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The access to the contents of this doctoral thesis it is limited to the acceptance of the use conditions set by the following Creative Commons license: https://creativecommons.org/licenses/?lang=en Supersymmetry with custodial triplets Mateo Garc´ıaPepin Director de tesi: Tutor de tesi: Prof. Mariano Quir´osCarcel´en Prof. Alex Pomarol Clotet Mem`oriade recerca presentada per a l’obtenci´odel t´ıtolde Doctor en F´ısica Institut de F´ısicad'Altes Energies Departament de F´ısica- Facultat de Ci`encies, Universitat Aut`onomade Barcelona May 2016 Agradecimientos / Acknowledgments Me gustar´ıaagradecer a mi director de tesis, Mariano Quir´os,todo su apoyo y dedicaci´on. iii Resumen / Abstract Gracias a resultados experimentales pero tambi´ena argumentos te´oricos,sabemos que el Modelo Est´andarde la f´ısicade part´ıculases solo una descripci´ona bajas energ´ıasde una estructura m´as fundamental. Supersimetr´ıa,una simetr´ıadel espacio-tiempo que relaciona bosones y fermiones, proporciona algunos de los candidatos para completar el Modelo Est´andarm´asfavorecidos desde un punto de vista te´orico.Sin embargo, la b´usquedasin resultado de part´ıculassupersim´etricas pone a estos modelos bajo cierta tensi´on, sobre todo porque muchas de las propiedades de super- simetr´ıaen su aplicaci´ona la f´ısicade part´ıculasest´andirectamente relacionadas con su presencia a escalas de energ´ıadel orden de las que est´ansiendo exploradas en LHC. Sin evidencias directas de supersimetr´ıa,>existe alguna medici´onindirecta que los f´ısicosde part´ıculaspodr´ıanusar para estudiar estos modelos? La part´ıculade Higgs descubierta en 2012 en LHC no es solo la ultima pieza del Modelo Est´andar,tambi´enes una nueva ventana que podr´ıaser ´util en el estudio de f´ısicam´asall´adel Modelo Est´andar. En la primera parte de esta tesis estudiamos las consecuencias del descubrimiento del bos´on de Higgs para versiones m´ınimas(construidas con el menor numero posible de elementos) de supersimetr´ıa. Encontramos que la masa del Higgs es m´aspesada de lo que uno esperar´ıaen las extensiones supersim´etricasdel Modelo Est´andarm´asm´ınimas.Por lo tanto concluimos que puede que la b´usquedade \minimalidad" a la hora de formular teor´ıas m´asall´adel Modelo Est´andar,no sea el camino m´asadecuado en este caso. Por eso construimos una realizaci´onun poco m´as\barroca" de supersimetr´ıacon la esperanza de que solucione el problema de la masa del Higgs, la teor´ıase llama \Modelo de Tripletes con Simetr´ıaCustodial". Este modelo presenta un sector de Higgs extendido y usa simetr´ıaspara resolver algunos de los problemas asociados a la introducci´onde nuevos grados de libertad en el potencial escalar de una teor´ıa,al mismo tiempo, es capaz de proporcionar una masa para el Higgs en acuerdo con la medici´onexperimental. Dedicamos la segunda parte de la tesis al estudio pormenorizado del Modelo de Tripletes con Simetr´ıaCustodial, de donde derivamos resultados muy interesantes con aplicaciones tanto en f´ısicade part´ıculascomo en cosmolog´ıa. v We know from experimental results but also from theoretical arguments that the very successful Standard Model of particle physics is just a low energy description of a more fundamental struc- ture. Supersymmetry, a space-time symmetry that relates bosons and fermions, provides some of the most theoretically favored candidates to complete the Standard Model. However, null results in the searches for supersymmetric particles put these models under stress, specially since many of the nice properties of supersymmetry at the particle physics level are directly tied with its presence at the energy scales that are now being probed at the LHC. With no direct evidence for supersymmetry, is there an indirect measurement that particle physicists could use to test these models? In 2012 the Higgs particle was discovered at LHC. Its discovery gives closure to the Standard Model but also opens up a new window that could be useful in the study of physics beyond the Standard Model. In the first part of this thesis we study the consequences of the Higgs discovery for minimal versions of supersymmetry. We find that the measured mass of the Higgs particle is heavier than what is expected by the minimal realizations of a supersymmetric Standard Model. We thus consider that the search for minimality, i.e. building models with the least number of elements, in the formulation of beyond the Standard Model theories may not be such a good guiding principle in this case and construct a more baroque realization