A $\Gamma_{3}$ modular symmetric approach for two-zero textures in left-right symmetric model

Abstract

The observed pattern for neutrino masses and mixing provides compelling evidence for Beyond Standard Model physics which further motivates the search for predictive frameworks that can simultaneously address flavor structure and its phenomenological consequences. This work particularly investigates the realization of all possible seven two-zero neutrino mass textures within the generic left-right symmetric model with $A_{4}$ modular symmetry. By considering modular weights 4,8 and 10, we systematically construct all the possible classes of 2-0 textures without the introduction of any flavon fields which enhances the predictive power of the framework. In this work, we also identify the texture classes capable of simultaneously accommodating current neutrino data, reproducing the observed baryon asymmetry and also yielding experimentally testable results for the effective Majorana neutrino mass for new physics contributions of neutrinoless double beta decay.