Radiative corrections toWand quark propagators in the resonance region

We discuss radiative corrections to $W$ and quark propagators in the resonance region $|s-M^2|\lesssim M\Gamma .$ We show that conventional mass renormalization, when applied to photonic or gluonic corrections, leads in next to leading order (NLO) to contributions proportional to $[M\Gamma /(s-M^2){]}^n,$ $(n=1,2,\dots ),$ i.e., to a non-convergent series in the resonance region, a difficulty that affects all unstable particles coupled to massless quanta. A solution of this problem, based on the concepts of pole mass and width, is presented. It elucidates the issue of renormalization of amplitudes involving unstable particles, and automatically circumvents the problem of apparent on-shell singularities. The roles of the Fried-Yennie gauge and the pinch technique prescription are discussed. Because of special properties of the photonic and gluonic contributions, and in contrast with the $Z$ case, the gauge dependence of the conventional on-shell definition of mass is unbounded in NLO. The evaluations of the width in the conventional and pole formulations are compared and shown to agree in NLO but not beyond.