Perturbative renormalization factors of $\Delta S = 1$ four-quark operators for domain-wall QCD

TL;DR

This paper computes one-loop perturbative renormalization factors for $\

Contribution

It provides the first perturbative calculation of renormalization factors for $\

Findings

Renormalization factors include gluon exchange and penguin diagrams.

Results enable more accurate lattice calculations of $K o \\pi\\pi$ decays.

Includes $O(g^2)$ corrections for domain-wall QCD.

Abstract

Renormalization factors for $\Delta S =1$ four-quark operators in the effective weak Hamiltonian are perturbatively evaluated in domain-wall QCD. The one-loop corrections of $\Delta S=1$ four-quark operators consist of two types of diagrams: one is gluon exchange between quark lines and the other is penguin diagrams containing quark loops. Combining both contributions, our results allow a lattice calculation of the amplitude for $K\to \pi\pi$ decays with $O(g^2)$ corrections included.