S-Matrix Approach to the $Z$ Line Shape

Abstract

We analyze the $Z$ line shape assuming the existence of an analytic, unitary S-matrix. As an example, from hadron production at LEP we determine $M_{Z}=91.134 \pm 0.020 \pm 0.020 \: ({\rm LEP})$ GeV, $\Gamma_{Z}=2.506 \pm 0.018$ GeV. This is in accordance with earlier results after performing a shift of the $Z$ mass value of about $\frac{1}{2}\Gamma_Z^2/M_Z = 34$ MeV. The cross section and related observables may be described by a small number of additional degrees of freedom without relying on a specific field-theoretic model.