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

TL;DR

This paper presents a one-loop perturbative matching of continuum and lattice four-fermion operators involving heavy-light systems, utilizing nonrelativistic QCD and improved staggered quarks, relevant for B meson mixing studies.

Contribution

It provides a comprehensive one-loop matching calculation for $bar$ operators using NRQCD and HISQ actions, including beyond Standard Model operators and systematic corrections.

Findings

Complete set of $bar$ operators matched at one loop.

Includes corrections up to order $rac{ m{ extstyle ext{QCD}}}{M_b}$ and $rac{ m{ extstyle ext{QCD}}}{aM_b}$.

Facilitates precise lattice QCD calculations of B-meson mixing parameters.

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 $\alpha_s/(aM_b)$.