Corrections to electroweak precision observables from mixings of an exotic vector boson in light of the CDF $W$-mass anomaly

Abstract

We enumerate various effective couplings that contribute to the mixings between an exotic vector boson $Z^{\prime }$ and the neutral electroweak vector bosons. The miscellaneous mixing patterns can be evaluated perturbatively. The effective oblique parameters $S^{\prime }$, $T^{\prime }$, and $U^{\prime }$ are calculated to compare with the electroweak precision test results. With the contributions to the non-negligible $U^{\prime }$ parameter from the ${ϵ}_{B,W}$ parameters and the aid of some other parameters to cancel the negative $T^{\prime }$, the recent CDF $W$-mass anomaly can therefore be explained.

Comments: S, T, U parameters are changed to the effective S', T', U'. Further detailed discussions about the parameter definitions and the corresponding effective operators are elaborated in the appendix. Figures are updated