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

We present an analytic expression for the two-loop QCD corrections to the decay process b → uW , 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 bWu 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.