Current Renormalisation in NRQCD for Semi-leptonic $B\to D$ Decays

Abstract

We present a calculation of the renormalisation constants for the temporal vector current, $Z_{V_0}$ and spatial axial current, $Z_{A_k}$, to $O(\alpha_s/M)$ for $B\to D$ transitions using the $O(1/M)$ NRQCD action for both $b$ and $c$ quarks evaluated for a large range of mass parameters. Considerations for the renormalisation of the spatial vector current and the temporal axial current are discussed and initial results for a mixed lattice current are presented for the spatial vector current.