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Masse Des Neutrinos Et Physique Au-Delà Du Modèle Standard

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Masse Des Neutrinos Et Physique Au-Delà Du Modèle Standard œa UNIVERSITE PARIS-SUD XI THESE Spécialité: PHYSIQUE THÉORIQUE Présentée pour obtenir le grade de Docteur de l'Université Paris XI par Pierre Hosteins Sujet: Masse des Neutrinos et Physique au-delà du Modèle Standard Soutenue le 10 Septembre 2007 devant la commission d'examen: MM. Asmaa Abada, Sacha Davidson, Emilian Dudas, rapporteur, Ulrich Ellwanger, président, Belen Gavela, Thomas Hambye, rapporteur, Stéphane Lavignac, directeur de thèse. 2 Remerciements : Un travail de thèse est un travail de longue haleine, au cours duquel se produisent inévitablement beaucoup de rencontres, de collaborations, d'échanges... Voila pourquoi, sans doute, il me semble que la liste des personnes a qui je suis redevable est devenue aussi longue ! Tâchons cependant de remercier chacun comme il le mérite. En relisant ce manuscrit je ne peux m'empêcher de penser a Stéphane Lavignac, que je me dois de remercier pour avoir accepté d'encadrer mon travail de thèse et qui m'a toujours apporté le soutien et les explications nécessaires, avec une patience admirable. Sa grande rigueur d'analyse et sa minutie m'offrent un exemple que je m'évertuerai à suivre avec la plus grande application. Ces travaux n'auraient pas pu voir le jour non plus sans mes autres collaborateurs que sont Carlos Savoy, Julien Welzel, Micaela Oertel, Aldo Deandrea, Asmâa Abada et François-Xavier Josse-Michaux, qui ont toujours été disponibles et avec qui j'ai eu un plaisir certain a travailler. C'est avec gratitude que je remercie Asmâa pour tous les conseils et recommandations qu'elle n'a cessé de me fournir tout au long de mes études au sein de l'Université Paris XL Au cours de ces trois années de travail dans le domaine de la Physique Au-delà de Modèle Standard, j'ai bénéficié du contact de toute la communauté des théoriciens de la région. Je tiens donc à re­ mercier tout le groupe de Saclay, Philippe Brax, Christophe Grojean, Géraldine Servant, qui a su répondre à mes premières questions d'étudiant, ô combien naïves, Marc Chemtob qui m'a fourni une aide précieuse pour rédiger un projet de recherches épineux, et tous les postdocs, Michèle Frigerio, Marco Cirelli, Marc Thormeier et Arunansu Sil. Il ne faut surtout pas oublier non plus les étudiants, Nicolas Châtillon d'abord, qui m'a offert nombre de réponses et un support non-négligeable lors de mon arrivée au SPhT, mais aussi Cédric Delaunay. De même, j'ai pu profiter de l'expérience et du soutien de membres du Laboratoire de Physique Théorique d'Orsay, en particulier Emilian Dudas, Yann Mambrini, Gregory Moreau, ou encore Maria-Cristina Timirgaziu. Dés lors que l'on parle de mon séjour au Service de Physique Théorique du CEA, je ne peux non plus m'empêcher de mentionner l'efficacité admirable et l'invariable bonne humeur du personnel adminis­ tratif, tout particulièrement Sylvie, Laure et Claudine, qui m'ont facilité l'existence d'une manière qui ne peut être réellement appréciée, malheureusement, que lorsqu'elle fait défaut. Je remercie en général tous les membres du SPhT pour leur accueil, mais en particulier les étudiants qui ont su éclairer mes pauses déjeuner pendant ces trois ans : Gerhard, Jérôme le gallois, Alexey et Nicolas qui ont partagé mon bureau et accueilli mes remarques et questions impromptues avec calme et diplomatie, Constantin Simpson, Cristian (c'est trop de la balle !), Loïc dont la langue n'a jamais su trouver le chemin de sa poche, Sylvain et son flegme naturel et enfin Michael (la vérité est ailleurs Michael, continue de chercher !). Je me dois également de remercier Yves Charon, non seulement pour m'avoir, en tant que directeur d'école doctorale, fourni les moyens financiers de me consacrer à la recherche, mais aussi pour être toujours d'un soutien indéfectible envers "ses étudiants", ainsi que pour son énergie et la force de ses 3 4 convictions. Au sein de cette même école doctorale il me semble aussi inévitable de remercier Bertrand Delamotte, pour ses explications parfois illuminantes sur la renormalisation et surtout pour m'avoir ouvert une fascinante fenêtre sur le monde de la renormalisation non-perturbative et enfin Sylvie Loeffel, pour son aide et son écoute. N'oublions pas non plus les différents collègues de l'Université avec qui j'ai beaucoup apprécié cette première expérience d'enseignement que fut le monitorat ! Merci à Elias Khan d'avoir accepté d'être mon tuteur. Si je suis redevable à toutes les personnes précédentes d'avoir apporté leur contribution directe soit à la compréhension de mon domaine, soit à