Neutrino phenomenology, W mass anomaly & muon $(g-2)$ in minimal type-III seesaw using $T^\prime$ modular symmetry

TL;DR

This paper develops a minimal type-III seesaw model with $T^\u2019$ modular symmetry to explain neutrino phenomenology, the W boson mass anomaly, and muon $(g-2)$, incorporating odd weight modular forms and analyzing lepton flavor violation.

Contribution

It introduces a novel minimal type-III seesaw model using $T^\u2019$ modular symmetry with odd weight forms, addressing neutrino data, W mass anomaly, and muon $(g-2)$.

Findings

Successfully explains neutrino oscillation data.

Provides a potential explanation for the W mass anomaly.

Offers constraints on right-handed fermion masses from lepton flavor violation.

Abstract

In this study, we attempt to introduce a model to illustrate neutrino phenomenology by incorporating two right-handed fermion triplet superfields, i.e., $\Sigma_{R_j}$, in the presence of the modular symmetry $\Gamma_3^\prime \simeq A_4^\prime$, a double cover of the $A_4$ modular symmetry. The motivation in utilizing double cover is, so far only even modular forms were considered for constructing modular invariant models, but, in this case, it is possible to extend the modular invariance approach to general integral weight modular forms, i.e., the odd weight modular forms. Hence, this type of amalgamation between $T^\prime$ modular symmetry and minimally extending the seesaw can correctly explain the neutrino phenomenology. Additionally, we have made an attempt to accommodate the most recent measurement of the $W$ boson mass, published by the CDF-II collaboration and shed some light on the recent results of muon $(g-2)$. Finally, we have discussed lepton flavor violation in order to establish a constraint on the mass of right-handed fermion.