(with ψ¯ ≡ ψ
†γ
0
) is not invariant
under SU(2)L. This paradox is solved by the introduction of the Higgs scalar field
(see next subsection). The SM Lagrangian can be now written2
, split for simplicity in
three parts, each describing the gauge bosons, the fermions and the scalar sector,
LSM = Lgauge + Lfermion + Lscalar, (2.9)
with
Lgauge = −
1
4
G
a
µνG
µν
a −
1
4
Wa
µνWµν
a −
1
4
BµνB
µν
, (2.10a)
Lfermion = iL¯Dµγ
µL + ie¯RDµγµeR
+ iQ¯Dµγ
µQ + iu¯RDµγ
µuR + i
¯dRDµγ
µ
dR
−

heL¯ΦeR + hdQ¯ΦdR + huQ¯ΦeuR + h.c.

(2.10b)
and
Lscalar = (DµΦ)†
(DµΦ) − V (Φ†Φ), (2.10c)
where
V (Φ†Φ) = µ
2Φ
†Φ + λ

Φ
†Φ
2
(2.11)
is the scalar Higgs potential. Φ is the conjugate of Φ, related to the charge conjugate e
by Φ =e iτ2Φ
⋆
, with τi the Pauli matrices. The covariant derivative acting on the Higgs
scalar field gives
DµΦ =
∂µ − ig1
1
2
Y Bµ − ig2T
a
2 Wa
µ

Φ. (2.12)
Before we proceed to the description of the Higgs mechanism, a last comment concerning the SM Lagrangian is in order. If we restore the generation indices, we see that
2For simplicity, from now on we are going to omit the generations indice
32 Particle Physics
the Yukawa couplings h are 3 × 3, in general complex, matrices. As any complex matrix, they can be diagonalized with the help of two unitary matrices VL and VR, which
are related by VR = U
†VL with U again a unitary matrix. The diagonalization in the
quark sector to the mass eigenstates induces a mixing among the flavors (generations),
described by the Cabibbo–Kobayashi–Maskawa (CKM) matrix [101, 102]. The CKM
matrix is defined by
VCKM ≡ V
u
L
†
V
d
L
†
, (2.13)
where V
u
L
, V
d
L
are the unitary matrices that diagonalize the Yukawa couplings Hu
, Hd
,
respectively. This product of the two matrices appears in the charged current when it
is expressed in terms of the observable mass eigenstates.
2.1.3 Mass generation through the Higgs mechanism
We will start by examining the scalar potential (2.11). The vacuum expectation value
(vev) of the Higgs field hΦi ≡ h0|Φ|0i is given by the minimum of the potential. For
µ
2 > 0, the potential is always non-negative and Φ has a zero vev. The hypothesis of
the Higgs mechanism is that µ
2 < 0. In this case, the field Φ will acquire a vev
hΦi =
1
2

0
v
!
with v =
r
−
µ2
λ
. (2.14)
Since the charged component of Φ still has a zero vev, the U(1)Q symmetry of quantum
electrodynamics (QED) remains unbroken.
We expand the field Φ around the minima v in terms of real fields, and at leading
order we have
Φ(x) =
θ2(x) + iθ1(x)
√
1
2
(v + H(x)) − iθ3(x)
!
=
1
√
2
e
iθa(x)τ
a

0
v + H(x)
!
. (2.15)
We can eliminate the unphysical degrees of freedom θa, using the fact that the theory
remains gauge invariant. Therefore, we perform the following SU(2)L gauge transformation on Φ (unitary gauge)
Φ(x) → e
−iθa(x)τ
a
Φ(x), (2.16)
so that
Φ(x) = 1
√
2

0
v + H(x)
!
. (2.17)
We are going to use the following definitions for the gauge fields
W±
µ ≡
1
2

W1
µ ∓ iW2
µ

, (2.18a)
Zµ ≡
1
p
g
2
1 + g
2
2

g2W3
µ − g1Bµ

, (2.18b)
Aµ ≡
1
p
g
2
1 + g
2
2

g1W3
µ + g2Bµ

, (2.1
2.2 Limits of the SM and the emergence of supersymmetry 33
Then, the kinetic term for Φ (see Eq. (2.10c)) can be written in the unitary gauge as
(DµΦ)†
(D
µΦ) = 1
2
(∂µH)
2 + M2
W W+
µ W−µ +
1
2
M2
ZZµZ
µ
, (2.19)
with
MW ≡
1
2
g2v and MZ ≡
1
2
q
g
2
1 + g
2
2
v. (2.20)
We see that the definitions (2.18) correspond to the physical states of the gauge bosons
that have acquired masses due to the non-zero Higgs vev, given by (2.20). The photon
has remained massless, which reflects the fact that after the spontaneous breakdown of
SU(2)L × U(1)Y the U(1)Q remained unbroken. Among the initial degrees of freedom
of the complex scalar field Φ, three were absorbed by W± and Z and one remained as
the neutral Higgs particle with squared mass
m2
H = 2λv2
. (2.21)
We note that λ should be positive so that the scalar potential (2.11) is bounded from
below.
Fermions also acquire masses due to the Higgs mechanism. The Yukawa terms in
the fermionic part (2.10b) of the SM Lagrangian are written, after expanding around
the vev in the unitary gauge,
LY = −
1
√
2
hee¯L(v + H)eR −
1
√
2
hd
¯dL(v + H)dR −
1
√
2
huu¯L(v + H)uR + h.c. . (2.22)
Therefore, we can identify the masses of the fermions as
me
i =
h
i
e
v
√
2
, md
i =
h
i
d
v
√
2
, mui =
h
i
u
v
√
2
, (2.23)
where we have written explicitly the generation indices.
2.2 Limits of the SM and the emergence of supersymmetry
2.2.1 General discussion of the SM problems
The SM has been proven extremely successful and has been tested in high precision
in many different experiments. It has predicted many new particles before their final
discovery and also explained how the particles gain their masses. Its last triumph was
of course the discovery of a boson that seems to be very similar to the Higgs boson of
the SM. However, it is generally accepted that the SM cannot be the ultimate theory. It
is not only observed phenomena that the SM does not explain; SM also faces important
theoretical issues.
The most prominent among the inconsistencies of the SM with observations is the
oscillations among neutrinos of different generations. In order for the oscillations to
34 Particle Physics
φ φ
k
Figure 2.1: The scalar one-loop diagram giving rise to quadratic divergences.
occur, neutrinos should have non-zero masses. However, minimal modifications of the
SM are able to fit with the data of neutrino physics. Another issue that a more complete theory has to face is the matter asymmetry, the observed dominance of matter
over antimatter in the Universe. In addition, in order to comply with the standard
cosmological model, it has to provide the appropriate particle(s) that drove the inflation. Last, but not least, we saw that in order to explain the DM that dominates the
Universe, a massive, stable weakly interacting particle must exist. Such a particle is
not present in the SM.
On the other hand, the SM also suffers from a theoretical perspective. For example,
the SM counts 19 free parameters; one expects that a fundamental theory would have
a much smaller number of free parameters. Simple modifications of the SM have been
proposed relating some of these parameters. Grand unified theories (GUTs) unify
the gauge couplings at a high scale ∼ 1016 GeV. However, this unification is only
approximate unless the GUT is embedded in a supersymmetric framework. Another
serious problem of the SM is that of naturalness. This will be the topic of the following
subsection.
2.2.2 The naturalness problem of the SM
The presence of fundamental scalar fields, like the Higgs, gives rise to quadratic divergences. The diagram of Fig. 2.1 contributes to the squared mass of the scalar
δm2 = λ
Z Λ
d
4k
(2π)
4
k
−2
. (2.24)
This contribution is approximated by δm2 ∼ λΛ
2/(16π
2
), quadratic in a cut-off Λ,
which should be finite. For the case of the Higgs scalar field, one has to include its
couplings to the gauge fields and the top quark3
. Therefore,
δm2
H =
3Λ2
8π
2v
2

4m2
t − 2M2
W − M2
Z − m2
H

+ O(ln Λ
µ
)

