The $B^{+}-B_{d}^{0}$ lifetime difference beyond leading logarithms

We compute perturbative QCD corrections to the lifetime splitting between the charged and neutral $B$ meson in the framework of the heavy quark expansion. These next-to-leading logarithmic corrections are necessary for a meaningful use of hadronic matrix elements of local operators from lattice gauge theory. We find the uncertainties associated with the choices of renormalization scale and scheme significantly reduced compared to the leading-order result. We include the full dependence on the charm-quark mass $m_c$ without any approximations. Using hadronic matrix elements estimated in the literature with lattice QCD we obtain $\tau(B^+)/\tau(B^0_d)=1.053\pm 0.027\pm 0.017$, where the effects of unquenching and $1/m_b$ corrections are not yet included. The lifetime difference of heavy baryons $\Xi^0_b$ and $\Xi^-_b$ is also briefly discussed.