Weak annihilation and the end-point spectrum in semileptonic B decays

A general relationship is formulated between the contributions of ‘Weak Annihilation’ (WA) to inclusive semileptonic decays of heavy flavour hadrons and the matrix elements of four-fermion operators. We argue that non-perturbative contributions from low-energy hadronic final states provide the dominant impact of WA on the semileptonic b → u width of B− mesons. In that case WA affects the lepton spectrum mainly in its end-point region - i.e. beyond the kinematical boundary for b → c transitions - and we expect the latter to look quite different in B− than in Bd decays. At present we are unable to make a truly quantitative prediction; yet a detailed experimental comparison of the B− and the Bd lepton spectra will enable us to determine the size of the relevant matrix elements and to check directly to what extent the factorization approximation works here. Using universal analyticity properties of the decay amplitude we analyse WA in the perturbative regime and rederive our earlier results about the absence of a power enhancement due to gluon emission in a more general way. We also address the problem of the invariant mass of hadrons in the final state in semileptonic B decays and identify non-trivial cancellations in 〈Mhadr2〉.