Naturalness and the Neutrino Matrix

TL;DR

This paper explores how neutrino mass and mixing data influence the structure of fermion mass matrices in grand unified theories, emphasizing natural hierarchical forms and potential model-building strategies.

Contribution

It demonstrates that naturalness assumptions lead to hierarchical Majorana and cascade Dirac neutrino matrices, and discusses model variations including partially lopsided matrices.

Findings

Hierarchical Majorana mass matrix for right-handed neutrinos

Partially cascade form for Dirac neutrino matrix

Partially lopsided matrices can help build natural models

Abstract

The observed pattern of neutrino mass splittings and mixing angles indicates that their family structure is significantly different from that of the charged fermions. We investigate the implications of these data for the fermion mass matrices in grand unified theories with a type-I seesaw mechanism. We show that, with simple assumptions, naturalness leads to a strongly hierarchical Majorana mass matrix for heavy right-handed neutrinos and a partially cascade form for the Dirac neutrino matrix. We consider various model building scenarios which could alter this conclusion, and discuss their consequences for the construction of a natural model. We find that including partially lopsided matrices can aid us in generating a satisfying model.