Non-perturbative renormalization of static-light four-fermion operators in quenched lattice QCD

TL;DR

This paper non-perturbatively studies the scale-dependent renormalization of four-fermion operators relevant for B-meson mixing in quenched lattice QCD, using Schrödinger functional schemes and static approximation for heavy quarks.

Contribution

It provides the first non-perturbative determination of renormalization factors and scheme matching for static-light four-fermion operators in quenched lattice QCD.

Findings

Computed non-perturbative renormalization group running in SF schemes.

Established relations between RGI operators and SF-renormalized operators.

Provided non-perturbative matching between lattice and SF schemes.

Abstract

We perform a non-perturbative study of the scale-dependent renormalization factors of a multiplicatively renormalizable basis of $\Delta{B}=2$ parity-odd four-fermion operators in quenched lattice QCD. Heavy quarks are treated in the static approximation with various lattice discretizations of the static action. Light quarks are described by non-perturbatively ${\rm O}(a)$ improved Wilson-type fermions. The renormalization group running is computed for a family of Schroedinger functional (SF) schemes through finite volume techniques in the continuum limit. We compute non-perturbatively the relation between the renormalization group invariant operators and their counterparts renormalized in the SF at a low energy scale. Furthermore, we provide non-perturbative estimates for the matching between the lattice regularized theory and all the SF schemes considered.