Spontaneous CP violation and non-Abelian family symmetry in SUSY

Abstract

We analyse the properties of generic models based on an SU (3) family symmetry providing a full description of quark charged lepton and neutrino masses and mixing angles. We show that a precise fit of the resulting fermion textures is consistent with CP being spontaneously broken in the flavour sector. The CP violating phases are determined by the scalar potential and we discuss how symmetries readily lead to a maximal phase controlling CP violation in the quark sector. In a specific model the CP violation to be expected in the neutrino sector is related to that in the quark sector and we determine this relation for two viable models. In addition to giving rise to the observed structure of quark and lepton masses this class of model solves both the CP and flavour problems normally associated with supersymmetric models. The flavour structure of the soft supersymmetry breaking terms is controlled by the family symmetry and we analyse some of the related phenomenological implications.

Exotic particles below the TeV from low scale flavour theories

“…The next step is to fulfill the no-anomaly requirements 10) corresponding to the vanishing of the strong, weak isospin, and the the two weak hypercharge anomalies, respectively. Since Q em = Y + T 3 , has vector-like representations, it is convenient to replace A Y and A ′ Y by the corresponding A em , more directly related to the X-chiralities fitted to fermion masses, and A ′ em (linear in Q em ).…”

Constraints on supersymmetric flavour models fromb→sγ

“…(13). This equation represents the most general parameterization of the Yukawa matrices for quarks and charged leptons with an SU(3) FS [2,3]. In any supersymmetric FS, the flavon fields also couple to the sfermions through the trilinear terms…”

“…The supersymmetric corrections change the profile of Yukawa matrices at the GUT scale. A SM analysis [2] determined the values for Y d (for symmetric matrices) as follows:…”

“…In this sense, it is natural to assume that FS can be postulated assuming these MFV conditions. If FS are embedded in a supersymmetric grand unified theory (GUT) [1,2], the Yukawa matrices have a well defined structure which contains off-diagonal terms at M GUT and which evolve to the EW scale, reproducing the observed fermion masses and mixings. However, every possible assumption for the supersymmetric flavour structure at M GUT can not be compatible with this version of MFV.…”

“…The approach we take here makes use of an underlying supergravity theory with an effective Kähler potential from which one can construct the potential and through minimization, calculate the soft squared masses and trilinear couplings. It turns out that in supersymmetric theories with non-Abelian FS, the Kähler potential [2] has fewer model dependent parameters than other sectors of the theory and hence can be effectively used to impose the size of the off-diagonal terms of soft squared mass and trilinear mass matrices at M GUT . Using the powerful tools of supergravity, one can then determine the structure in the supersymmetric sector at M GUT and test its consequences at the EW scale.…”