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

P Boyle·C Davies
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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 $O(α_s\frac{\vec{p}}{M})$ 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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P Boyle, C Davies. 2000-05-25. One loop renormalisation of Lattice NRQCD currents for semileptonic $B\to D^{(\ast)}$ decays to order $\frac{\vec{p}}{M}$. https://doi.org/10.1103/physrevd.62.074507

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