Muon ($g-2$) and W-boson mass Anomaly in a Model Based on $Z_4$ Symmetry with Vector like Fermion

Abstract

The latest results of CDF-II collaboration show a discrepancy of $7σ$ with standard model expectations. There is, also, a $4.2σ$ discrepancy in the measurement of muon magnetic moment reported by Fermilab. We study the connection between neutrino masses, dark matter, muon ($g-2$) and W-boson mass anomaly within a single coherent framework based on $Z_{4}$ extension of the scotogenic model with vector like lepton (VLL). Neutrino masses are generated at one loop level. The inert doublet, also, provide a solution to W-boson mass anomaly through correction in oblique parameters $S$, $T$ and $U$. The coupling of VLL triplet $ψ_T$ to inert doublet $η$ provides positive contribution to muon anomalous magnetic moment. In the model, the VLL triplet provides a lepton portal to dark matter ($η_R^0$). The model predicts a lower bound $m_{ee}>0.025$ eV at 3$σ$, which is well within the sensitivity reach of the $0νββ$ decay experiments. The model explains muon anomalous magnetic moment $Δa_μ$ for $1.3<y_ψ<2.8$ and mass of DM candidate in the range $152\text{ GeV}<M_{η_{R}^{0}}<195\text{ GeV}$. The explanation of W-boson mass anomaly, further, constrain the mass of DM candidate, $M_{η_{R}^{0}}$, in the range $154\text{ GeV}<M_{η_{R}^{0}}<174\text{ GeV}$.