$O(α_{s}a)$ matching coefficients for axial vector current and $ΔB$$=$2 operator

We present a calculation of the perturbative matching coefficients including mixing with higher dimensional operators for the temporal component of the heavy-light axial current, $A_{4}$, and the $ΔB=2$ operator, $O_S$. For $A_{4}^{\scriptsize static, NRQCD}$, calculations with various RG-improved gauge actions are peformed. Matching coefficients with NRQCD and heavy-clover actions are also compared.

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