Probing the chiral weak Hamiltonian at finite volumes

Details Probing the chiral weak Hamiltonian at finite volumes Probing the chiral weak Hamiltonian at finite volumes

2006-07-20

arxiv.org/abs/hep-lat/0607027v2

JHEP 0610:069,2006

Physics

High Energy Physics

High Energy Physics - Lattice

37 pages. v2: some additions and clarifications; published version

Scientific paper

10.1088/1126-6708/2006/10/069

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.

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