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Non-leptonic kaon decays are often described through an effective chiral weakHamiltonian, whose couplings ("low-energy constants") encode allnon-perturbative QCD physics. It has recently been suggested that theselow-energy constants could be determined at finite volumes by matching thenon-perturbatively measured three-point correlation functions between the weakHamiltonian and two left-handed flavour currents, to analytic predictionsfollowing from chiral perturbation theory. Here we complete the analytic sidein two respects: by inspecting how small ("epsilon-regime") and intermediate orlarge ("p-regime") quark masses connect to each other, and by including in thediscussion the two leading Delta I = 1/2 operators. We show that theepsilon-regime offers a straightforward strategy for disentangling thecoefficients of the Delta I = 1/2 operators, and that in the p-regimefinite-volume effects are significant in these observables once thepseudoscalar mass M and the box length L are in the regime ML \lsim 5.0.Comment: 37 pages. v2: some additions and clarifications; published versio

Probing the chiral weak Hamiltonian at finite volumes