Dynamical mass matrices from moduli fields

TL;DR

This paper explores how fermion mass matrices in supergravity derived from superstring theories depend on moduli fields, revealing structures similar to models with $U(1)$ family symmetry and discussing implications for flavor physics.

Contribution

It demonstrates that moduli-dependent Yukawa matrices can naturally produce observed fermion hierarchies without inducing flavor-changing neutral currents.

Findings

Yukawa matrices resemble those from $U(1)$ family symmetry models

FCNC effects at Planck scale are zero due to soft terms

A dynamical scenario explains fermion mass hierarchies

Abstract

We review recent work on the structure of the fermion mass matrices in supergravity effective superstrings. They are generally given at low energy by non-trivial functions of the gauge singlet moduli fields. Interesting structures appear in particular if they are homogeneous functions of zero degree in the moduli. In this case we find Yukawa matrices very similar to the ones obtained by imposing a $U(1)$ family symmetry to reproduce the observed hierarchy of masses and mixing angles. The role of the $U(1)$ symmetry is played here by the modular symmetry. The Flavor Changing Neutral Currents effects at the Planck scale coming from the soft terms are identically zero. A dynamical scenario is discussed which allow to generate the observed hierarchies.