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

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

2000-03-31

arxiv.org/abs/hep-lat/0003026v2

Phys.Rev. D62 (2000) 074507

Physics

High Energy Physics

High Energy Physics - Lattice

24 Pages, 18 Figures

Scientific paper

10.1103/PhysRevD.62.074507

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.

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