Perturbative matching of lattice and continuum heavy-light currents with NRQCD heavy quarks

The temporal and spatial components of the heavy-light vector current and the spatial components of the axial-vector current are expressed in terms of lattice-regulated operators suitable for simulations of B and D mesons. The currents are constructed by matching the appropriate scattering amplitudes in continuum QCD and a lattice model to one-loop order in perturbation theory. In the lattice theory, the heavy quarks are treated using the nonrelativistic (NRQCD) formulation and the light quarks are described by the tadpole-improved clover action. The light quarks are treated as massless. Our currents include relativistic and discretization corrections through $O({\alpha }_s/M,a{\alpha }_s),$ where M is the heavy-quark mass, a is the lattice spacing, and ${\alpha }_s$ is the QCD coupling. As in our previous construction of the temporal component of the heavy-light axial-vector current, mixing between several lattice operators is encountered at one-loop order, and $O\left(a{\alpha }_s\right)$ dimension-four improvement terms are identified.