, (2.25)
where we have used Eq. (2.21) and m2
H ≡ m2
0 + δm2
H.
3Since the contribution to the squared mass correction are quadratic in the Yukawa couplings (or
quark masses), the lighter quarks can be neglected
2.2.3 A way out 35
Taking Λ as a fundamental scale Λ ∼ MP l ∼ 1019 GeV we have
m2
0 = m2
H −
3Λ2
8π
2v
2

4m2
t − 2M2
W − M2
Z − m2
H

(2.26)
and we can see that m2
0 has to be adjusted to a precision of about 30 orders of magnitude
in order to achieve an EW scale Higgs mass. This is considered as an intolerable finetuning, which is against the general belief that the observable properties of a theory
have to be stable under small variations of the fundamental (bare) parameters. It is
exactly the above behavior that is considered as unnatural. Although the SM could
be self-consistent without imposing a large scale, grand unification of the parameters
introduce a hierarchy problem between the different scales.
A more strict definition of naturalness comes from ’t Hooft [103], which we rewrite
here:
At an energy scale µ, a physical parameter or set of physical parameters
αi(µ) is allowed to be very small only if the replacement αi(µ) = 0 would
increase the symmetry of the system.
Clearly, this is not the case here. Although mH is small compared to the fundamental
scale Λ, it is not protected by any symmetry and a fine-tuning is necessary.
2.2.3 A way out
The naturalness in the ’t Hooft sense is inspired by quantum electrodynamics, which is
the archetype for a natural theory. For example, the corrections to the electron mass
me are themselves proportional to me, with a dimensionless proportionality factor that
behaves like ∼ ln Λ. In general, fermion masses are protected by the chiral symmetry; small values (compared to the fundamental scale) of these masses enhances the
symmetry.
If a new symmetry exists in nature, relating fermion fields to scalar fields, then each
scalar mass would be related somehow to the corresponding fermion mass. Therefore,
the scalar mass itself can be naturally small compared to Λ, since this would mean
that the fermion mass is small, which enhances the chiral symmetry. Such a symmetry,
relating bosons to fermions and vice versa, is known as supersymmetry [104, 105].
Actually, as we will see later, if this new symmetry remains unbroken, the masses of
the conjugate bosons and fermions would have to be equal.
In order to make the above statement more concrete, we consider a toy model with
two additional complex scalar fields feL and feR. We will discuss only the quadratic
divergences that come from corrections to the Higgs mass due to a fermion. The
generalization for the contributions from the gauge bosons or the self-interaction is
straightforward. The interactions in this toy model of the new scalar fields with the
Higgs are described by the Lagrangian
Lfefφe = λfe|φ|
2

|feL|
2 + |feR|
2

. (2.27
36 Particle Physics
It can be easily checked that the quadratic divergence coming from a fermion at one
loop is exactly canceled, as long as the new quartic coupling λfe obeys the relation
λfe = −λ
2
f
(λf is the Yukawa coupling for the fermion f).
2.3 A brief summary of Supersymmetry
Supersymmetry (SUSY) is a symmetry relating fermions and bosons. The supersymmetry transformation should turn a boson state into a fermion state and vice versa. If
Q is the operator that generates such transformations, then
Q |bosoni = |fermioni Q |fermioni = |bosoni. (2.28)
Due to commutation and anticommutation rules of bosons and fermions, Q has to
be an anticommuting spinor operator, carrying spin angular momentum 1/2. Since
spinors are complex objects, the hermitian conjugate Q†
is also a symmetry operator4
.
There is a no-go theorem, the Coleman-Mandula theorem [106], that restricts the
conserved charges which transform as tensors under the Lorentz group to the generators
of translations Pµ and the generators of Lorentz transformations Mµν. Although this
theorem can be evaded in the case of supersymmetry due to the anticommutation
properties of Q, Q†
[107], it restricts the underlying algebra of supersymmetry [108].
Therefore, the basic supersymmetric algebra can be written as5
{Q, Q†
} = P
µ
, (2.29a)
{Q, Q} = {Q
†
, Q†
} = 0, (2.29b)
[P
µ
, Q] = [P
µ
, Q] = 0. (2.29c)
In the following, we summarize the basic conclusions derived from this algebra.
• The single-particle states of a supersymmetric theory fall into irreducible representations of the SUSY algebra, called supermultiplets. A supermultiplet contains
both fermion and boson states, called superpartners.
• Superpartners must have equal masses: Consider |Ωi and |Ω
′
i as the superpartners, |Ω
′
i should be proportional to some combination of the Q and Q† operators
acting on |Ωi, up to a space-time translation or rotation. Since −P
2
commutes
with Q, Q† and all space-time translation and rotation operators, |Ωi, |Ω
′
i will
have equal eigenvalues of −P
2 and thus equal masses.
• Superpartners must be in the same representation of gauge groups, since Q, Q†
commute with the generators of gauge transformations. This means that they
have equal charges, weak isospin and color degrees of freedom.
4We will confine ourselves to the phenomenologically more interesting case of N = 1 supersymmetry, with N referring to the number of distinct copies of Q, Q†
.
5We present a simplified version, omitting spinor indices in Q and Q†
.
2.3 A brief summary of Supersymmetry 37
• Each supermultiplet contains an equal number of fermion and boson degrees of
freedom (nF and nB, respectively): Consider the operator (−1)2s
, with s the spin
angular momentum, and the states |ii that have the same eigenvalue p
µ of P
µ
.
Then, using the SUSY algebra (2.29) and the completeness relation P
i
|ii hi| =
1, we have P
i
hi|(−1)2sP
µ
|ii = 0. On the other hand, P
i
hi|(−1)2sP
µ
|ii =
p
µTr [(−1)2s
] ∝ nB − nF . Therefore, nF = nB.
As addendum to the last point, we see that two kind of supermultiplets are possible
(neglecting gravity):
• A chiral (or matter or scalar ) supermultiplet, which consists of a single Weyl
fermion (with two spin helicity states, nF = 2) and two real scalars (each with
nB = 1), which can be replaced by a single complex scalar field.
• A gauge (or vector ) supermultiplet, which consists of a massless spin 1 boson
(two helicity states, nB = 2) and a massless spin 1/2 fermion (nF = 2).
Other combinations either are reduced to combinations of the above supermultiplets
or lead to non-renormalizable interactions.
It is possible to study supersymmetry in a geometric approach, using a space-time
manifold extended by four fermionic (Grassmann) coordinates. This manifold is called
superspace. The fields, in turn, expressed in terms of the extended set of coordinates
are called superfields. We are not going to discuss the technical details of this topic
(the interested reader may refer to the rich bibliography, for example [109–111]).
However, it is important to mention a very useful function of the superfields, the
superpotential. A generic form of a (renormalizable) superpotential in terms of the
superfields Φ is the following b
W =
1
2
MijΦbiΦbj +
1
6
y
ijkΦbiΦbjΦbk. (2.30)
The Lagrangian density can always be written according to the superpotential. The
superpotential has also to fulfill some requirements. In order for the Lagrangian to
be supersymmetric invariant, W has to be holomorphic in the complex scalar fields
(it does not involve hermitian conjugates Φb† of the superfields). Conventionally, W
involves only left chiral superfields. Instead of the SU(2)L singlet right chiral fermion
fields, one can use their left chiral charge conjugates.
As we mentioned before, the members of a supermultiplet have equal masses. This
contradicts our experience, since the partners of the light SM particles would have been
detected long time ago. Hence, the supersymmetry should be broken at a large energy
scale. The common approach is that SUSY is broken in a hidden sector, very weakly
coupled to the visible sector. Then, one has to explain how the SUSY breaking mediated to the visible sector. The two most popular scenarios are the gravity mediation
scenario [112–114] and the Gauge-Mediated SUSY Breaking (GSMB) [113, 115–117],
where the mediation occurs through gauge interactions.
There are two approaches with which one can address the SUSY breaking. In the
first approach, one refers to a GUT unification and determines the supersymmetric
38 Particle Physics
breaking parameters at low energies through the renormalization group equations.
This approach results in a small number of free parameters. In the second approach,
the starting point is the low energy scale. In this case, the SUSY breaking has to be
parametrized by the addition of breaking terms to the low energy Lagrangian. This
results in a larger set of free parameters. These terms should not reintroduce quadratic
divergences to the scalar masses, since the cancellation of these divergences was the
main motivation for SUSY. Then, one talks about soft breaking terms.
2.4 The Minimal Supersymmetric Standard Model
One can construct a supersymmetric version of the standard model with a minimal
content of particles. This model is known as the Minimal Supersymmetric Standard
Model (MSSM). In a SUSY extension of the SM, each of the SM particles is either in a
chiral or in a gauge supermultiplet, and should have a superpartner with spin differing
by 1/2.
The spin-0 partners of quarks and leptons are called squarks and sleptons, respectively (or collectively sfermions), and they have to reside in chiral supermultiplets.
The left- and right-handed components of fermions are distinct 2-component Weyl
fermions with different gauge transformations in the SM, so that each must have its
own complex scalar superpartner. The gauge bosons of the SM reside in gauge supermultiplets, along with their spin-1/2 superpartners, which are called gauginos. Every
gaugino field, like its gauge boson partner, transforms as the adjoint representation of
the corresponding gauge group. They have left- and right-handed components which
are charge conjugates of each other: (λeL)
c = λeR.
The Higgs boson, since it is a spin-0 particle, should reside in a chiral supermultiplet. However, we saw (in the fermionic part of the SM Lagrangian, Eq. (2.10b))
that the Y = 1/2 Higgs in the SM can give mass to both up- and down-type quarks,
only if the conjugate Higgs field with Y = −1/2 is involved. Since in the superpotential there are no conjugate fields, two Higgs doublets have to be introduced. Each
Higgs supermultiplet would have hypercharge Y = +1/2 or Y = −1/2. The Higgs
with the negative hypercharge gives mass to the down-type fermions and it is called
down-type Higgs (Hd, or H1 in the SLHA convention [118]) and the other one gives
mass to up-type fermions and it is called up-type Higgs (Hu, or H2).
The MSSM respects a discrete Z2 symmetry, the R-parity. If one writes the most
general terms in the supersymmetric Lagrangian (still gauge-invariant and holomorphic), some of them would lead to non-observed processes. The most obvious constraint
comes from the non-observed proton decay, which arises from a term that violates both
lepton and baryon numbers (L and B, respectively) by one unit. In order to avoid these
terms, R-parity, a multiplicative conserved quantum number, is introduced, defined as
PR = (−1)3(B−L)+2s
, (2.31)
with s the spin of the particle.
The R even particles are the SM particles, whereas the R odd are the new particles
introduced by the MSSM and are called supersymmetric particles. Due to R-parity,
2.4 The Minimal Supersymmetric Standard Model 39
if it is exactly conserved, there can be no mixing among odd and even particles and,
additionally, each interaction vertex in the theory can only involve an even number of
supersymmetric particles. The phenomenological consequences are quite important.
First, the lightest among the odd-parity particles is stable. This particle is known
as the lightest supersymmetric particle (LSP). Second, in collider experiments, supersymmetric particles can only be produced in pairs. The first of these consequences
was a breakthrough for the incorporation of DM into a general theory. If the LSP is
electrically neutral, it interacts only weakly and it consists an attractive candidate for
DM.
We are not going to enter further into the details of the MSSM6
. Although MSSM
offers a possible DM candidate, there is a strong theoretical reason to move from the
minimal model. This reason is the so-called µ-problem of the MSSM, with which we
begin the discussion of the next chapter, where we shall describe more thoroughly the
Next-to-Minimal Supersymmetric Standard Model.
6We refer to [110] for an excellent and detailed description of MSSM.
40 Particle Physics
Part II
Dark Matter in the
Next-to-Minimal Supersymmetric
Standard Model

