Radiative Corrections to W and Quark Propagators in the Resonance Region

TL;DR

This paper addresses issues with mass renormalization of unstable particles like W bosons and quarks in the resonance region, proposing a pole-based approach to resolve convergence and gauge dependence problems.

Contribution

It introduces a pole mass and width framework for unstable particles, improving the theoretical consistency of radiative corrections in the resonance region.

Findings

Conventional mass renormalization leads to non-convergent series in the resonance region.

Pole mass and width definitions reduce gauge dependence issues.

On-shell and pole widths coincide when higher-order terms are neglected.

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.