Naturally large Yukawa hierarchies

TL;DR

This paper proposes a mechanism where spontaneous breaking of flavor symmetry naturally generates large Yukawa hierarchies and realistic quark mixing matrices, aligning with the minimal flavor violation hypothesis.

Contribution

It introduces a model with scalar Yukawa fields and logarithmic terms that produce exponential hierarchies and realistic mixing, a novel realization of flavor symmetry breaking.

Findings

Yukawa hierarchies emerge naturally from the model.

Quark mixing matrix approaches a diagonal form.

The scenario aligns with minimal flavor violation.

Abstract

The spontaneous breaking of the $SU(3)^5$ quark/lepton flavor symmetry by means of three multiplets of scalar `Yukawa fields' admits vacua with one O(1) and two vanishing vacuum expectation values (vevs) for each multiplet. If the number of generations is equal to three, and only in this case, the vanishing vevs are lifted to exponentially suppressed entries by the inclusion of symmetry invariant logarithmic terms. A strong hierarchy for the Yukawa couplings and a quark mixing matrix that approaches a diagonal form are obtained in a natural way from O(1) parameters. This scenario provides a concrete realization of the minimal flavor violation hypothesis.