Perturbative renormalization factors of four-quark operators for improved Wilson fermion action and Iwasaki gauge action

TL;DR

This paper computes perturbative renormalization factors and improvement coefficients for four-quark operators using improved Wilson fermions and Iwasaki gauge action, aiding precise lattice QCD calculations of kaon decays.

Contribution

It provides the first perturbative calculation of renormalization factors for parity odd four-quark operators with these specific lattice actions, focusing on operators relevant to $K o ext{pi pi}$ decays.

Findings

Calculated renormalization factors for four-quark operators.

Operators are multiplicatively renormalized without mixing.

Results applicable to $K o ext{pi pi}$ decay amplitude studies.

Abstract

The renormalization factor and O(a) improvement coefficient of four-quark operators are calculated perturbatively for the improved Wilson fermion action with clover term and the Iwasaki gauge action. With an application to the $K\to\pi\pi$ decay amplitude in mind, the calculation is restricted to the parity odd operator, for which the operators are multiplicatively renormalized without any mixing to operators that have different chiral structures.