Non-perturbative renormalisation of left-left four-fermion operators with Neuberger fermions

TL;DR

This paper presents a method for non-perturbative renormalisation of four-fermion operators using Neuberger fermions, crucial for understanding kaon decays in particle physics.

Contribution

It introduces a strategy to match Neuberger fermion results with Wilson fermions for operator renormalisation, advancing lattice QCD techniques.

Findings

Successful matching of Neuberger and Wilson fermion results

Renormalisation constants for four-quark operators obtained

Enhanced precision in kaon decay constant calculations

Abstract

We outline a general strategy for the non-perturbative renormalisation of composite operators in discretisations based on Neuberger fermions, via a matching to results obtained with Wilson-type fermions. As an application, we consider the renormalisation of the four-quark operators entering the Delta S=1 and Delta S=2 effective Hamiltonians. Our results are an essential ingredient for the determination of the low-energy constants governing non-leptonic kaon decays.