Renormalization of the \Delta B=2 four-quark operators in lattice NRQCD

TL;DR

This paper computes one-loop perturbative renormalization constants for B=2 four-quark operators in lattice NRQCD, improving previous results by removing certain systematic errors and enabling more accurate calculations of B-meson mixing parameters.

Contribution

It provides the first one-loop matching coefficients for B=2 operators in lattice NRQCD, enhancing the precision of B-meson mixing studies.

Findings

Renormalization constants calculated at one-loop order.

Reanalysis of previous matrix element results with new coefficients.

Results free from /(aM_b) systematic errors.

Abstract

We calculate perturbative renormalization constants for the \Delta B=2 four-quark operators in lattice NRQCD. Continuum operators \bar{b}\gamma_{\mu}(1-\gamma_5)q~ \bar{b}\gamma_{\mu}(1-\gamma_5)q and \bar{b}(1-\gamma_5)q~\bar{b}(1-\gamma_5)q, which are necessary in evaluating the mass and width differences in $B^0_{d(s)}-\bar{B}^0_{d(s)}$ systems, are matched at one-loop with corresponding lattice operators constructed from the NRQCD heavy quarks and the ${\cal O}(a)$-improved light quarks. Using these perturbative coefficients, we also reanalyse our previous simulation results for the matrix elements of the above operators. Our new results are free from the systematic error of ${\cal O}(\alpha_s/(aM_b))$ in contrast to the previous ones with matching coefficients evaluated in the static limit.