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

The latest results of CDF-II collaboration show a discrepancy of $7\sigma$ with standard model expectations. There is, also, a $4.2\sigma$ 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 $\psi_T$ to inert doublet $\eta$ provides positive contribution to muon anomalous magnetic moment. In the model, the VLL triplet provides a lepton portal to dark matter ($\eta_R^0$). The model predicts a lower bound $m_{ee}>0.025$ eV at 3$\sigma$, which is well within the sensitivity reach of the $0\nu\beta\beta$ decay experiments. The model explains muon anomalous magnetic moment $\Delta a_\mu$ for $1.3<y_\psi<2.8$ and mass of DM candidate in the range $152\text{ GeV}<M_{\eta_{R}^{0}}<195\text{ GeV}$. The explanation of W-boson mass anomaly, further, constrain the mass of DM candidate, $M_{\eta_{R}^{0}}$, in the range $154\text{ GeV}<M_{\eta_{R}^{0}}<174\text{ GeV}$.