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

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 ΔI = 3/2 weak operator, at next-to-leading order in finite volume SU(3)_L × SU(3)_R chiral perturbation theory, in the so-called -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 g₂₇, which determines the ΔI = 3/2 amplitude of the weak decays K→ππ as well as the kaon mixing parameter _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.