Analysis of the DeltaI=1/2 Rule and e'/e with Overlap Fermions

TL;DR

This paper investigates the renormalization of the DeltaS=1 weak Hamiltonian using overlap fermions, highlighting how chiral symmetry and the GIM mechanism simplify calculations of K-->pi pi and related matrix elements.

Contribution

It demonstrates that overlap fermions allow for simplified, subtraction-free calculations of certain weak decay matrix elements due to chiral symmetry and the GIM mechanism.

Findings

K-->pi pi matrix elements can be computed without power subtractions.

e'/e amplitudes require only one divergent subtraction, manageable non-perturbatively.

Chiral symmetry at finite lattice spacing aids in simplifying weak decay calculations.

Abstract

We study the renormalization of the DeltaS=1 effective weak Hamiltonian with overlap fermions. The mixing coefficients among dimension-six operators are computed at one loop in perturbation theory. As a consequence of the chiral symmetry at finite lattice spacing and of the GIM mechanism, which turns out to be quadratic in the masses, the K-->pi pi and K -->pi matrix elements relevant for the Delta I =1/2 rule can be computed without any power subtractions. The analogous amplitudes for e'/e require one divergent subtraction only, which can be performed non-perturbatively using K-->0 matrix elements.