Second Order QCD Corrections to $\Gamma(t \to Wb)$

TL;DR

This paper calculates second-order QCD corrections to the top quark decay into a W boson and a bottom quark, using a novel expansion method that accounts for finite W mass effects and cross-checks with related decay processes.

Contribution

It introduces a new expansion technique for calculating higher-order QCD corrections to top decay, including finite W mass effects, validated by cross-checks with other decay calculations.

Findings

Second-order QCD corrections significantly affect decay rate.

Method effectively incorporates finite W mass effects.

Results agree with existing two-loop QED corrections and decay rate calculations.

Abstract

Corrections of $O(\alpha_s^2)$ to the decay of the top quark into a W boson and a bottom quark are calculated. The method is based on an expansion of the top quark propagator for small external momentum, q, as compared to the top quark mass, M_t. The physical point q^2 = M_t^2 is reached through Pad\'e approximations. The described method allows to take effects induced by a finite W boson mass into account. The numerical relevance of the result is discussed. Important cross-checks against recent results for the decay rate $b \to u l \bar\nu$ and the two-loop QED corrections to $\mu$-decay are performed.