Comment on "Flavored leptogenesis and neutrino mass with $A_4$ symmetry" [JHEP12(2021)051, arXiv:2106.06773]

TL;DR

This paper critiques a recent $A_4$ flavor symmetry model for neutrino masses, identifying a missing Majorana mass term and providing a correction to improve the model's accuracy.

Contribution

It highlights an overlooked Majorana mass term in a previous model and offers a correction to ensure all invariant terms are properly included.

Findings

Identification of a missing Majorana mass term in the model

Correction of the neutrino mass matrix structure

Emphasis on including all invariant terms in model building

Abstract

Recently, in ref. \cite{A4Datta} Datta et al. [arXiv:2106.06773] proposed an $A_4$ flavor symmetric model supplemented by $Z_2\times Z_3$ symmetry which can accommodate the appropriate lepton mixing and neutrino masses via Type-I seesaw mechanism. They have constructed a minimal model with only one $SU(2)_L$ doublet scalar and six flavons that generate a specific flavor structure, favors the normal hierarchy of light neutrinos and narrows down the range of Dirac CP violating phase. Taking into account the contribution of all invariant terms, under all symmetries, is very important in the model building process, however, in ref. \cite{A4Datta} the authors miss a Majorana mass term which contributes to and changes the structure of the Majorana mass matrix of the right handed neutrinos. In this comment paper, we point out the above issue and provide a solution to fill in the missing term in ref. \cite{A4Datta}.