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Dynamical Yukawa Couplings

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Dynamical Yukawa Couplings Dynamical Yukawa Couplings Memoria de Tesis Doctoral realizada por Rodrigo Alonso de Pablo y dirigida por Bel´enGavela Legazpi Catedr´aticadel Departamento de F´ısica Te´orica Universidad Aut´onomade Madrid Presentada ante el Departamento de F´ısicaTe´orica arXiv:1307.1904v1 [hep-ph] 7 Jul 2013 de la Universidad Aut´onomade Madrid para la obtenci´ondel T´ıtulo PhilosophiæDoctor (PhD) Madrid Junio de 2013 ii Tribunal Presidente Luciano Maiani Secretaria Maria Jos´eHerrero Vocales Alberto Casas Christophe Grojean Alejandro Pomarol Suplentes Pilar Hern´andez Stefano Rigolin Expertos Doctores Gino Isidori Silvia Pascoli Contents List of Figures iii List of Tables v 1 Objetivo y motivaci´on 1 2 Aim and Motivation 5 3 Introduction 9 3.1 Forces of the Standard Model . .9 3.2 Matter Content . 12 3.2.1 Neutrino Masses . 14 3.2.2 The Flavour Symmetry . 16 4 Flavour Physics 21 4.1 Flavour in the Standard Model + type I Seesaw Model . 21 4.2 Flavour Beyond the Standard Model . 25 4.3 Flavour Phenomenology . 27 4.4 Minimal Flavour Violation . 29 5 Spontaneous Flavour Symmetry Breaking 31 5.1 Flavour Fields Representation . 33 5.2 The Scalar Potential . 36 5.2.1 Generalities on Minimization . 37 i CONTENTS 6 Quark Sector 41 6.1 Bi-fundamental Flavour Scalar Fields . 41 6.1.1 Two Family Case . 41 6.1.1.1 The Jacobian . 44 6.1.1.2 The Potential at the Renormalizable Level . 48 6.1.1.3 The Potential at the Non-Renormalizable Level . 56 6.1.2 Three Family Case . 57 6.1.2.1 The Jacobian . 59 6.1.2.2 The Potential at the Renormalizable Level . 65 6.1.2.3 The Potential at the Non-Renormalizable Level . 68 6.2 Flavour Scalar Fields in the Fundamental . 69 6.2.1 The Potential at the Renormalizable Level . 71 6.3 Combining fundamentals and bi-fundamentals . 74 7 Lepton Sector 77 7.1 Two Family Case . 78 7.1.1 The Jacobian . 81 7.1.2 The Potential at the Renormalizable Level . 83 7.2 Three Family case . 88 7.2.1 The Jacobian . 90 7.2.2 The Potential at the Renormalizable Level . 92 7.2.3 Realistic mixing and spectrum . 100 8 Resumen y Conclusiones 103 9 Summary and Conclusions 109 10 Appendix 115 q 10.1 GF -invariant renormalizable potential formulae of the vevs of YD;U 115 l 10.2 GF -invariant renormalizable potential formulae of the vevs of YE,ν 117 10.3 Perturbations on a extremal degenerate neutrino matrix . 120 References 125 ii List of Figures 3.1 The three types of seesaw model . 15 4.1 Experimentally allowed regions for the CKM mixing parametersρ ¯ andη ¯ .................................. 28 5.1 Yukawa Couplings as vevs of flavour fields . 32 q 6.1 I-manifold spanned by GF invariants built with YU;D for fixed IU , ID and 2 quark generations . 47 6.2 Regions for the different quark mass configurations allowed at the absolute minimum in the hU − hD plane for g < 0 . 54 q 6.3 I-manifold spanned by GF invariants built with YU for fixed IU and 3 quark generations . 63 7.1 Regions for the different lepton mass configurations allowed at the absolute minimum in the hν − hE plane for g < 0 . 99 iii LIST OF FIGURES iv List of Tables 3.1 The Higgs field charges under G ................... 11 3.2 Fermion content of the SM . 13 3.3 Right-handed neutrino charges under the SM group . 15 3.4 Representations of the fermion fields under the non-abelian part of GF .................................. 17 3.5 Representations of the fermion fields under the abelian part of GF 17 4.1 Bounds on the different operators, see text for details. 29 4.2 Spurious transformations of the Yukawa couplings under GF ... 30 q 5.1 GF representation of the quark sector bi-fundamental scalar fields for ng fermion generations . 33 l 5.2 GF representation of the lepton sector bi-fundamental scalar fields for ng fermion generations . 33 5.3 Representation of the quark sector fundamental scalar fields for ng fermion generations . 34 5.4 Representation of the lepton sector fundamental scalar fields for ng fermion generations . 