Obliquely Scrutinizing a Hidden SM-like Gauge Model

In view of the recent high precision measurement of the Standard Model $W$ boson mass at the CDF II detector, we compute the contributions to the oblique parameters $S$, $T$ and $U$ coming from the two additional Higgs doublets (one inert and one hidden) as well as the hidden neutral dark gauge bosons and extra heavy fermions in the gauged two-Higgs-doublet model (G2HDM). While the effects from the hidden Higgs doublet and new heavy fermions are found to be minuscule, the hidden gauge sector $SU(2)_H \times U(1)_X$ with gauge coupling strength $\gtrsim 10^{-2}$ and gauge boson mass $\gtrsim 100$ GeV can readily explain the $W$ boson mass anomaly but nevertheless excluded by the dilepton high-mass resonance searches at the Large Hadron Collider. On the other hand, the new global fits to the oblique parameters due to the new $W$ boson mass measurement can give discernible impacts on the mass splitting and mixing angle for the inert Higgs doublet in G2HDM. We also study the impact to the signal strength of diphoton mode of the 125 GeV Higgs boson $h \to \gamma \gamma$ and the detectability of the yet to observe process $h \to Z \gamma$ at the High Luminosity Large Hadron Collider. Current constraints for the dark matter candidate $W^\prime$ including the dark matter relic density, dark matter direct detections and invisible Higgs decays are also taken into account in this study.