W Mass Anomaly from CDF-II and Neutrino Phenomenology in Minimal Type-III Seesaw Using T \(^\prime \) Modular Symmetry

In this paper we try to present a model by extending the standard model (SM) with two right handed fermion triplet superfields i.e. \(\Sigma _{R_i}\) in presence of modular symmetry \(\Gamma _3^\prime \) \(\sim \) \(\mathrm A_4^\prime \) i.e. double cover of \(\mathrm A_4\) modular symmetry also known as \( \mathrm T^\prime \) modular symmetry. It is crucial to identify seesaw models in order to explain neutrino mass which is naturally lowered by the exchange of heavy right handed particles at tree level. As a result, we utilize type-III seesaw mechanism in which involves right handed fermionic triplet for getting the correct mass for active neutrinos as realized from experimental data. The minimal extension (MSSM) with the type-III seesaw is able to explain neutrino phenomenology accurately. The \(\mathrm T^\prime \) symmetry has been used to analyze the different possible neutrino mass matrices which are expressed in-terms of modulus \(\tau \) introduced to break the modular symmetry. Our predictions include observables like neutrino mass square differences, mixing angles in the leptonic sector, Dirac phase and the mass scale of neutrinos by suitably fixing model parameters. Alongside, we are also able to explain the recent measurements of the W boson mass published by CDF collaboration. Our goal is to explain both the phenomenologies with the same parameter region.