CDF-II $W$ Boson Mass Anomaly in the Canonical Scotogenic Neutrino-Dark Matter Model

The CDF-II collaboration's recent high-precision measurement of $W$ boson mass indicates new physics contribution(s) beyond the Standard Model. We investigate the possibility of the well-known canonical Scotogenic model to explain the CDF-II measurement. The Scotogenic model is a popular scenario beyond the Standard Model that induces neutrino masses at the 1-loop level and includes a viable dark matter candidate, either scalar or fermionic. For both scalar and fermionic dark matter possibilities, we simultaneously examine the constraints coming from (a) neutrino mass, oscillation, neutrinoless double beta decay and lepton flavour violation experiments, (b) from LEP and LHC (c) from dark matter relic density and direct detection experiments (d) from the oblique $S,T,U$ parameter values consistent with CDF-II $W$ boson measurement. We demonstrate that the new CDF-II measurement rules out the feasible parameter space of the scalar dark matter in the high mass regions ($m_{\eta_{R}} \gtrsim 500~\text{GeV}$), while still allowing the intermediate mass regions $54~\text{GeV} \lesssim m_{\eta_{R}} \lesssim 76~\text{GeV}$. We also showed that the fermionic dark matter candidate in the canonical Scotogenic model, in the range $M_{N_{1}} \lesssim 500~\text{GeV} $ , can simultaneously explain all the aforementioned issues. Furthermore, we investigated how the recent findings from ATLAS 2023 impact this study.