Z' and the Appelquist-Carrazzone decoupling
  We consider the electroweak theory with an additional neutral vector boson $Z^\prime$ at one loop. We propose a renormalization scheme which makes the decoupling of heavy $Z^\prime$ effects manifest. The proposed scheme justifies the usual procedure of performing fits to the electroweak data by combining the full SM loop corrections to observables with the tree level corrections due to the extended gauge structure. Using this scheme we discuss in the model with extra an $U(1)^\prime$ group factor 1-loop results for the $\rho$ parameters defined in several different ways. 
P.H. Chankowski, S. Pokorski, J. Wagner