Renormalization factor of four fermi operators with clover fermion and Iwasaki gauge action

TL;DR

This paper computes the perturbative renormalization factors for four-quark operators using clover fermions and Iwasaki gauge action, focusing on parity odd operators relevant to $K o\pi\pi$ decay.

Contribution

It provides the first perturbative calculation of renormalization factors for these operators with improved Wilson fermions and Iwasaki gauge action, specifically for parity odd operators.

Findings

Renormalization factors are obtained perturbatively for the specified operators.

The calculation is relevant for $K o\pi\pi$ decay amplitude studies.

Operators are multiplicatively renormalizable without mixing for the parity odd case.

Abstract

Renormalization factors of four-quark operators are perturbatively calculated for the improved Wilson fermion with clover term and the Iwasaki gauge action. A main application shall be the $K\to\pi\pi$ decay amplitude and the calculation is restricted to the parity odd operator, for which the operators are multiplicatively renormalizable without mixing with wrong operators that have different chiral structures.