Erratum: Differential distributions in semileptonic decays of heavy flavors in QCD

Width Difference in the B-B[over ¯] System at Next-to-Next-to-Leading Order of QCD

We extend the theoretical prediction for the width difference ΔΓ_{q} in the mixing of neutral B mesons in the Standard Model to next-to-next-to-leading order in α_{s}. To this aim, we calculate three-loop diagrams with two |ΔB|=1 current-current operators analytically. In the matching between |ΔB|=1 and |ΔB|=2 effective theories, we regularize the infrared divergences dimensionally and take into account all relevant evanescent operators. Further elements of the calculation are the two-loop renormalization matrix Z_{ij} for the |ΔB|=2 operators and the O(α_{s}^{2}) corrections to the finite renormalization that ensures the 1/m_{b} suppression of the operator R_{0} at two-loop order. Our theoretical prediction reads ΔΓ_{s}/ΔM_{s}=(4.33±0.93)×10^{-3} if expressed in terms of the bottom mass in the MS[over ¯] scheme and ΔΓ_{s}/ΔM_{s}=(4.20±0.95)×10^{-3} for the use of the potential-subtracted mass. While the controversy on |V_{cb}| affects both ΔΓ_{s} and ΔM_{s}, the ratio ΔΓ_{s}/ΔM_{s} is not affected by the uncertainty in |V_{cb}|.

Inclusive Semileptonic Decays from Lattice QCD

We develop a method to compute the inclusive semileptonic decay rate of hadrons fully nonperturbatively using lattice QCD simulations. The sum over all possible final states is achieved by a calculation of the forward-scattering matrix elements on the lattice, and the phase-space integral is evaluated using their dependence on the time separation between two inserted currents. We perform a pilot lattice computation for the B[over ¯]_{s}→X_{c}ℓν[over ¯] decay with an unphysical bottom quark mass and compare the results with the corresponding OPE calculation. The method to treat the inclusive processes on the lattice can be applied to other processes, such as the lepton-nucleon inelastic scattering.