CHAPTER 3
THE NEXT-TO-MINIMAL
SUPERSYMMETRIC STANDARD
MODEL
The Next-to-Minimal Supersymmetric Standard Model (NMSSM) is an extension of
the MSSM by a chiral, SU(2)L singlet superfield Sb (see [119, 120] for reviews). The
introduction of this field solves the µ-problem1
from which the MSSM suffers, but
also leads to a different phenomenology from that of the minimal model. The scalar
component of the additional field mixes with the scalar Higgs doublets, leading to three
CP-even mass eigenstates and two CP-odd eigenstates (as in the MSSM a doublet-like
pair of charged Higgs also exists). On the other hand, the fermionic component of the
singlet (singlino) mixes with gauginos and higgsinos, forming five neutral states, the
neutralinos.
Concerning the CP-even sector, a new possibility opens. The lightest Higgs mass
eigenstate may have evaded the detection due to a sizeable singlet component. Besides,
the SM-like Higgs is naturally heavier than in the MSSM [123–126]. Therefore, a SMlike Higgs mass ∼ 125 GeV is much easier to explain [127–141]. The singlet component
of the CP-odd Higgs also allows for a potentially very light pseudoscalar with suppressed couplings to SM particles, with various consequences, especially on low energy
observables (for example, [142–145]). The singlino component of the neutralino may
also play an important role for both collider phenomenology and DM. This is the case
when the neutralino is the LSP and the lightest neutralino has a significant singlino
component.
We start the discussion about the NMSSM by describing the µ-problem and how
this is solved in the context of the NMSSM. In Sec. 3.2 we introduce the NMSSM
Lagrangian and we write the mass matrices of the Higgs sector particles and the su1However, historically, the introduction of a singlet field preceded the µ-problem, e.g. [104, 105,
121, 122].
44 The Next-to-Minimal Supersymmetric Standard Model
persymmetric particles, at tree level. We continue by examining, in Sec. 3.3, the DM
candidates in the NMSSM and particularly the neutralino. The processes which determine the neutralino relic density are described in Sec. 3.4. The detection possibilities
of a potential NMSSM neutralino as DM are discussed in (Sec. 3.5). We close this
chapter (Sec. 3.6) by examining possible ways to include non-zero neutrino masses and
the additional DM candidates that are introduced.
3.1 Motivation – The µ-problem of the MSSM
As we saw, the minimal extension of the SM, the MSSM, contains two Higgs SU(2)L
doublets Hu and Hd. The Lagrangian of the MSSM should contain a supersymmetric
mass term, µHuHd, for these two doublets. There are several reasons, which we will
subsequently review, that require the existence of such a term. On the other hand,
the fact that |µ| cannot be very large, actually it should be of the order of the EW
scale, brings back the problem of naturalness. A parameter of the model should be
much smaller than the “natural” scale (the GUT or the Planck scale) before the EW
symmetry breaking. This leads to the so-called µ-problem of the MSSM [146].
The reasons that such a term should exist in the Lagrangian of the MSSM are
mainly phenomenological. The doublets Hu and Hd are components of chiral superfields that also contain fermionic SU(2)L doublets. Their electrically charged components mix with the superpartners of the W± bosons, forming two charged Dirac
fermions, the charginos. The unsuccessful searches for charginos in LEP have excluded
charginos with masses almost up to its kinetic limit (∼ 104 GeV) [147]. Since the µ term
determines the mass of the charginos, µ cannot be zero and actually |µ| >∼ 100 GeV,
independently of the other free parameters of the model. Moreover, µ = 0 would result
in a Peccei-Quinn symmetry of the Higgs sector and an undesirable massless axion.
Finally, there is one more reason for µ 6= 0 related to the mass generation by the Higgs
mechanism. The term µHuHd will be accompanied by a soft SUSY breaking term
BµHuHd. This term is necessary so that both neutral components of Hu and Hd are
non-vanishing at the minimum of the potential.
The Higgs mechanism also requires that µ is not too large. In order to generate
the EW symmetry breaking, the Higgs potential has to be unstable at its origin Hu =
Hd = 0. Soft SUSY breaking terms for Hu and Hd of the order of the SUSY breaking
scale generate such an instability. However, the µ induced squared masses for Hu,
Hd are always positive and would destroy the instability in case they dominate the
negative soft mass terms.
The NMSSM is able to solve the µ-problem by dynamically generating the mass
µ. This is achieved by the introduction of an SU(2)L singlet scalar field S. When S
acquires a vev, a mass term for the Hu and Hd emerges with an effective mass µeff of
the correct order, as long as the vev is of the order of the SUSY breaking scale. This
can be obtained in a more “natural” way through the soft SUSY breaking terms.
3.2 The NMSSM Lagrangian 45
3.2 The NMSSM Lagrangian
All the necessary information for the Lagrangian of the NMSSM can be extracted from
the superpotential and the soft SUSY breaking Lagrangian, containing the soft gaugino and scalar masses, and the trilinear couplings. We begin with the superpotential,
writing all the interactions of the NMSSM superfields, which include the MSSM superfields and the additional gauge singlet chiral superfield2 Sb. Hence, the superpotential
reads
W = λSbHbu · Hbd +
1
3
κSb3
+ huQb · HbuUbc
R + hdHbd · QbDbc
R + heHbd · LbEbc
R.
(3.1)
The couplings to quarks and leptons have to be understood as 3 × 3 matrices and the
quark and lepton fields as vectors in the flavor space. The SU(2)L doublet superfields
are given (as in the MSSM) by
Qb =

