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

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.

26 pages, 19 figures, 3 tables

References in corpus (15)

• Measurement of the Positive Muon Anomalous Magnetic Moment to 0.46 ppm
• The $g-2$ of charged leptons, $\alpha (M_Z^2)$ and the hyperfine splitting of muonium
• Hadronic contribution to the muon anomalous magnetic moment to next-to-next-to-leading order
• Measurement of the anomalous precession frequency of the muon in the Fermilab Muon g-2 experiment
• Type-III see-saw at LHC
• Towards a complete $A_4\times SU(5)$ SUSY GUT
• Upper Bound on the Mass of the Type III Seesaw Triplet in an SU(5) Model
• A Minimal Type II Seesaw Model
• SUSY Breaking Constraints on Modular flavor $S_3$ Invariant $SU(5)$ GUT Model
• Triplet Extended Supersymmetric Standard Model
• Interpreting the $W$-mass anomaly in the vectorlike quark models
• Lepton FCNC in Type III Seesaw Model
• Radiative Neutrino Mass in Type III Seesaw Model
• Two A5 modular symmetries for Golden Ratio 2 mixing
• The Minimal Type-II Seesaw Model and Flavor-dependent Leptogenesis