Probing maximal zero textures with broken cyclic symmetry in inverse seesaw

TL;DR

This paper investigates neutrino mass matrices with cyclic symmetry and maximal zero textures within the inverse seesaw framework, exploring symmetry breaking methods and their compatibility with experimental data, leading to specific predictions on neutrino parameters.

Contribution

It introduces two approaches to incorporate cyclic symmetry in inverse seesaw neutrino models and analyzes their phenomenological viability, including symmetry breaking effects and predictions.

Findings

Symmetry breaking in the charged lepton sector can produce viable neutrino mixing patterns.

Predictions include constrained CP phases and inverted hierarchy of neutrino masses.

Significant implications for neutrinoless double beta decay and total neutrino mass sum.

Abstract

Within the framework of inverse seesaw mechanism we investigate neutrino mass matrices invariant under cyclic symmetry ($Z_3$) with maximal zero texture (6 zero textures). We explore two different approaches to obtain the cyclic symmetry invariant form of the constituent matrices. In the first one we consider explicit cyclic symmetry in the neutrino sector of the Lagrangian which dictates the emerged effective neutrino mass matrix ($m_\nu$) to be symmetry invariant and hence leads to a degeneracy in masses. We then consider explicit breaking of the symmetry through a dimensionless parameter $\epsilon^{\prime}$ to remove the degeneracy. It is seen that the method doesn't support the current neutrino oscillation global fit data even after considering the correction from cyclic symmetry invariant charged lepton mass matrix ($m_l$) unless the breaking parameter is too large. In the second method, we assume the same forms of the neutrino mass matrices, however, symmetry is broken in the charged lepton sector. All the structures of the mass matrices are now dictated by an effective residual symmetry of some larger symmetry group in the Lagrangian. For illustration, we exemplify a toy model based on softly broken $A_4$ symmetry group which leads to one of the combination of $m_l$, $m_D$, $M_{RS}$ and $\mu$ to generate effective $m_\nu$. All the emerged mass matrices predict a constraint range of the CP violating phases and atmospheric mixing angle along with an inverted hierarchical structure of the neutrino masses. Further, significant predictions on $\beta\beta0\nu$ decay parameter $|m_{11}|$ and the sum of the three light neutrino masses ($\Sigma_im_i$) are also obtained.