UbL
DbL
!
, Lb =

νb
EbL
!
, Hbu =

Hb +
u
Hb0
u
!
, Hbd =

Hb0
d
Hb −
d
!
(3.2)
and the product of two doublets is given by, for example, Qb · Hbu = UbLHb0
u − Hb +
u DbL.
An important fact to note is that the superpotential given by (3.1) does not include all possible renormalizable couplings (which respect R-parity). The most general
superpotential would also include the terms
W ⊃ µHbu · Hbd +
1
2
µ
′Sb2 + ξF s, b (3.3)
with the first two terms corresponding to supersymmetric masses and the third one,
with ξF of dimension mass2
, to a tadpole term. However, the above dimensionful
parameters µ, µ
′ and ξF should be of the order of the SUSY breaking scale, a fact
that contradicts the motivation behind the NMSSM. Here, we omit these terms and
we will work with the scale invariant superpotential (3.1). The Lagrangian of a scale
invariant superpotential possesses an accidental Z3 symmetry, which corresponds to a
multiplication of all the components of all chiral fields by a phase ei2π/3
.
The corresponding soft SUSY breaking masses and couplings are
−Lsof t = m2
Hu
|Hu|
2 + m2
Hd
|Hd|
2 + m2
S
|S|
2
+ m2
Q|Q|
2 + m2
D|DR|
2 + m2
U
|UR|
2 + m2
L
|L|
2 + m2
E|ER|
2
+

huAuQ · HuU
c
R − hdAdQ · HdD
c
R − heAeL · HdE
c
R
+λAλHu · HdS +
1
3
κAκS
3 + h.c.

+
1
2
M1λ1λ1 +
1
2
M2λ
i
2λ
i
2 +
1
2
M3λ
a
3λ
a
3
,
(3.4)
2Here, the hatted capital letters denote chiral superfields, whereas the corresponding unhatted
ones indicate their complex scalar components.
46 The Next-to-Minimal Supersymmetric Standard Model
where we have also included the soft breaking masses for the gauginos. λ1 is the U(1)Y
gaugino (bino), λ
i
2 with i = 1, 2, 3 is the SU(2)L gaugino (winos) and, finally, the λ
a
3
with a = 1, . . . , 8 denotes the SU(3)c gaugino (gluinos).
The scalar potential, expressed by the so-called D and F terms, can be written
explicitly using the general formula
V =
1
2

D
aD
a + D
′2

+ F
⋆
i Fi
, (3.5)
where
D
a = g2Φ
∗
i T
a
ijΦj (3.6a)
D
′ =
1
2
g1YiΦ
∗
i Φi (3.6b)
Fi =
∂W
∂Φi
. (3.6c)
We remind that T
a are the SU(2)L generators and Yi the hypercharge of the scalar
field Φi
. The Yukawa interactions and fermion mass terms are given by the general
Lagrangian
LY ukawa = −
1
2
∂
2W
∂Φi∂Φj
ψiψj + h.c.
, (3.7)
using the superpotential (3.1). The two-component spinor ψi
is the superpartner of
the scalar Φi
.
3.2.1 Higgs sector
Using the general form of the scalar potential, the following Higgs potential is derived
VHiggs =

λ

H
+
u H
−
d − H
0
uH
0
d

+ κS2

2
+

m2
Hu + |λS|
2

H
0
u

2
+

H
+
u

2

+

m2
Hd + |λS|
2

H
0
d

2
+

H
−
d

2

+
1
8

g
2
1 + g
2
2

H
0
u

2
+

H
+
u

2
−

H
0
d

2
−

H
−
d

2
2
+
1
2
g
2
2

H
+
u H
0
d
⋆
+ H
0
uH
−
d
⋆

2
+ m2
S
|S|
2 +

λAλ

H
+
u H
−
d − H
0
uH
0
d

S +
1
3
κAκS
3 + h.c.

.
(3.8)
The neutral physical Higgs states are defined through the relations
H
0
u = vu +
1
√
2
(HuR + iHuI ), H0
d = vd +
1
√
2
(HdR + iHdI ),
S = s +
1
√
2
(SR + iSI ),
3.2.1 Higgs sector 47
where vu, vd and s are, respectively, the real vevs of Hu, Hd and S, which have to be
obtained from the minima of the scalar potential (3.8), after expanding the fields using
Eq. (3.9). We notice that when S acquires a vev, a term µeffHbu · Hbd appears in the
superpotential, with
µeff = λs, (3.10)
solving the µ-problem.
Therefore, the Higgs sector of the NMSSM is characterized by the seven parameters
λ, κ, m2
Hu
, m2
Hd
, m2
S
, Aλ and Aκ. One can express the three soft masses by the three
vevs using the minimization equations of the Higgs potential (3.8), which are given by
vu

m2
Hu + µ
2
eff + λ
2
v
2
d +
1
2
g
2

v
2
u − v
2
d

− vdµeff(Aλ + κs) = 0
vd

m2
Hd + µ
2
eff + λ
2
v
2
u +
1
2
g
2

v
2
d − v
2
u

− vuµeff(Aλ + κs) = 0
s

m2
S + κAκs + 2κ
2σ
2 + λ
2

v
2
u + v
2
d

− 2λκvuvd

− λAλvuvd = 0,
(3.11)
where we have defined
g
2 ≡
1
2

g
2
1 + g
2
2

. (3.12)
One can also define the β angle by
tan β =
vu
vd
. (3.13)
The Z boson mass is given by MZ = gv with v
2 = v
2
u + v
2
d ≃ (174 GeV)2
. Hence, with
MZ given, the set of parameters that describes the Higgs sector of the NMSSM can be
chosen to be the following
λ, κ, Aλ, Aκ, tan b and µeff. (3.14)
CP-even Higgs masses
One can obtain the Higgs mass matrices at tree level by expanding the Higgs potential
(3.8) around the vevs, using Eq. (3.9). We begin by writing3
the squared mass matrix
M2
S
of the scalar Higgses in the basis (HdR, HuR, SR):
M2
S =


g
2
v
2
d + µ tan βBeff (2λ
2 − g
2
) vuvd − µBeff 2λµvd − λ (Aλ + 2κs) vu
g
2
v
2
u +
µ
tan βBeff 2λµvu − λ (Aλ + 2κs) vd
λAλ
vuvd
s + κAκs + (2κs)
2

 ,
(3.15)
where we have defined Beff ≡ Aλ + κs (it plays the role of the B parameter of the
MSSM).
3For economy of space, we omit in this expression the subscript from µ
48 The Next-to-Minimal Supersymmetric Standard Model
Although an analytical diagonalization of the above 3 × 3 mass matrix is lengthy,
there is a crucial conclusion that comes from the approximate diagonalization of the
upper 2 × 2 submatrix. If it is rotated by an angle β, one of its diagonal elements
is M2
Z
(cos2 2β +
λ
2
g
2 sin2
2β) which is an upper bound for its lightest eigenvalue. The
first term is the same one as in the MSSM. The conclusion is that in the NMSSM
the lightest CP-even Higgs can be heavier than the corresponding of the MSSM, as
long as λ is large and tan β relatively small. Therefore, it is much easier to explain
the observed mass of the SM-like Higgs. However, λ is bounded from above in order
to avoid the appearance of the Landau pole below the GUT scale. Depending on the
other free parameters, λ should obey λ <∼ 0.7.
CP-odd Higgs masses
For the pseudoscalar case, the squared mass matrix in the basis (HdI , HuI , SI ) is
M2
P =


