Correlators of left charges and weak operators in finite volume chiral perturbation theory

TL;DR

This paper calculates specific correlators in finite volume chiral perturbation theory at next-to-leading order, aiming to connect lattice measurements with fundamental parameters like F and g_27 relevant for weak decays.

Contribution

It provides the first detailed next-to-leading order computations of these correlators in the epsilon-regime, including quenched approximations, facilitating parameter extraction from lattice data.

Findings

Matching correlators can determine F and g_27 from lattice data.

Quenched and full theories yield similar ratios at this order.

Correlator ratios are robust across quenched and unquenched formulations.

Abstract

We compute the two-point correlator between left-handed flavour charges, and the three-point correlator between two left-handed charges and one strangeness violating \Delta I=3/2 weak operator, at next-to-leading order in finite volume SU(3)_L x SU(3)_R chiral perturbation theory, in the so-called epsilon-regime. Matching these results with the corresponding lattice measurements would in principle allow to extract the pion decay constant F, and the effective chiral theory parameter g_27, which determines the \Delta I = 3/2 amplitude of the weak decays K to \pi\pi as well as the kaon mixing parameter B_K in the chiral limit. We repeat the calculations in the replica formulation of quenched chiral perturbation theory, finding only mild modifications. In particular, a properly chosen ratio of the three-point and two-point functions is shown to be identical in the full and quenched theories at this order.