Leptonic CP Violation Induced by Approximately mu-tau Symmetric Seesaw Mechanism

TL;DR

This paper explores how approximate mu-tau symmetry in a minimal seesaw model influences leptonic CP violation, linking CP phases to symmetry-breaking interactions and analyzing their effects on neutrino mixing.

Contribution

It demonstrates how mu-tau symmetry breaking interactions generate CP phases and connects the neutrino mass hierarchy to symmetry properties in a minimal seesaw framework.

Findings

CP-violating Majorana phase is suppressed to about 0.1 radians.

CP-violating Dirac phase is proportional to symmetry-breaking phases alpha and beta.

Normal hierarchy corresponds to mu-tau symmetry in heavy neutrinos.

Abstract

Assuming a minimal seesaw model with two heavy neutrinos (N), we examine effects of leptonic CP violation induced by approximate mu-tau symmetric interactions. As long as N is subject to the mu-tau symmetry, we can choose CP phases of Dirac mass terms without loss of generality in such a way that these phases arise from mu-tau symmetry breaking interactions. In the case that no phase is present in heavy neutrino mass terms, leptonic CP phases are controlled by two phases alpha and beta. The similar consideration is extended to N blind to the mu-tau symmetry. It is argued that N subject (blind) to the mu-tau symmetry necessarily describes the normal (inverted) mass hierarchy. We restrict ourselves to mu-tau symmetric textures giving the tri-bimaximal mixing and calculate flavor neutrino masses to estimate CP-violating Dirac and Majorana phases as well as neutrino mixing angles as functions of alpha and beta. Since alpha and beta are generated by mu-tau symmetry breaking interactions, CP-violating Majorana phase tends to be suppressed and is found to be at most O(0.1) radian. On the other hand, CP-violating Dirac phase tends to show a proportionality to alpha or to beta.