of supersymmetry, the Supersymmetric Custodial Triplet Model. This theory features an extended Higgs sector and uses symmetry as a tool to get rid of some of the problems associated with the introduction of new degrees of freedom to the scalar potential of a theory, at the same time, it is able to provide a Higgs that fits properly the experimental measurement of its mass. We devoted the second part of the thesis to an in depth study of the Supersymmetric Custodial Triplet Model, deriving very interesting results that can be useful both for particle physics, and cosmology. vi List of published works REFEREED ARTICLES 1. Diphoton and Diboson Probes of Fermiophobic Higgs Bosons at the LHC Antonio Delgado, Mateo Garcia-Pepin, Mariano Quiros, Jose Santiago, Roberto Vega-Morales Submitted to PRD for publication, arXiv:1603.0096 [hep-ph] 2. Strong electroweak phase transition from Supersymmetric Custodial Triplets Mateo Garcia-Pepin, Mariano Quiros Submitted to JHEP for publication, arXiv:1602.01351 [hep-ph] 3. GMSB with Light Stops Antonio Delgado, Mateo Garcia-Pepin, Mariano Quiros JHEP 1508 (2015) 159, arXiv:1505.07469 [hep-ph] 4. Dark Matter from the Supersymmetric Custodial Triplet Model Antonio Delgado, Mateo Garcia-Pepin, Bryan Ostdiek, Mariano Quiros Phys. Rev. D 92, no. 1, 015011 (2015), arXiv:1504.02486 [hep-ph] 5. Supersymmetric Custodial Higgs Triplets and the Breaking of Universality Mateo Garcia-Pepin, Stefania Gori, Mariano Quiros, Roberto Vega, Roberto Vega-Morales, Tien-Tien Yu Phys. Rev. D 91, no. 1, 015016 (2015) , arXiv:1409.5737 [hep-ph] 6. Electroweak and supersymmetry breaking from the Higgs boson discovery Antonio Delgado, Mateo Garcia-Pepin, Mariano Quiros Phys. Rev. D 90 (2014) no.1, 015016, arXiv:1312.3235 [hep-ph] 7. Supersymmetric Custodial Triplets Luis Cort, Mateo Garcia-Pepin, Mariano Quiros Phys. Rev. D 88 (2013) no.7, 075010 , arXiv:1308.4025 [hep-ph] CONFERENCE PROCEEDINGS 1. Gauge mediation with light stops Antonio Delgado, Mateo Garcia-Pepin, Mariano Quiros Planck 2015, Ioannina (Greece) PoS PLANCK 2015 (2015) 109, arXiv:1511.03254 [hep-ph] vii Contents Agradecimientos / Acknowledgments iii Resumen / Abstractv Published works vii Abbreviations xiii Introduction1 Part I: Particle physics in the LHC era9 1 The Standard Model of particle physics9 1.1 Particle content and Lagrangian............................9 1.2 Electroweak symmetry breaking............................. 11 1.3 SM accidental symmetries and custodial symmetry.................. 16 1.4 Open puzzles in fundamental physics.......................... 18 1.5 The hierarchy problem and naturalness........................ 19 2 Supersymmetry and the MSSM 25 2.1 What is supersymmetry?................................ 25 2.2 N = 1 supersymmetric field theories.......................... 26 2.3 Supersymmetry breaking................................. 30 2.4 The MSSM......................................... 35 2.5 The importance of the scale............................... 37 2.6 Further phenomenological advantages of SUSY.................... 39 3 The MSSM after the Higgs discovery 41 3.1 EWSB in SUSY with a 125 GeV Higgs......................... 42 3.2 The messenger scale ................................. 47 M 3.3 Discussion: 0 and the reasons to go beyond the MSSM............... 53 Q ix Contents Part II: Supersymmetric custodial triplets 57 4 The Supersymmetric Custodial Triplet Model 57 4.1 Triplets and custodial symmetry: The GM model................... 58 4.2 Introduction to the SCTM: Tree level definitions................... 59 4.3 The Higgs sector..................................... 62 4.4 Parameter dependece and decoupling considerations................. 66 4.5 The fermion sector.................................... 70 4.6 Comments about unitarity restoration in the model.................. 72 4.7 A study of the light Higgs behavior........................... 73 4.8 Discussion: Towards the realistic SCTM........................ 76 5 The SCTM at the quantum level 79 5.1 Custodially breaking SCTM............................... 79 5.2 A study with universal soft terms............................ 81 5.3 Gauge mediated supersymmetry breaking in the SCTM............... 90 5.4 Discussion: General features of the SCTM....................... 101 6 DM phenomenology with custodial triplets 105 6.1 The status of neutralino DM.............................. 105 6.2 Phenomenological approach to the SCTM....................... 106 6.3 Dark matter phenomenology.............................. 113 6.4 Discussion......................................... 120 7 Properties