Towards the minimal seesaw model via CP violation of neutrinos

TL;DR

This paper explores how CP violation in the minimal seesaw model with two right-handed neutrinos can determine the neutrino mass matrix structure, proposing new minimal Dirac mass matrices consistent with flavor symmetries and mixing patterns.

Contribution

It introduces new minimal Dirac neutrino mass matrices within the minimal seesaw framework, linking CP violation observations to flavor structure and residual symmetries, especially for the TM1 mixing pattern.

Findings

CP violating phase constrains Dirac mass matrix structure

New minimal Dirac mass matrices proposed for TM1 mixing

Reproduction of mass matrices via gauge singlet flavons with S4 symmetry

Abstract

We study the minimal seesaw model, where two right-handed Majorana neutrinos are introduced, focusing on the CP violating phase. In addition, we take the trimaximal mixing pattern for the neutrino flavor where the charged lepton mass matrix is diagonal. Thanks to this symmetric framework, the $3\times 2$ Dirac neutrino mass matrix is given in terms of a few parameters. Numerical studies reveal that the observation of the CP violating phase can determine the flavor structure of the Dirac neutrino mass matrix in the minimal seesaw model. In particular, new minimal Dirac neutrino mass matrices are proposed in the case of $\rm TM_1$, which is derived by the additional 2-3 family mixing to the tri-bimaximal mixing basis in the normal hierarchy of neutrino masses. Our analyses include the Littlest seesaw model by King {\it et al.}, which is one of the specific one in our results. Furthermore, it is remarked that our $3\times 2$ Dirac neutrino mass matrix is reproduced by introducing gauge singlet flavons with the specific alignments of the VEV's. These alignments suggest the residual symmetry of $S_4$ group.