Flavour Geometry and Effective Yukawa Couplings in the MSSM

TL;DR

This paper introduces a geometric method to analyze flavour structures in the MSSM, deriving conditions for basis independence and calculating effective Yukawa couplings at large tan(beta), emphasizing the role of non-universal soft terms.

Contribution

It develops a novel geometric framework for flavour decomposition in the MSSM and computes effective Yukawa couplings considering non-universal soft terms.

Findings

Conditions for basis independence in flavour space derived

Effective Yukawa couplings enhanced at large tan(beta) calculated

Non-universal soft terms significantly affect flavour-violating couplings

Abstract

We present a new geometric approach to the flavour decomposition of an arbitrary soft supersymmetry-breaking sector in the MSSM. Our approach is based on the geometry that results from the quark and lepton Yukawa couplings, and enables us to derive the necessary and sufficient conditions for a linearly-independent basis of matrices related to the completeness of the internal [SU(3) x U(1)]^5 flavour space. In a second step, we calculate the effective Yukawa couplings that are enhanced at large values of tan(beta) for general soft supersymmetry-breaking mass parameters. We highlight the contributions due to non-universal terms in the flavour decompositions of the sfermion mass matrices. We present numerical examples illustrating how such terms are induced by renormalization-group evolution starting from universal input boundary conditions, and demonstrate their importance for the flavour-violating effective Yukawa couplings of quarks.