TeV Scale Resonant Leptogenesis with triplet Fermion in Connection to Muon $g-2$

We propose an extension of the minimal scotogenic model with a triplet fermion and a singlet scalar. An imposed $Z_{4}\times Z_{2}$ symmetry allows only diagonal Yukawa couplings among different generations of SM leptons and right-handed singlet neutrinos. 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 lightest right-handed neutrino decay. A net lepton asymmetry can be generated in the muonic sector from $N_{2}$ and triplet fermion decay through resonant leptogenesis scenario. The Yukawa coupling of triplet plays significant role both in leptogenesis and in the anomalous magnetic moment of the muon. 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 Muon $(g-2)$ and dark matter both favor the same parameter space for mass of the dark matter and the triplet fermion.