Weak low-energy couplings from topological zero-mode wavefunctions

TL;DR

This paper introduces a novel lattice QCD method to determine low-energy couplings of the weak Hamiltonian by matching topological pole structures with chiral effective theory, supported by NLO calculations and preliminary data.

Contribution

It presents a new approach using topological poles in lattice QCD to extract weak couplings, including NLO chiral perturbation theory calculations and initial numerical results.

Findings

Derived low-energy couplings from topological pole matching.

Performed NLO chiral perturbation theory calculations.

Obtained preliminary numerical results supporting the method.

Abstract

We discuss a new method to determine the low-energy couplings of the $\Delta S=1$ weak Hamiltonian in the $\epsilon$-regime. It relies on a matching of the topological poles in $1/m^2$ of three-point functions of two pseudoscalar densities and a four-fermion operator computed in lattice QCD, to the same observables in the Chiral Effective Theory. We present the results of a NLO computation in chiral perturbation theory of these correlation functions together with some preliminary numerical results.