µeff (Aλ + κs) tan β µeff (Aλ + κs) λvu (Aλ − 2κs)
µeff
tan β
(Aλ + κs) λvd (Aλ − 2κs)
λ (Aλ + 4κs)
vuvd
s − 3κAκs

 . (3.16)
One eigenstate of this matrix corresponds to an unphysical massless Goldstone
boson G. In order to drop the Goldstone boson, we write the matrix in the basis
(A, G, SI ) by rotating the upper 2 × 2 submatrix by an angle β. After dropping the
massless mode, the 2 × 2 squared mass matrix turns out to be
M2
P =
2µeff
sin 2β
(Aλ + κs) λ (Aλ − 2κs) v
λ (Aλ + 4κs)
vuvd
s − 3Aκs
!
. (3.17)
Charged Higgs mass
The charged Higgs squared mass matrix is given, in the basis (H+
u
, H−
d
⋆
), by
M2
± =

µeff (Aλ + κs) + vuvd

1
2
g
2
2 − λ

cot β 1
1 tan β
!
, (3.18)
which contains one Goldstone boson and one physical mass eigenstate H± with eigenvalue
m2
± =
2µeff
sin 2β
(Aλ + κs) + v
2

1
2
g
2
2 − λ

. (3.19)
3.2.2 Sfermion sector
The mass matrix for the up-type squarks is given in the basis (ueR, ueL) by
Mu =

m2
u + h
2
u
v
2
u −
1
3
(v
2
u − v
2
d
) g
2
1 hu (Auvu − µeffvd)
hu (Auvu − µeffvd) m2
Q + h
2
u
v
2
u +
1
12 (v
2
u − v
2
d
) (g
2
1 − 3g
2
2
)
!
, (3.20)
3.2.3 Gaugino and higgsino sector 49
whereas for down-type squarks the mass matrix reads in the basis (deR, deL)
Md =

m2
d + h
2
d
v
2
d −
1
6
(v
2
u − v
2
d
) g
2
1 hd (Advd − µeffvu)
hd (Advd − µeffvu) m2
Q + h
2
d
v
2
d +
1
12 (v
2
u − v
2
d
) (g
2
1 − 3g
2
2
)
!
. (3.21)
The off-diagonal terms are proportional to the Yukawa coupling hu for the up-type
squarks and hd for the down-type ones. Therefore, the two lightest generations remain
approximately unmixed. For the third generation, the mass matrices are diagonalized
by a rotation by an angle θT and θB, respectively, for the stop and sbottom. The mass
eigenstates are, then, given by
et1 = cos θT
etL + sin θT
etR, et2 = cos θT
etL − sin θT
etR, (3.22)
eb1 = cos θB
ebL + sin θB
ebR, eb2 = cos θB
ebL − sin θB
ebR. (3.23)
In the slepton sector, for a similar reason, only the left- and right-handed staus are
mixed and their mass matrix
Mτ =

m2
E3 + h
2
τ
v
2
d −
1
2
(v
2
u − v
2
d
) g
2
1 hτ (Aτ vd − µeffvu)
hτ (Aτ vd − µeffvu) m2
L3 + h
2
τ
v
2
d −
1
4
(v
2
u − v
2
d
) (g
2
1 − g
2
2
)
!
(3.24)
is diagonalized after a rotation by an angle θτ . Their mass eigenstates are given by
τe1 = cos θτ τeL + sin θτ τeR, τe2 = cos θτ τeL − sin θτ τeR. (3.25)
Finally, the sneutrino masses are
mνe = m2
L −
1
4

v
2
u − v
2
d
g
2
1 + g
2
2

. (3.26)
3.2.3 Gaugino and higgsino sector
The gauginos λ1 and λ
3
2 mix with the neutral higgsinos ψ
0
d
, ψ
0
u
and ψS to form neutral
particles, the neutralinos. The 5 × 5 mass matrix of the neutralinos is written in the
basis
(−iλ1, −iλ3
2
, ψ0
d
, ψ0
u
, ψS) ≡ (B, e W , f He0
d
, He0
u
, Se) (3.27)
as
M0 =


M1 0 − √
1
2
g1vd √
1
2
g1vu 0
M2 √
1
2
g2vd − √
1
2
g2vu 0
0 −µeff −λvu
0 −λvd
2κs


. (3.28)
The mass matrix (3.28) is diagonalized by an orthogonal matrix Nij . The mass eigenstates of the neutralinos are usually denoted by χ
0
i
, with i = 1, . . . , 5, with increasing
masses (i = 1 corresponds to the lightest neutralino). These are given by
χ
0
i = Ni1Be + Ni2Wf + Ni3He0
d + Ni4He0
u + Ni5S. e (3.2
50 The Next-to-Minimal Supersymmetric Standard Model
We use the convention of a real matrix Nij , so that the physical masses mχ
0
i
are real,
but not necessarily positive.
In the charged sector, the SU(2)L charged gauginos λ
− = √
1
2
(λ
1
2 + iλ2
2
), λ
+ =
√
1
2
(λ
1
2 − iλ2
2
) mix with the charged higgsinos ψ
−
d
and ψ
+
u
, forming the charginos ψ
±:
ψ
± =

