Probing the chiral weak Hamiltonian at finite volumes

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