Perturbative renormalization of the $\Delta B=2$ four-quark operators in lattice NRQCD

TL;DR

This paper computes the one-loop renormalization constants for $=2$ four-quark operators in lattice NRQCD, enabling more accurate evaluation of bag parameters relevant for B-meson mixing.

Contribution

It provides the first perturbative calculation of renormalization constants for these operators in the context of $O(1/M)$ NRQCD and improved Wilson light quark actions.

Findings

Calculated one-loop coefficients for heavy and light quark actions.

Removed $O(")$ errors from previous bag parameter calculations.

Reanalyzed previous results with improved renormalization constants.

Abstract

We present a perturbative calculation of the renormalization constants for the $\Delta B=2$ four-quark operators, which is needed to evaluate the bag parameters $B_B$ and $B_S$ in lattice QCD. The one-loop coefficients are calculated for the $O(1/M)$ NRQCD heavy quark action and the $O(a)$-improved Wilson action for light quark. Using these coefficients, which remove $O(\alpha_s/aM)$ error, we reanalyze our previous calculation of the bag parameters.