−iλ±
ψ
±
u
!
. (3.30)
The chargino mass matrix in the basis (ψ
−, ψ+) is
M± =

M2 g2vu
g2vd µeff !
. (3.31)
Since it is not symmetric, the diagonalization requires different rotations of ψ
− and
ψ
+. We denote these rotations by U and V , respectively, so that the mass eigenstates
are obtained by
χ
− = Uψ−, χ+ = V ψ+. (3.32)
3.3 DM Candidates in the NMSSM
Let us first review the characteristics that a DM candidate particle should have. First,
it should be massive in order to account for the missing mass in the galaxies. Second,
it must be electrically and color neutral. Otherwise, it would have condensed with
baryonic matter, forming anomalous heavy isotopes. Such isotopes are absent in nature. Finally, it should be stable and interact only weakly, in order to fit the observed
relic density.
In the NMSSM there are two possible candidates. Both can be stable particles if
they are the LSPs of the supersymmetric spectrum. The first one is the sneutrino (see
[148,149] for early discussions on MSSM sneutrino LSP). However, although sneutrinos
are WIMPs, their large coupling to the Z bosons result in a too large annihilation cross
section. Hence, if they were the DM particles, their relic density would have been very
small compared to the observed value. Exceptions are very massive sneutrinos, heavier
than about 5 TeV [150]. Furthermore, the same coupling result in a large scattering
cross section off the nuclei of the detectors. Therefore, sneutrinos are also excluded by
direct detection experiments.
The other possibility is the lightest neutralino. Neutralinos fulfill successfully, at
least in principle, all the requirements for a DM candidate. However, the resulting
relic density, although weakly interacting, may vary over many orders of magnitude as
a function of the free parameters of the theory. In the next sections we will investigate
further the properties of the lightest neutralino as the DM particle. We begin by
studying its annihilation that determines the DM relic density.
3.4 Neutralino relic density 51
3.4 Neutralino relic density
We remind that the neutralinos are mixed states composed of bino, wino, higgsinos
and the singlino. The exact content of the lightest neutralino determines its pair
annihilation channels and, therefore, its relic density (for detailed analyses, we refer
to [151–154]). Subsequently, we will briefly describe the neutralino pair annihilation
in various scenarios. We classify these scenarios with respect to the lightest neutralino
content.
Before we proceed, we should mention another mechanism that affects the neutralino LSP relic density. If there is a supersymmetric particle with mass close to the
LSP (but always larger), it would be abundant during the freeze-out and LSP coannihilations with this particle would contribute to the total annihilation cross section.
This particle, which is the Next-to-Lightest Supersymmetric Particle (NLSP), is most
commonly a stau or a stop. In the above sense, coannihilations refer not only to the
LSP–NLSP coannihilations, but also to the NLSP–NLSP annihilations, since the latter
reduce the number density of the NLSPs [155].
• Bino-like LSP
In principle, if the lightest neutralino is mostly bino-like, the total annihilation
cross section is expected to be small. Therefore, a bino-like neutralino LSP would
have been overabundant. The reason for this is that there is only one available
annihilation channel via t-channel sfermion exchange, since all couplings to gauge
bosons require a higgsino component. The cross section is even more reduced
when the sfermion mass is large.
However, there are still two ways to achieve the correct relic density. The first one
is using the coannihilation effect: if there is a sfermion with a mass slightly larger
(some GeV) than the LSP mass, their coannihilations can be proved to reduce
efficiently the relic density to the desired value. The second one concerns a binolike LSP, with a very small but non-negligible higgsino component. In this case,
if in addition the lightest CP-odd Higgs A1 is light enough, the annihilation to a
pair A1A1 (through an s-channel CP-even Higgs Hi exchange) can be enhanced
via Hi resonances. In this scenario a fine-tuning of the masses is necessary.
• Higgsino-like LSP
A mostly higgsino LSP is as well problematic. The strong couplings of the higgsinos to the gauge bosons lead to very large annihilation cross section. Therefore,
a possible higgsino LSP would have a very small relic density.
• Mixed bino–higgsino LSP
In this case, as it was probably expected, one can easily fit the relic density to
the observed value. This kind of LSP annihilates to W+W−, ZZ, W±H∓, ZHi
,
HiAj
, b
¯b and τ
+τ
− through s-channel Z or Higgs boson exchange or t-channel
neutralino or chargino exchange. The last two channels are the dominant ones
when the Higgs coupling to down-type fermions is enhanced, which occurs more
commonly in the regime of relatively large tan β. The annihilation channel to a
52 The Next-to-Minimal Supersymmetric Standard Model
pair of top quarks also contributes to the total cross section, if it is kinematically
allowed. However, in order to achieve the correct relic density, the higgsino
component cannot be very large.
• Singlino-like LSP
Since a mostly singlino LSP has small couplings to SM particles, the resulting relic
density is expected to be large. However, there are some annihilation channels
that can be enhanced in order to reduce the relic density. These include the
s-channel (scalar or pseudoscalar) Higgs exchange and the t-channel neutralino
exchange.
For the former, any Higgs with sufficient large singlet component gives an important contribution to the cross section, increasing with the parameter κ (since
the singlino-singlino-singlet coupling is proportional to κ). Concerning the latter
annihilation, in order to enhance it, one needs large values of the parameter λ.
In this case, the neutralino-neutralino-singlet coupling, which is proportional to
λ, is large and the annihilation proceeds giving a pair of scalar HsHs or a pair
of pseudoscalar AsAs singlet like Higgs.
As in the case of bino-like LSP, one can also use the effect of s-channel resonances
or coannihilations. In the latter case, an efficient NLSP can be the neutralino
χ
0
2
or the lightest stau τe1. In the case that the neutralino NLSP is higgsinolike, the LSP-NLSP coannihilation through a (doublet-like) Higgs exchange can
be proved very efficient. A stau NLSP reduces the relic density through NLSPNLSP annihilations, which is the only possibility in the case that both parameters
κ and λ are small. We refer to [156,157] for further discussion on this possibility.
Assuming universality conditions the wino mass M2 has to be larger than the bino
mass M1 (M2 ∼ 2M1). This is the reason that we have not considered a wino-like LSP.
3.5 Detection of neutralino DM
3.5.1 Direct detection
Since neutralinos are Majorana fermions, the effective Lagrangian describing their
elastic scattering with a quark in a nucleon can be written, in the Dirac fermion
notation, as [158]
Leff = a
SI
i χ¯
0
1χ
0
1
q¯iqi + a
SD
i χ¯
0
1γ5γµχ
0
1
q¯iγ5γ
µ
qi
, (3.33)
with i = u, d corresponding to up- and down-type quarks, respectively. The Lagrangian has to be understood as summing over the quark generations.
In this expression, we have omitted terms containing the operator ψγ¯
5ψ or a combination of ψγ¯
5γµψ and ψγ¯
µψ (with ψ = χ, q). This is a well qualified assumption:
Due to the small velocity of WIMPs, the momentum transfer ~q is very small compared
3.5.1 Direct detection 53
to the reduced mass of the WIMP-nucleus system. In the extreme limit of zero momentum transfer, the above operators vanish4
. Hence, we are left with the Lagrangian
(3.33) consisting of two terms, the first one corresponding to spin-independent (SI)
interactions and the second to spin-dependent (SD) ones. In the following, we will
focus again only to SI scattering, since the detector sensitivity to SD scattering is low,
as it has been already mentioned in Sec. 1.5.1.
The SI cross section for the neutralino-nucleus scattering can be written as [158]
(see, also, [159])
σ
SI
tot =
4m2
r
π
[Zfp + (A − Z)fn]
2
. (3.34)
mr is the neutralino-nucleus reduced mass mr =
mχmN
mχ+mN
, and Z, A are the atomic and
the nucleon number, respectively. It is more common, however, to use an expression
for the cross section normalized to the nucleon. In this case, on has for the neutralinoproton scattering
σ
SI
p =
4
π

mpmχ
0
1
mp + mχ
0
1
!2
f
2
p ≃
4m2
χ
0
1
π
f
2
p
, (3.35)
with a similar expression for the neutron.
The form factor fp is related to the couplings a to quarks through the expression
(omitting the “SI” superscripts)
fp
mp
=
X
q=u,d,s
f
p
T q
aq
mq
+
2
27
fT G X
q=c,b,t
aq
mq
. (3.36)
A similar expression may be obtained for the neutron form factor fn, by the replacement
p → n in the previous expression (henceforth, we focus to neutralino-proton scattering).
The parameters fT q are defined by the quark mass matrix elements
hp| mqqq¯ |pi = mpfT q, (3.37)
which corresponds to the contribution of the quark q to the proton mass and the
parameter fT G is related to them by
fT G = 1 −
X
q=u,d,s
fT q. (3.38)
The above parameters can be obtained by the following quantities
σπN =
1
2
(mu + md)(Bu + Bd) and σ0 =
1
2
(mu + md)(Bu + Bd − 2Bs,) (3.39)
with Bq = hN| qq¯ |Ni, which are obtained by chiral perturbation theory [160] or by
lattice simulations. Unfortunately, the uncertainties on the values of these quantities
are large (see [161], for more recent values and error bars).
4While there are possible circumstances in which the operators of (3.33) are also suppressed and,
therefore, comparable to the operators omitted, they are not phenomenologically interesting.
54 The Next-to-Minimal Supersymmetric Standard Model
χ
0
1
χ
0
1
χ
0
1 χ
0
1
qe
q q
q q
Hi
Figure 3.1: Feynman diagrams contributing to the elastic neutralino-quark scalar scattering amplitude at tree level.
The SI neutralino-nucleon interactions arise from t-channel Higgs exchange and
s-channel squark exchange at tree level (see Fig. 3.1), with one-loop contributions from
neutralino-gluon interactions. In practice, the s-channel Higgs exchange contribution
to the scattering amplitude dominates, especially due to the large masses of squarks.
In this case, the effective couplings a are given by
a
SI
d =
X
3
i=1
1
m2
Hi
C
1
i Cχ
0
1χ
0
1Hi
, aSI
u =
X
3
i=1
1
m2
Hi
C
2
i Cχ
0
1χ
0
1Hi
. (3.40)
C
1
i
and C
2
i
are the Higgs Hi couplings to down- and up-type quarks, respectively, given
by
C
1
i =
g2md
2MW cos β
Si1, C2
i =
g2mu
2MW sin β
Si2, (3.41)
with S the mixing matrix of the CP-even Higgs mass eigenstates and md, mu the
corresponding quark mass. We see from Eqs. (3.36) and (3.41) that the final cross
section (3.35) is independent of each quark mass. We write for completeness the
neutralino-neutralino-Higgs coupling Cχ
0
1χ
0
1Hi
:
Cχ
0
1χ
0
1Hi =
√
2λ (Si1N14N15 + Si2N13N15 + Si3N13N14) −
√
2κSi3N
2
15
+ g1 (Si111N13 − Si2N11N14) − g2 (Si1N12N13 − Si2N12N14), (3.42)
with N the neutralino mixing matrix given in (3.29).
The resulting cross section is proportional to m−4
Hi
. In the NMSSM, it is possible
for the lightest scalar Higgs eigenstate to be quite light, evading detection due to its
singlet nature. This scenario can give rise to large values of SI scattering cross section,
provided that the doublet components of th

[Julien Barthe]

Tu as raison.
La seule question qui vaille: les premiers post de de DH, il y a 7 ans étaient-ils d’emblée hostiles et quelle forme prennent-ils sur les autres forums qu’il fréquente ? Et quand je dis « qui vaille » j’ai conscience d’exagérer un poil .
Il n’y a pas de paradoxe. Je fais deux hypothèses:
– il se tient au plaisir d’exprimer sa détestation et d’offenser sans conséquences et en toute licence. Plaisir qui s’accroît dans la détestation qu’il suscite.
– n’ayant pas la puissance nécessaire pour susciter l’intérêt de François ou des autres membres du forum, il trouve dans la détestation qu’il suscite une forme d’attention qui joue comme une reconnaissance de substitution.
Les deux hypothèses ne s’excluent pas forcément.
J’ajoute que la licence est à la fois pour lui une chance et une damnation.

