Radiative Corrections to W and Quark Propagators in the Resonance Region

Abstract

It is shown that conventional mass renormalization, when applied to photonic or gluonic corrections to unstable particle propagators, leads to non-convergent series in the resonance region. A solution of this problem, based on the concepts of pole mass and width, is presented. In contrast with the Z case, the conventional on-shell definition of mass for W bosons and unstable quarks contains an unbounded gauge dependence in next-to-leading order. The on-shell and pole definitions of width are shown to coincide if terms of O(\Gamma^2) and higher are neglected, but not otherwise.