Two-Loop QCD Corrections to the Heavy-to-Light Quark Decay

TL;DR

This paper provides an analytic calculation of two-loop QCD corrections to the decay of a b-quark into an u-quark and an off-shell W boson, aiding the precise theoretical understanding of semileptonic B-meson decays.

Contribution

It presents the first complete analytic expressions for two-loop QCD corrections to the b -> u W* decay process, including form factors in terms of Harmonic Polylogarithms.

Findings

Analytic form factors expressed as Laurent series in (d-4)

Form factors depend on the invariant mass of leptonic decay products

Results facilitate precise predictions for semileptonic B-meson decays

Abstract

We present an analytic expression for the two-loop QCD corrections to the decay process b -> u W^*, where b and u are a massive and massless quark, respectively, while W^* is an off-shell charged weak boson. Since the W-boson can subsequently decay in a lepton anti-neutrino pair, the results of this paper are a first step towards a fully analytic computation of differential distributions for the semileptonic decay of a b-quark. The latter partonic process plays a crucial role in the study of inclusive semileptonic charmless decays of B-mesons. The three independent form factors characterizing the b W u vertex are provided in form of a Laurent series in (d-4), where d is the space-time dimension. The coefficients in the series are expressed in terms of Harmonic Polylogarithms of maximal weight 4, and are functions of the invariant mass of the leptonic decay products of the W-boson.