[Demi Habile]

Julien Barthe: Et tu fais quoi du fait que mon numéro a débuté avec le numéro de deleatur qui s’imaginait que ça pouvait être une idée de se vanter de trouver ça rigolo de me pousser à bout?
.
Rien. Parce que ça n’a rien de compatible avec ton analyse à deux balles.

[Julien Barthe]

« On m’a dit que de moi tu médis l’an passé ».
Tu passes ton temps à invoquer une première offense. Tu es le loup de la fable sans la puissance. Je t’ai assez accordé d’attention pour aujourd’hui et pour ce mois-ci. Continue à jouir du pouvoir de nuisance qu’on te concède.

[Demi Habile]

Julien Barthe: T’as du mal avec les faits hein.

[Julien Barthe]

Toi, tu as du mal avec l’effet. Tu es une énergie ressentimentale cantonnée à la virtualité.

[Demi Habile]

Julien Barthe: Tu prends de l’avance pour demain là?

[..Graindorge]

Demi Habile
Non tout le monde ne t’est pas hostile
mais pourquoi faire payer à tout le monde ta grande colère contre deleatur qui est en vacances?
Tu trouves ce forum nul? Tu trouves tout le monde ici nul? Pourquoi tu restes et depuis 10 ans?

[Demi Habile]

Graindorge: Je suis arrivé dans le coin en faisant une recherche sur le bouquin de Ruffin concernant la psychiatrie.
.
https://www.librairielabuissonniere.com/livre/13260190-un-depute-a-l-hp-francois-ruffin-fakir
.
Ca dit Décembre 2017 et on peut faire comme si la date de mon arrivée avait été Décembre 2017 pour t’aider un peu à sauver la face. Reste que ça ne fait pas 7 ans que je suis dans le coin et si t’en es à essayer de me faire croire que ça fait dix ans que je traine dans le coin c’est parce que tu n’es qu’une conne qui reprend le compte de François dans l’espoir de se faire aimer par le type qui le méprise. Je l’ai déjà souligné que je n’étais arrivé qu’au début de l’année 2018 et t’en as rien à foutre car dans le fond tu rêves d’une chose, c’est que François t’estime là où il s’est toujours essuyé les pieds sur ta gueule de conne.

[..Graindorge]

Demi Habile: je n’invente rien: tu as dit que ça faisait 10 ans dans un message
Je vois pas pourquoi j’aurais inventé ce nombre. Mais 7 ou 8 ou 10 . Pas grave.
Et arrête d’insulter punaise!
Et tu donnes une importance à François qu’il n’a pas
Et je sais pas si tu lis les messages mais je donne pas dans le cirage de pompes et le fayotage. Avec personne. Et si chez les parisiens dire parfois le bien qu’on pense c’est du cirage alors c’est votre problème, pas le mien. Quand je te dis des trucs sympas et que je penses, tu dis : c’est nuuuul, tu m’prends pour un gros con gnagnagna… Alors je dis plus rien et c’est comme ça que tu contribues à la liberté d’expression
Les gens et les choses n’ont que l’importance qu’on leur donne.
À tout hasard, tu pourrais partager ici l’article de Rufin en HP stp? Si et seulement si tu veux/peux
Sinon pas grave

[Demi Habile]

Graindorge: Ferme ta gueule pauvre conne, j’en ai rien à foutre de ce que tu peux raconter.

[..Graindorge]

Par contre toi tu peux l’ouvrir sur des kilomètres et embêter tout le monde dans tous les topics/entrées et ce jusqu’au 31 juillet et ça te plaît.
Les insultes non stop: lis bien la notice: ça doit être les effets secondaires de tes médicaments. Je vois que ça

[maelstrom]

je ne comprend toujours pas le problème de fond/les raisons de cette histoire de spam

[Fanny]

Schnoups, je suis d’accord, je n’avais pas pensé à cet aspect, et c’est intéressant qu’il ait un pied dans le monde de la même manière que tout un chacun. Concernant l’indécidable, j’ai quand même aimé que le questionnement sur la sincérité ou non de sa parole et de ses actes vienne contaminer presque chaque instant. L’épisode du sourire n’était peut-être pas le bon exemple, mais cela de la machine à laver par exemple est bien sujet à ce doute. J’ai trouvé que ça me rendait plus attentive qu’à l’ordinaire à chaque mot échangé, à chaque moue, même dans des scènes a priori banales. Comme si tout le suspense était logé là, dans le langage et dans les gestes, qui se prêtent en permanence à une double lecture. Et ça m’a fait sentir également à quel point nous pouvons être en posture de représentation jusque dans le quotidien. Savoir identifier une panne ce n’est pas seulement une question pratico-pratique, c’est encore une manière de s’afficher compétent, de se mettre en valeur.

[Schnoups]

Oui, on est d’accord, bien sur que le fait d’être perdu fait parti du jeu, on se pose beaucoup de questions, c’est vraiment ce qui caractérise la première partie du film pour moi. Il me semble bien qu’au bout d’une heure de film, une fois Julius dans le lit avec sa chanteuse on monte d’un cran. On monte d’un cran sur la confusion et dans le même sur quelque chose de très clair : lui – lui aimant se construire un monde, excellant dans le fait de raconter des histoires, et ce que j’essayais de mettre en valeur dans l’autre topic – il s’agit aussi d’interprétation, d’incarnation et d’intensité.
L’histoire de l’homme nu dans la rue : idée géniale de faire circuler cette histoire qui à nous, nous apparait lui appartenir puisqu’il est le premier à la raconter, il la raconte deux fois et lorsque la chanteuse le fait à son tour on est vraiment surpris, plus le film avance et plus on creuse le personnage. Mais là encore pourquoi faire circuler cette histoire ? Ce n’est pas seulement pour nous montrer qu’il pensait qu’elle venait vraiment de lui. On constate qu’il apparait profondément triste, comme si elle se foutait de lui, mais aussi peut être parce qu’on lui a retiré la paternité de l’histoire. Ce qu’on constate aussi c’est qu’il la raconte mieux qu’elle. En gros ce que je veux dire c’est qu’il y a d’autres choses qui intéressent le réalisateur. Je crois que plus le film avance plus il fusionne avec son personnage, jusqu’à ces images mentales et la fin qui se passe du son des paroles et qui monte en puissance musicale avec notre héros racontant une histoire géniale, magique, le cadeau du collègue croyant.

[Schnoups]

Je re précise, pour l’histoire qui circule, on a beau se dire une fois qu’on voit à peu près à qui on a affaire que c’est certainement une histoire volée, on la lui attribue plus qu’à elle. Le choc est double, nous voyant qu’il a fait l’erreur de raconter une histoire volée devant la personne qui la lui a racontée et lui réalisant qu’elle n’est pas à lui et peut être aussi qu’il s’est planté. Bref, tout ça est effectivement vertigineux. Reste que ce qui m’intéresse au delà de ça c’est le fait qu’il la raconte mieux qu’elle et que le témoin direct n’est pas celui qui va être le plus jouissif/intéressant à écouter.

