ZZ' Mixing and Radiative Corrections at LEP I

Abstract

We present a method for a common treatment of $Z'$ exchange, QED corrections, and weak loops in $e^+ e^-$ annihilation. QED corrections are taken into account by convoluting a hard-scattering cross section containing $\gamma,\ Z,$ and $Z'$ exchange. Weak corrections and $ZZ'$ mixing are treated simultaneously by a generalization of weak form factors. Using the properly extended Standard Model program for the $Z$ line shape, ZFITTER, we perform and compare two different analyses of the 1990 LEP~I data in terms of theories based on the E$_6$-group and in terms of LR-symmetric models. From the LEP~I data alone, the $ZZ'$ mixing angle may be limited to $|\theta_M| \le 0.01$ and the $Z'$ mass to $M_2 > 118$--148 GeV, depending on the model (95\%~CL).