Consequences of the $\mu$-$\tau$ reflection symmetry for leptogenesis in a seesaw model with diagonal Dirac neutrino mass matrix

TL;DR

This paper explores how $bla$-$ au$ reflection symmetry influences leptogenesis in a type-I seesaw model with a diagonal Dirac neutrino mass matrix, revealing conditions under which leptogenesis can occur and the role of renormalization effects.

Contribution

It provides a detailed analysis of the phenomenological implications of $bla$-$ au$ reflection symmetry for leptogenesis, including parameter constraints and the impact of renormalization group evolution.

Findings

Leptogenesis is viable only in the two-flavor regime under this symmetry.

Leptogenesis cannot occur for the specific case of r=1.

Renormalization group effects can induce leptogenesis in certain scenarios.

Abstract

In this paper, we have studied the consequences of the $\mu$-$\tau$ reflection symmetry for leptogenesis in the type-I seesaw model with diagonal Dirac neutrino mass matrix. We have first obtained the phenomenologically allowed values of the model parameters, which show that there may exist zero or equal entries in the Majorana mass matrix for the right-handed neutrinos, and then studied their predictions for three right-handed neutrino masses, which show that there may exist two nearly degenerate right-handed neutrinos. Then, we have studied the consequences of the model for leptogenesis. Due to the $\mu$-$\tau$ reflection symmetry, leptogenesis can only work in the two-flavor regime. Furthermore, leptogenesis cannot work for the particular case of $r=1$. Accordingly, for some benchmark values of $r \neq 1$, we have given the constraints of leptogenesis for relevant parameters. Furthermore, we have investigated the possibilities of leptogenesis being induced by the renormalization group evolution effects for two particular scenarios. For the particular case of $r=1$, the renormalization group evolution effects will break the orthogonality relations among different columns of $M^{}_{\rm D}$ and consequently induce leptogenesis to work. For the low-scale resonant leptogenesis scenario which is realized for nearly degenerate right-handed neutrinos, the renormalization group evolution effects can break the $\mu$-$\tau$ reflection symmetry and consequently induce leptogenesis to work.