Non-perturbative renormalization of four-quark operators and B_K with Schroedinger functional scheme in quenched domain-wall QCD

TL;DR

This paper develops a non-perturbative method to accurately determine the renormalization factors for four-quark operators in quenched domain-wall QCD, improving the precision of $B_K$ calculations relevant for CP violation studies.

Contribution

It provides the first non-perturbative renormalization factors for $ riangle S=2$ four-quark operators in quenched domain-wall QCD using the Schroedinger functional scheme, and applies these to refine $B_K$ values.

Findings

Non-perturbative renormalization factors are consistent with perturbative estimates.

Chiral symmetry breaking effects are numerically small.

The renormalized $B_K$ agrees well with previous results after applying the new factors.

Abstract

We present non-perturbative renormalization factors for $\Delta S=2$ four-quark operators in quenched domain-wall QCD using the Schroedinger functional method. Non-perturbative renormalization factor for $B_K$ is evaluated at hadronic scale. Combined with the non-perturbative RG running obtained by the Alpha collaboration, our result yields renormalization factor which converts lattice bare $B_K$ to the renormalization group invariant one. We apply the renormalization factor to bare $B_K$ previously obtained by the CP-PACS collaboration with the quenched domain-wall QCD(DWQCD). We compare our result with previous ones obtained by perturbative renormalization factors, different renormalization schemes or different quark actions. We also show that chiral symmetry breaking effects in the renormalization factor are numerically small.