la bonne ambiance dans laquelle j'ai pu travailler au laboratoire, il n'en reste pas moins que je suis redevable également à tous ceux dont l'apport n'a pas été professionnel, mais qui ont, par leur soutien et leurs qualités humaines, contribué sans aucun doute à la réussite de ce projet. Les premières qui me viennent en tête immédiatement et qui ont, depuis bien plus longtemps que la durée de cette thèse, apporté un soutien indéfectible à toutes mes entreprises, y compris à mes études de physique fondamentale, sont bien entendu les membres de ma famille. Les occasions sont rares de remercier les gens qui sont présents au quotidien depuis si longtemps et je saisis cette opportunité de souligner un soutien qui s'est exprimé a tous les niveaux. Un grand merci à tous les gens de l'ASC AM avec qui j'ai partagé pains et pintes avec une joie toujours renouvelée ! N'ont pas manqué également de me changer les idées les sorties cinéphiles avec Aurore, les explorations culinaires du Soleil Levant avec Rémy ou encore les parties de badmington avec Benoit, qui ne sera jamais arrivé à hisser mon niveau à un degré acceptable... Je n'oublie pas non plus mes ex-collègues, Rémi et Brice, inimitables. D'une grande importance m'a aussi été le contact que j'ai gardé avec les "bordelais", Laurent, Math­ ieu, Damien, Alex, Thibaut et Gratouille, que j'ai virtuellement maltraités avec un immense plaisir ! Au rang des gens qui ont eu à me supporter sept jours sur sept, il faut absolument mentionner mes colocataires de Cernay et de Bures, Delphine, Mickaël, Sophie, Thibaut et surtout Mélanie (deux ans c'est quand même quelque chose !). Merci à Alexandre Astier pour les nombreux éclats de rire ! Certaines personnes, quant à elles, m'auront cotôyé autant dans la sphère privée que professionnelle et apporté de précieuses réflexions à plus d'un titre. Merci donc à Chloé Papineau et (une nouvelle fois) à Julien Welzel et tous mes voeux de réussite pour la suite ! Enfin je suis reconnaissant à Thomas Hambye et Emilian Dudas pour avoir accepté de rapporter ce manuscrit, ainsi qu'à Sacha Davidson, Ulrich Ellwanger, Belen Gavela et une fois encore Stéphane Lavignac et Asmâa Abada pour avoir accepté de faire partie du jury lors de ma soutenance. Contents 1 Introduction 7 2 Seesaw Mechanism and Supersymmetric Grand Unification 11 2.1 Seesaw basics 11 2.2 Supersymmetry 14 2.2.1 The supersymmetry algebra and its representations 15 2.2.2 Couplings and non-renormalisation 17 2.2.3 Supergraphs 20 2.3 Grand Unified Theories 21 2.3.1 A simple example : SU(5) 22 2.3.2 S"O(10) and the seesaw 24 2.3.3 Fermion masses 28 2.4 Leptogenesis 30 2.4.1 Baryon asymmetry 30 2.4.2 Sphalerons and electroweak phase transition 32 2.4.3 Basics of Leptogenesis 33 2.4.4 Boltzmann equations 36 2.4.5 Gravitino constraints 39 3 Left-Right Symmetric Seesaw and Leptogenesis 43 3.1 Left-Right symmetric seesaw mechanism 44 3.1.1 Seesaw Duality 44 3.1.2 Reconstruction procedure 45 3.1.3 Spectrum and mixings in a simple 5O(10) model 48 3.2 Phenomenological Consequences 54 3.2.1 Lepton Flavour Violation 55 3.2.2 Leptogenesis in the LR symmetric seesaw 57 3.3 Flavour Effects in Leptogenesis 59 3.3.1 Equilibrium of charged lepton couplings 59 3.3.2 Flavoured Boltzmann Equations 61 3.3.3 Contribution of A^ 63 3.4 A Model with Realistic Fermion Masses 66 3.4.1 Symmetric corrections 66 3.4.2 Anti-symmetric corrections 68 3.4.3 SUSY threshold corrections 70 3.5 Application to the Left-Right symmetric seesaw 72 3.5.1 Inclusion of flavours 72 5 6 3.5.2 Mass corrections 75 3.5.3 Dependence on the different parameters 75 3.6 Conclusion 79 4 Neutrino Masses in 5D Models 81 4.1 Introduction 81 4.2 Extra dimensions 82 4.2.1 Compactification 82 4.2.2 Orbifold 84 4.2.3 Branes and field localisation 86 4.2.4 New possibilities from extra dimensions 87 4.3 Supersymmetry in 5 dimensions 89 4.3.1 M = 1 SUSY in 5D as M = 2 SUSY in 4D 89 4.3.2 TV = 2 representations 90 4.3.3 R-symmetry and the Yukawa problem 91 4.4 Quantum corrections in flat extra-dimensional models 92 4.4.1 Non-renormalisability of extra-dimensional field theories 92 4.4.2 Chain of EFTs and power law running 94 4.5 A concrete MSSM model 96 4.5.1 4D results 97 4.5.2 Localisation and model building 98 4.5.3 Model with matter in the bulk 99 4.5.4 Model with matter on the brane 102 4.5.5 Conclusion 106 5 Conclusion 107 A Boltzmann Equations 109 B One Loop Computations in 5D Models 113 B.0.6 Actions 113 B.0.7 Useful KK sums 116 B.0.8 Wave function renormalisation 119 Chapter 1 Introduction The Standard Model (SM) of particle physics is the present theory describing extremely successfully the fundamental interactions of Nature (excluding Gravity).
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