Matching factors for Delta S=1 four-quark operators in RI/SMOM schemes

TL;DR

This paper develops RI/SMOM schemes for non-perturbative renormalization of Delta S=1 four-quark operators in lattice flavor physics, providing one-loop matching to MS-bar and discussing operator mixing.

Contribution

It introduces new RI/SMOM schemes for four-quark operators and derives one-loop matching factors to MS-bar, enhancing non-perturbative renormalization methods.

Findings

Derived one-loop matching factors for RI/SMOM to MS-bar.

Provided compact expressions for finite one-loop amplitudes.

Discussed operator mixing in different scheme classes.

Abstract

The non-perturbative renormalization of four-quark operators plays a significant role in lattice studies of flavor physics. For this purpose, we define regularization-independent symmetric momentum-subtraction (RI/SMOM) schemes for Delta S=1 flavor-changing four-quark operators and provide one-loop matching factors to the MS-bar scheme in naive dimensional regularization. The mixing of two-quark operators is discussed in terms of two different classes of schemes. We provide a compact expression for the finite one-loop amplitudes which allows for a straightforward definition of further RI/SMOM schemes.