One loop renormalisation of Lattice NRQCD currents for semileptonic $B\to D^{(\ast )}$ decays to order $\frac{\vec{p}}{M}$

Abstract

We present the results of a perturbative calculation to match the axial and vector currents for semileptonic $B\to D^{(\ast )}$ decays in lattice NRQCD to the continuum \MSb scheme. The matching is performed to $O({\alpha }_s\frac{\vec{p}}{M})$ in Feynman gauge and in the on-shell renormalisation scheme. The spatial and temporal components of the currents renormalise differently; to this order the matching involves a straightforward renormalisation for the $V_0$ and $A_k$ currents, and a rank two and four mixing matrix for the $A_0$ and $V_k$ currents respectively. The resultant one loop corrections are of $O(5$, boding well for the accuracy of forthcoming simulations.

24 Pages, 18 Figures

References in corpus (2)

• B decays on the lattice
• Semi-leptonic decays heavy-light to heavy light

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