Renormalization-group evolution of the fermion mass matrices

TL;DR

This paper analyzes how fermion mass matrices evolve with energy scale using one-loop RGEs, identifying invariant unitary matrices and providing RGE-corrected mass matrices, especially for textures with zeros and tribimaximal mixing.

Contribution

It introduces a method to decouple RGEs for fermion mass matrices assuming dominant Yukawa couplings, enabling explicit RGE corrections for specific textures and mixing patterns.

Findings

Unitary matrices diagonalizing up-type quark and charged lepton masses are invariant with energy scale.

RGE corrections can be explicitly computed for fermion matrices with texture zeros.

The approach applies to lepton matrices with tribimaximal mixing.

Abstract

The one-loop renormalization-group equations (RGEs) running behavior of quark and lepton mass matrices with general structures are studied simultaneously. Suppose the non-linear terms of RGEs are dominated by the Yukawa couplings of top quark and {\tau} lepton, the unitary matrices that diagonalize the mass matrices of up-type quark and charged lepton in Hermitian basis are found as invariant with energy scale. Based on this result, we can decouple the RGEs and obtain the RGE corrected mass matrices of fermion. As examples, we consider the renormalization-group evolution of fermion matrices with four or five texture zeros and of lepton mass matrices which realize the tribimaximal mixing.