[Ostros]

Cette scène est très forte. On se dit qu’elle joue avec lui. Que c’est son histoire a lui car dans le récit qui nous est fait c’est lui qui la raconte en premier et plusieurs fois et si bien. On se dit un bref instant qu’elle est intelligente et essaie d’entrer dans son jeu. Et à ce moment-là il y a eu une résistance chez moi, j’étais de son côté à lui. Pour moi c’était son histoire à lui, et elle qui lui avait piquée pour rire.
Et juste après, j’ai été déçue qu’elle ne soit pas joueuse avec cette histoire. Qu’elle lui rappelle que c’est elle qui la lui avait raconté, que c’est son vécu à elle. Si elle avait joué avec cette histoire ou une autre, cest à dire lui piqué un truc qu’il a dit (même s’il l’a lui même volé à qqun d’autre), si elle avait eu ce détachement-là elle me serait apparu comme nettement plus intéressante, haute.
Mais ce qu’on entrevoit de lui face à une personne qui jouerait à passer ses histoires dans sa bouche à elle, c’est que ça le trouble négativement. C’est pas quelque chose qui le ferait marrer. Ces accaparements d’histoires apparaît dans cette situation être quelque chose de sérieux pour lui. Pour elle c’est la vérité qui est une affaire sérieuse. Elle ne lui tient pas ouvertement rigueur d’avoir chipé son histoire, mais plus tard elle aura besoin de jouer la psy et de le faire parler de son passé. Cliché des thérapies. Et des discussions amicales qui rejouent les thérapies. C’est pour cela que je n’arrive pas à voir les images vides censées représenter des souvenirs comme autre chose que de l’ironie. Du cliché de l’enfance désolée. Qui répond au cliché de la conversation sérieuse, authentique de la copine qui cherche à aider / sauver son copain, forcément perdu (selon elle).
Le titre anglais est Impostor, je me demande si c’est aussi le titre original. Je trouve que ça gâche. Axiome c’est parfait.

[Schnoups]

Je l’aime bien moi cette discussion sur les souvenirs.
C’est la version tendre de la confrontation, pas de crise d’épilepsie, pas de couille sur table mais la question sur les souvenirs achève leur histoire.
C’est perturbant pour lui d’avoir quelqu’un en face qui te dit que non, ce souvenir n’est pas le tien, parce qu’à partir du moment où on l’a fait sien, c’est difficile de s’en détacher. Je vais parler d’un truc perso pour illustrer l’affaire. J’ai une sœur jumelle, une vraie, je le précise parce que la fusion a été intense, ce qui a son importance. Par fusion j’entends rapidement un effet de complémentarité par exemple dans les réactions face aux situations, si elle s’énervait trop je calmais, et vice versa. Et puis on déroulait des phrases semblables en même temps, les mêmes rêves les mêmes nuits, une façon aussi de se comprendre sans parler qui allait jusqu’à interpeller les potes. On a évidemment énormément de souvenirs communs ensemble. Certaines anecdotes sont précieuses, car drôles et assez remarquables, et sur certaines nous étions sûres elle comme moi que ce n’était pas à l’autre que c’était arrivé. Un jour on s’est vraiment vraiment franchement engueulées sur la paternité d’une histoire. Pour dire à quel point c’est perturbant : c’est avec ce genre de choses qu’on commence à se dire que c’est allé trop loin, qu’il faut mettre des distances. On avait pourtant l’habitude de ça et accepté l’impossibilité de détacher les souvenirs d’enfances par exemple. Mais des souvenirs d’adultes récents, c’était différent.
Je bifurque un peu, l’an dernier j’ai revu toutes les interventions télé d’Eric et Ramzy, tout ce que j’ai pu trouver parce que c’est là qu’ils me font le plus rire et que leur relation me plait beaucoup. Ils ont eu une amitié très proche, très intense, très semblable de celle que j’ai eue avec ma sœur, jusqu’à leur affiche de spectacle avec leurs visages mélangés et ensuite il y a eu rupture entre eux. C’est pas possible de tenir comme ça trop longtemps, si on continue on perd quelque chose.
Julius ne cesse d’avancer et de changer d’interlocuteur, s’il ne le fait pas tout s’écroule, il ne tient pas la durée, cette manière d’exister ne peut être qu’éphémère, découpée.

[Claire N]

Merci ! J’adore ton post, c’est fascinant limite fantastique

[Claire N]

En échange je te file une histoire historique vraie
Sur le lien entre frères / sœurs :
On m’a raconté que l’inventeur de l’EEG avait un jour fait une chute de cheval ou il avait failli perdre la vie, une grande terreur s’était emparée de lui .
Il entretenait une correspondance avec sa sœur
Dans la lettre qu’il reçu quelques temps après sa frayeur ; sa sœur lui écrit un sentiment presque paranormal d’inquiétude pour la vie de son frère l’ayant envahi le jour de cette chute dont elle ne savait rien
Il se mis alors en tête d’expliquer cette expérience ; avec comme hypothèses scientifiques de départ que des ondes cérébrales pouvaient permettre une communication entre les etres
Il ne trouva pas ce qui l’avait mu dans la recherche, mais découvrit effectivement un moyen d’enregistrer l’activité cérébrale et l’EEG dont l’utilisation est toujours considérée comme scientifique fiable et sérieuse
C’est un petit clin d’œil à la «  crise «  de Julius au passage

[Malice]

Dans un registre moins paranormal mais après tout peut-être un peu quand même, je signale Camille Kouchner et son frère jumeau, atteints de maladies pulmonaires au même moment de leurs vies où le passé douloureux du frère commençait à sérieusement leur entamer le moral ( j’euphémise)

[Schnoups]

Merci pour la petite histoire, c’est sûr que c’est étrange les jumeaux.

[nefa]

avec axiome, ce qui m’a bien touché, outre le film, c’est dans le post à Fanny : « Aussi rien de nouveau sous le soleil, entre les particules en suspension, une main ressemble toujours à une main,… »

Cinéma – Page 9

[nefa]

le lien va pas au #56444
donc controlf Fanny, quatrième occurrence

[Malice]

ps bon retour à Schnoups, tu deviens quoi?

[Schnoups]

Et coucou Malice
ça va, j’ai trouvé un boulot où je travaille le jours avec tous mes mercredis, mes WE, et vacances scolaires. Je suis, je suis ?
Non! pas prof. Je suis AESH dans un lycée professionnel et je m’éclate. C’est un poil précaire mais c’est passionnant. On verra sur la durée.
Après être passée par les usines, Leclerc, astsem, le boulot de nuit et les Serres du Forez, c’est le paradis, ça faisait 7 ans que j’étais pas restée plus de 3 mois sur un même boulot. Leclerc les amis, mise en rayon chez Leclerc c’était quelque chose. J’ai regretté de pas avoir tenu plus de 5 semaines.
Et j’emménage dans un mini hameau au-dessus d’un boulanger, avec poules, ânes et surtout, surtout des toilettes sèches.

[Tony]

T’es où dans le forez?si c’est pas indiscret?

[Schnoups]

Augerolles, une modeste bourgade pas loin de Courpière, entre Thiers et Ambert.
Tu connais ?
ça va, ton gros orteil gauche ?

[Tony]

Non,je connais la plaine du Forez mais côté Montbrison,toi t’es plutôt du côté de Clermont,enfin je crois que c’est dans ces coins là,la cambrousse quoi!
J’ai pas compris la blague sur l’orteil, j’ai jamais rien eu à signaler à cet endroit?

[Tony]

Sinon oui ça va,on est presque en vacances!

[Schnoups]

Ouais c’est la cambrousse.
Sur cinéma page 9, j’ai révélé au monde que je t’avais conseillé Axiome avant François pensant que tu te jetterais dessus et que, follement conquis par ce bijou, tu te serais ensuite précipité sur ton clavier pour le conseiller aux sitistes. Comme tu ne l’as pas fait je proposais de te griller le gros orteil gauche au prochain barbecue.
J’étais contente de lire que tu l’as apprécié. Et je comprends aussi ton idée de dire qu’il y a comme une remise en question totale de ce qu’on a vu dans le film., avec la question de notre propre croyance de spectateur.

[Tony]

Ok j’avoue,bon c’était mal tombé quand tu me l’as conseillé j’ étais très occupé…en tout cas t’as bien fait de le signaler à François,on tous été ébloui grâce à toi!

[Schnoups]

Je vais pouvoir mourir en paix.
Sinon je conseille de revoir Pickpocket, ça raisonne bien avec Axiome.

[Auteur]

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