Determination of the $\Delta S=1$ weak Hamiltonian in the SU(4) chiral limit through topological zero-mode wave functions

Abstract

A new method to determine the low-energy couplings of the $\Delta S=1$ weak Hamiltonian is presented. It relies on a matching of the topological poles in $1/m^2$ of three-point correlators of two pseudoscalar densities and a four-fermion operator, measured in lattice QCD, to the same observables computed in the $\epsilon$-regime of chiral perturbation theory. We test this method in a theory with a light charm quark, i.e. with an SU(4) flavour symmetry. Quenched numerical measurements are performed in a 2 fm box, and chiral perturbation theory predictions are worked out up to next-to-leading order. The matching of the two sides allows to determine the weak low-energy couplings in the SU(4) limit. We compare the results with a previous determination, based on three-point correlators containing two left-handed currents, and discuss the merits and drawbacks of the two procedures.

38 pages, 9 figures

References in corpus (6)

• Deflation acceleration of lattice QCD simulations
• Precision study of the SU(3) topological susceptibility in the continuum
• Overlap Hypercube Fermions in QCD Simulations Near the Chiral Limit
• K-->pipi amplitudes from lattice QCD with a light charm quark
• Non-perturbative renormalisation of left-left four-fermion operators with Neuberger fermions
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Cited by in corpus (6)

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• Exploring the role of the charm quark in the $\Delta I=1/2$ rule
• Extracting the electro-magnetic pion form factor from QCD in a finite volume