W boson mass in the NP models with extra $U(1)$ gauge group

The precise measurement of the W boson mass is closely related to the contributions of new physics (NP), which can significantly constrain the parameter space of NP models, particularly those with an additional $U(1)$ local gauge group. The inclusion of a new $Z'$ gauge boson and gauge couplings in these models can contribute to the oblique parameters $S$, $T$, $U$ and W boson mass at tree level. In this study, we calculate and analyze the oblique parameters $S$, $T$, $U$ and W boson mass in such NP models, taking into account the effects of kinetic mixing, and it is found that the kinetic mixing effects can make significant contributions to these oblique parameters and W boson mass. Based on the obtained numerical results, the recently measured W boson mass at CDF II or ATLAS can be satisfied by choosing appropriate values of gauge coupling constants and extra $U(1)$ group charges of leptons or scalar doublets. In addition, if the leptonic Yukawa couplings are invariant under the extra $U(1)$ local gauge group, the contributions to $S$, $T$, $U$ and W boson mass can be eliminated by redefining the gauge boson fields through eliminating the neutral currents involving charged leptons.