Matching lattice and continuum four-fermion operators with nonrelativistic QCD and highly improved staggered quarks

Abstract

We match continuum and lattice heavy-light four-fermion operators at one loop in perturbation theory. For the heavy quarks we use nonrelativistic QCD and for the massless light quarks the highly improved staggered quark action. We include the full set of $\Delta B=2$ operators relevant to neutral $B$ mixing both within and beyond the Standard Model and match through order ${\alpha }_s$, ${\Lambda }_{\mathrm{QCD}}/M_b$, and ${\alpha }_s/(a{M}_b)$.

arXiv comment13 pages, 10 figures. Version accepted by Phys. Rev. D: one diagram added (Fig.4) and text updated accordingly. Typographic errors corrected

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• Short-distance matrix elements for $D^0$-meson mixing for $N_f=2+1$ lattice QCD
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• Improving the theoretical prediction for the $B_s-{\bar{B}}_s$ width difference: matrix elements of next-to-leading order $\Delta B=2$ operators