TeV scale Leptogenesis with triplet Fermion in Connection to Muon \(g-2\) and W mass anomaly

We propose extending the minimal scotogenic model with a triplet fermion and a singlet scalar. All the fields change non-trivially under an additional \(Z_{4}\times Z_{2}\) symmetry. The \(Z_{4}\times Z_{2}\) symmetry allows only diagonal Yukawa couplings among different generations of SM leptons and right-handed singlet neutrinos. The one-loop radiative diagrams generate neutrino mass. The Yukawa coupling of the triplet fermion with the inert doublet positively contributes to the muon anomalous magnetic moment. The imposed \(Z_{4}\times Z_{2}\) symmetry forbids the conventional leptogenesis from the right-handed neutrino decay. A net lepton asymmetry can be generated in the muonic sector from triplet fermion decay. Involvement of the Yukawa coupling both in leptogenesis and in the anomalous magnetic moment of the muon results in a strong correlation between leptogenesis and the recent Fermi lab result. We show a viable parameter space for TeV scale leptogenesis while explaining the Fermi lab results. The inert scalar is the dark matter candidate in this model. The model also poses the potential to explain the latest results on W boson mass from the CDF-II experiment.