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

TL;DR

This paper performs a one-loop perturbative calculation to accurately match lattice NRQCD currents to the continuum scheme for semileptonic B to D(*) decays, improving the precision of theoretical predictions.

Contribution

It provides the first order (rac{\u2192}{M}) matching calculations for axial and vector currents in lattice NRQCD, including different renormalisation for spatial and temporal components.

Findings

One-loop corrections are approximately 5%

Matching involves straightforward renormalisation for some currents

Results support improved accuracy in future lattice simulations

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.