Probing the chiral weak Hamiltonian at finite volumes

TL;DR

This paper explores how finite-volume lattice QCD can be used to determine low-energy constants in the chiral weak Hamiltonian relevant for non-leptonic kaon decays, analyzing different quark mass regimes and operator contributions.

Contribution

It extends the analytic framework for matching lattice measurements to chiral perturbation theory by including the epsilon- and p-regimes and the leading Delta I = 1/2 operators.

Findings

The epsilon-regime simplifies disentangling operator coefficients.

Finite-volume effects are significant for ML  5.0 in the p-regime.

The study clarifies the connection between small and large quark mass regimes.

Abstract

Non-leptonic kaon decays are often described through an effective chiral weak Hamiltonian, whose couplings ("low-energy constants") encode all non-perturbative QCD physics. It has recently been suggested that these low-energy constants could be determined at finite volumes by matching the non-perturbatively measured three-point correlation functions between the weak Hamiltonian and two left-handed flavour currents, to analytic predictions following from chiral perturbation theory. Here we complete the analytic side in two respects: by inspecting how small ("epsilon-regime") and intermediate or large ("p-regime") quark masses connect to each other, and by including in the discussion the two leading Delta I = 1/2 operators. We show that the epsilon-regime offers a straightforward strategy for disentangling the coefficients of the Delta I = 1/2 operators, and that in the p-regime finite-volume effects are significant in these observables once the pseudoscalar mass M and the box length L are in the regime ML \lsim 5.0.