$B-L$ model in light of the CDF II result

Recent CDF II collaboration's result on $W$ mass measurements contradict Standard Model prediction, requiring new physics to explain this anomaly. Such new physics may manifest through tree-level or loop-level corrections to the mass of the $W$ boson. In this work, we investigate the possibility that the CDF-II result is indicative of new physics not directly changing the $W$ boson mass but rather the $Z$ boson mass. Since the $Z$ boson mass goes as an input into the Standard Model prediction for $W$ boson mass, this change in $Z$ mass ultimately leads to the discrepancy between the CDF-II measurement and the Standard Model expectation. We demonstrate this idea through one of the simplest and most studied $U(1)$ gauge extensions of the Standard Model, namely the gauged $U(1)_{B-L}$ extension. We demonstrate that $B-L$ extended models can explain the revised best-fit values for $S$, $T$, and $U$ following the CDF II results. We studied the parameter space of models with and without mixing between neutral gauge bosons. We also reviewed the dark matter constraints and demonstrated that there is parameter space that is compatible with the current $W$ boson mass, relic abundance, and direct detection experiments.