A bottom-up approach to fermion mass hierarchy: a case with vector-like fermions

TL;DR

This paper explores how extending the standard model with vector-like fermions can naturally produce fermion mass hierarchies, suggesting that small Yukawa couplings may result from fine-tuning due to mixing effects.

Contribution

It introduces a bottom-up method to analyze fermion mass hierarchies using vector-like fermions, highlighting potential for Yukawa unification and sensitivity to parameter variations.

Findings

Yukawa coupling matrices can have elements of order one.

Yukawa coupling unification is possible beyond the extended model.

Mass hierarchies may arise from fine-tuning of matrix elements.

Abstract

We propose a bottom-up approach that a structure of a high-energy physics is explored by accumulating existence proofs and/or no-go theorems in the standard model or its extension. As an illustration, we study fermion mass hierarchies based on an extension of the standard model with vector-like fermions. It is shown that a magnitude of elements of Yukawa coupling matrices can become $O(1)$ and a Yukawa coupling unification can be realized in a theory beyond the extended model, if vector-like fermions mix with three families. In this case, small Yukawa couplings in the standard model can be highly sensitive to a small variation of matrix elements, and it seems that the mass hierarchy occurs as a result of a fine tuning.