Non-perturbative running and renormalization of kaon four-quark operators with nf=2+1 domain-wall fermions

TL;DR

This paper calculates non-perturbative renormalization factors for four-quark operators relevant to kaon decay processes using lattice QCD with domain-wall fermions, providing scale evolution and scheme conversions.

Contribution

It presents the first non-perturbative determination of renormalization factors for $K o\pi\pi$ decay operators with nf=2+1 domain-wall fermions, including scale evolution and scheme matching.

Findings

Renormalization factors computed at 1.145 GeV in multiple schemes.

Non-perturbative scale evolution matrix obtained up to 3 GeV.

Connection to MSbar scheme established at 3 GeV.

Abstract

We compute the renormalization factors of four-quark operators needed for the study of $K\to\pi\pi$ decay in the $\Delta I=3/2$ channel. We evaluate the Z-factors at a low energy scale ($\mu_0=1.145 \GeV$) using four different non-exceptional RI-SMOM schemes on a large, coarse lattice ($a\sim 0.14\fm$) on which the bare matrix elements are also computed. Then we compute the universal, non-perturbative, scale evolution matrix of these renormalization factors between $\mu_0$ and $3\GeV$. We give the numerical results for the different steps of the computation in two different non-exceptional lattice schemes, and the connection to $\msbar$ at $3\GeV$ is made using one-loop perturbation theory.