Probing the chiral weak Hamiltonian at finite volumes

Abstract

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.

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

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• Finite volume effects for meson masses and decay constants
• Topological susceptibility in the SU(3) gauge theory
• Lattice gauge action suppressing near-zero modes of H_W
• Twist-two matrix elements at finite and infinite volume
• Radiative Kaon Decays and the Penguin Contribution to the Delta I = 1/2 Rule
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• A strategy to study the role of the charm quark in explaining the Delta{I}=1/2 rule
• A nucleon in a tiny box
• Simulating Full QCD with the Fixed Point Action
• Quarks with Twisted Boundary Conditions in the Epsilon Regime
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• Effect of low-lying fermion modes in the $\epsilon$-regime of QCD
• Simulating an arbitrary number of flavors of dynamical overlap fermions
• The $B_K$ Kaon Parameter in the Chiral Limit
• Determining F_pi from spectral sum rules
• Charm mass dependence of the weak Hamiltonian in chiral perturbation theory
• Quenched penguins and the Delta I=1/2 rule

Cited by in corpus (8)

• Two-flavor lattice QCD simulation in the epsilon-regime with exact chiral symmetry
• Two-flavor lattice QCD in the epsilon-regime and chiral Random Matrix Theory
• Finite Volume Scaling of Pseudo Nambu-Goldstone Bosons in QCD
• K-->pipi amplitudes from lattice QCD with a light charm quark
• Partially quenched chiral perturbation theory in the epsilon-regime
• Non-leptonic kaon decays at large $N_c$
• Determination of the $\Delta S=1$ weak Hamiltonian in the SU(4) chiral limit through topological zero-mode wave functions
• Exploring the role of the charm quark in the $\Delta I=1/2$ rule