Studies on Generalized Warped Five-Dimensional Models

Abstract

Durant la passada d`ecada, els models de dimensions extra corbades han estat estudiats com a candidats per a completar el Model Est`andard (ME) de la f´ısica de part´ıcules. En aquesta tesi estudiarem una s`erie d’aspectes dels models amb una dimensi´o extra corbada; en particular, la possibilitat de generalitzar la ben coneguda soluci´o de Randall-Sundrum (RS), la qual es basa en la m`etrica Anti-de Sitter (AdS). Primer, discutim la construcci´o dels models de soft-wall, que s´on una modificaci ´o de RS on la brana infraroja ha sigut substitu¨ıda per una singularitat nua a la m`etrica. Donem receptes per a construir models consistents d’aquests tipus i estudiem com la longitud de la dimensi´o extra pot ser estabilitzada. Tamb´e estudiem l’espectre de les fluctuacions que apareixen en els models de soft-wall, i trobem que podem obtenir des d’un espectre continu a partir d’una certa massa fins a un espectre discret amb un espaiament variable. Discutim les possibles aplicacions dels models de soft-wall, i finalment presentem un model concret on es pot generar una jerarquia ultravioleta/infraroja prou gran sense necessitat de cap ajust fi. Despr´es, retornem a la construcci´o original amb dues branes per tal d’estudiar com la simetria electrod`ebil pot ser trencada en models amb m`etriques generalitzades quan el bos´o de Higgs es propaga a l’engr´os de la dimensi´o extra. Veiem com les cotes sobre l’escala dels modes de Kaluza-Klein (KK), que apareixen a causa dels observables electrod`ebils de precisi´o, poden ser redu¨ıdes quan el Higgs est`a localitzat a prop de la brana infraroja. Apliquem els nostres resultats a una extensi´o m´ınima del ME en 5D, i considerem la geometria AdS i una deformaci´o d’aquesta inspirada pels models de soft-wall. Trobemque la geometria deformada redueix enormement les cotes sobre l’escala de KK, fins al punt en qu`e els estats de KK es poden trobar dins del rang de l’LHC i el problema de la petita jerarquia pot ser eliminat sense requerir la introducci´o de cap simetria custodial. Finalment, estudiem la propagaci´o de tots els fermions del ME al llarg de la dimensi´o extra, la qual cosa fem servir per tractar el problema del sabor en el ME. Trobem expressions generals i expl´ıcites per als observables electrod`ebils oblics i no oblics, aix´ı com per als operadors que violen sabor i la simetria CP. Apliquem aquest resultat al model RS i al model amb geometria deformada, per la qual cosa fem un estudi estad´ıstic a partir d’un conjunt aleatori d’acoblaments de Yukawa en 5D. La comparaci´o de les prediccions amb les dades experimentals actuals mostren una millora de les cotes en el nostre model en comparaci´o amb RS.

Models of warped extra-dimensions have been studied over the last decade as candidates to complete the Standard Model (SM) of particle physics, for they provide a natural mechanism to address its hierarchy problem. In this thesis we study a number of aspects of the five-dimensional warped models, and in particular the possibility of generalizing the well-known Randall-Sundrum (RS) solution, which is based on the Anti-de Sitter metric (AdS). We first discuss on the construction of soft-wall models, which are a modification of RS where the infrared brane is substituted by a naked singularity in the metric. We provide recipes for constructing consistent models of this kind and address the issue of how the length of the extra dimension can be stabilized. We also discuss on the spectrum of fluctuations that arise in soft-wall models, finding that it can range from a continuous spectrum above a mass gap to a discrete spectrum with a variable level spacing. We discuss on the possible applications of soft-wall models, and finally present a concrete model where a large ultraviolet/infrared hierarchy can be generated without any fine-tuning. Next, we return to the original two-brane setup to study how the electroweak symmetry can be broken in warped models with generalized metrics when the Higgs boson propagates in the bulk. We show how the bounds on the Kaluza-Klein (KK) scale that arise from electroweak precision observables can be alleviated when the Higgs is localized towards the infrared brane. We apply our results to a minimal 5D extension of the SM and consider the AdS geometry and a deformation of it inspired by soft-walls. We find that the deformed geometry greatly reduces the bounds on the KK scale, to a point where the KK states can be within the range of the LHC and the little hierarchy problem can be removed without requiring the introduction of any custodial symmetry. Finally, we study the propagation of all SM fermions in the bulk of the extra dimension, which we use to address the flavor puzzle of the SM. We find general explicit expressions for oblique and non-oblique electroweak observables, as well as flavor and CP violating operators. We apply these results to the RS model and the model with deformed geometry, for which we perform a statistical analysis departing from a random set of 5D Yukawa couplings. The comparison of the predictions with the current experimental data exhibits an improvement of the bounds in our model with respect to the RS model.