35 v LIST OF TABLES vi Glossary J - Jacobian of the change of coordinates from the physical parameters to the invari- ants LHC - Large Hadron Collider ME - Modelo Est´andar CKM - Cabibbo-Kobayashi-Maskawa [quark n - Number of fermion generations mixing matrix] g NH - Normal Hierarchy CP - Parity and Charge conjugation PJ - Problema de la Jerarqu´ıa EFT - Effective Field Theory EWSB - Electroweak Symmetry Breaking PMNS - Pontecorvo-Maki-Nakagawa- FCNC - Flavour Changing Neutral Current Sakata [lepton mixing matrix] FSB - Flavour Symmetry Breaking QFT - Quantum Field Theory G - Gauge Group of the Standard Model: QCD - Quantum Chromodynamics RESE - Rotura Espont´anea de Simetr´ıa SU(3)c × SU(2)L × U(1)Y 5 Electrod´ebil GF - Flavour Group: U(ng) × O(ng) A= SM - Standard Model GF - Explicitly Axial Symmetry Breaking 5 case Flavour Group: SU(ng) × SO(ng) Y - Flavour scalar fields in the bi- GIM - Glashow-Iliopoulos-Maiani [mecha- fundamental representation nism] χ - Flavour scalar fields in the fundamental HP - Hierarchy Problem representation IH - Inverted Hierarchy LIST OF TABLES viii 1 Objetivo y motivaci´on El campo de f´ısicade part´ıculasse encuentra actualmente en un punto crucial. La exploraci´ondel mecanismo de rotura espont´aneade simetr´ıaelectrod´ebil(RESE) en el gran colisionador de hadrones (LHC) ha desvelado la presencia de un bos´on que se asemeja al escalar de Higgs (1, 2) dada la precisi´onde los datos exper- imentales disponibles (3, 4). La descripci´ondel Modelo Est´andar (ME) de la generaci´onde masas (5, 6, 7) ha demostrado ser acertada y la auto-interacci´on del bos´onde Higgs que desencadena la RESE es ahora la quinta fuerza de la naturaleza, junto con la gravedad, el eletromagnetismo la interacci´ond´ebil y la fuerte. Esta nueva fuerza, como el resto de las fuerzas cuantizadas, var´ıaen inten- sidad dependiendo de la escala a la que se la examine, pero al contrario que la fuerza d´ebilo fuerte, esto plantea un problema (8) ya que a una escala de alta energ´ıao corta distancia del orden de 10−12fm el mecanismo de RESE se deses- tabilizar´ıa,pues el acoplo cu´articose cancelar´ıa(9, 10). Dicho problema podr´ıa ser resuelto por la introducci´onde nueva f´ısica,lo cual conduce a otra cuesti´on te´orica,el Problema de la Jerarqu´ıa(PJ). Cualquier tipo de nueva f´ısicaque se acople a la part´ıculade Higgs produce gen´ericamente una contribuci´onradiativa al t´erminode masa de dicho bos´ondel orden de la nueva escala, lo que significar´ıa que la escala electrod´ebiles naturalmente cercana a la escala de f´ısicam´asalta que interacciona con los campos del ME. Las propuestas para solucionar este problema pueden ser clasificadas en soluciones de f´ısicaperturbativa, siendo el paradigma la supersimetr´ıa,y ansazts de din´amica fuerte. Supersimetr´ıaes una 1 1. OBJETIVO Y MOTIVACION´ elegante simetr´ıaentre bosones y fermiones que implica cancelaciones sistem´aticas entre las contribuciones radiativas bos´onicasy fermi´onicas al t´erminode masa del Higgs. Por otro lado la hip´otesisde que el bos´onde Higgs sea un estado ligado producido por nueva din´amicafuerte implica que el mecanismo de RESE del ME es simplemente una descripci´onefectiva que debe ser completada por una teor´ıa m´asfundamental. Todas estas hip´otesissuponen naturalmente nueva f´ısicaa la escala del TeV y est´ansiendo testeadas de manera decisiva en el LHC. En el frente cosmol´ogico la interacci´on gravitatoria ha sido la fuente de nuevos desaf´ıosen f´ısicade part´ıculas. El universo est´aexpandi´endoseaceleradamente, algo que en cosmolog´ıaest´andarrequiere la presencia de \energ´ıaoscura", una energ´ıade vac´ıocuya presi´onnegativa provoca que el universo se ensanche con velocidad creciente. Estimaciones naif en la teor´ıaest´andarde la contribuci´on a este tipo de energ´ıadifieren del valor observado 120 ´ordenesde magnitud, un hecho que muestra enf´aticamente nuestra ignorancia sobre la naturaleza de la energ´ıaoscura. Cosmolog´ıay astrof´ısicaproporcionaron la s´olidaevidencia de materia extra no bari´onicaen el universo, llamada `materia oscura", como otra muestra experimental no explicable en el ME. Hay un activo programa experi- mental para la b´usquedade materia oscura en este din´amicosector de f´ısica de part´ıculas.La tercera evidencia de nueva f´ısicaen cosmolog´ıaproviene de un he- cho muy familar del mundo visible: est´aconstituido de mucha mas materia que antimateria, y aunque el ME proporciona una fuente de exceso de part´ıculassobre antipart´ıculasel resultado no es suficiente para explicar la proporci´onobservada. La parte de nueva f´ısicaque concierne m´asde cerca al ME es el hecho de que los neutrinos han demostrado ser masivos. La evidencia de masa de neutrinos proveniente de los datos de oscilaci´ones una de las selectas evidencias de nueva f´ısica mas all´adel ME. En este sector la b´usquedade violaci´onlept´onicade conjugaci´onde carga y paridad (CP), transiciones de sabor de leptones cargados y la relaci´onfundamental entre neutrinos y antineutrinos; su car´acterMajorana o Dirac, tienen ambiciosos programas experimentales que producir´an resultados en los pr´oximosa~nos. Para completar la lista de desaf´ıos en f´ısica de part´ıculas, deben ser men- cionados la tarea pendiente de la cuantizaci´onde gravedad y el presente pobre entendimiento del vac´ıode QCD representado en el problema-θ. 2 El tema de esta tesis es un problema horizontal: el puzle de sabor.
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