Determination of the $\Delta S = 1$ weak Hamiltonian in the SU(4) chiral limit through topological zero-mode wave functions

TL;DR

This paper introduces a novel lattice QCD method to determine the $ riangle S=1$ weak Hamiltonian's low-energy couplings by matching topological zero-mode wave functions in the SU(4) chiral limit, tested with quenched simulations.

Contribution

It presents a new approach using topological pole matching in lattice QCD to extract weak couplings in the SU(4) chiral limit, extending previous methods.

Findings

Successfully determined weak low-energy couplings in SU(4) limit

Compared new method with previous approaches, highlighting advantages and limitations

Validated the method with quenched lattice QCD measurements and chiral perturbation theory

Abstract

A new method to determine the low-energy couplings of the $\Delta S=1$ weak Hamiltonian is presented. It relies on a matching of the topological poles in $1/m^2$ of three-point correlators of two pseudoscalar densities and a four-fermion operator, measured in lattice QCD, to the same observables computed in the $\epsilon$-regime of chiral perturbation theory. We test this method in a theory with a light charm quark, i.e. with an SU(4) flavour symmetry. Quenched numerical measurements are performed in a 2 fm box, and chiral perturbation theory predictions are worked out up to next-to-leading order. The matching of the two sides allows to determine the weak low-energy couplings in the SU(4) limit. We compare the results with a previous determination, based on three-point correlators containing two left-handed currents, and discuss the merits and drawbacks of the two procedures.