Master integrals for double real radiation emission in heavy-to-light quark decay

We evaluate analytically the master integrals for double real radiation emission in the b→ uW∗ decay, 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 the present paper constitute a further step toward a fully analytic computation of differential distributions for the semileptonic decay of a b quark at NNLO in QCD. The latter partonic process plays a crucial role in the study of inclusive semileptonic charmless decays of B mesons. Our results are expressed in terms of multiple polylogarithms of maximum weight four.