Precise prediction for the mass of the W boson in gauged U(1) extensions of the standard model

We present the one-loop radiative corrections to the muon decay in U(1)(z) extensions of the standard model. We compute the mass of the W boson using those corrections and compare it to an approximation of the complete one-loop prediction implemented in automated computational tools. We point out that the truncation of the complete formulas become unreliable if the mass of the Z' boson, corresponding to the new U(1)(z) gauge group, is larger than about 1 TeV.