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ABSTRACT: We compute the leading-order low-energy constants of the DeltaS=1 effective weak Hamiltonian in the quenched approximation of QCD with up, down, strange, and charm quarks degenerate and light. They are extracted by comparing the predictions of finite-volume chiral perturbation theory with lattice QCD computations of suitable correlation functions carried out with quark masses ranging from a few MeV up to half of the physical strange mass. We observe a DeltaI=1/2 enhancement in this corner of the parameter space of the theory. Although matching with the experimental result is not observed for the DeltaI=1/2 amplitude, our computation suggests large QCD contributions to the physical DeltaI=1/2 rule in the GIM limit, and represents the first step to quantify the role of the charm-quark mass in K-->pipi amplitudes. The use of fermions with an exact chiral symmetry is an essential ingredient in our computation.
Physical Review Letters 02/2007; 98(8):082003. · 7.37 Impact Factor
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ABSTRACT: We outline a general strategy for the non-perturbative renormalisation of composite operators in discretisations based on Neuberger fermions, via a matching to results obtained with Wilson-type fermions. As an application, we consider the renormalisation of the four-quark operators entering the ΔS=1 and ΔS=2 effective Hamiltonians. Our results are an essential ingredient for the determination of the low-energy constants governing non-leptonic kaon decays.
Physics Letters B. 07/2006;
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ABSTRACT: Using quenched chiral perturbation theory, we compute the long-distance behaviour of two-point functions of flavour non-singlet axial and vector currents in a finite volume, for small quark masses, and at a fixed gauge-field topology. We also present the corresponding predictions for the unquenched theory at fixed topology. These results can in principle be used to measure the low-energy constants of the chiral Lagrangian, from lattice simulations in volumes much smaller than one pion Compton wavelength. We show that quenching has a dramatic effect on the vector correlator, which is argued to vanish to all orders, while the axial correlator appears to be a robust observable only moderately sensitive to quenching.
Nuclear Physics B. 11/2002;
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ABSTRACT: We present our preliminary results for three-point correlation functions involving the operators entering the $\Delta{S}=1$ effective Hamiltonian with an active charm quark, obtained using overlap fermions in the quenched approximation. This is the first computation carried out for valence quark masses small enough so as to permit a matching to Quenched Chiral Perturbation Theory in the $\epsilon$-regime. The commonly observed large statistical fluctuations are tamed by means of low-mode averaging techniques, combined with restrictions to individual topological sectors. We also discuss the matching of the resulting hadronic matrix elements to the effective low-energy constants for $\Delta{S}=1$ transitions. This involves (a) finite-volume corrections which can be evaluated at NLO in Quenched Chiral Perturbation Theory, and (b) the short-distance renormalization of the relevant four-quark operators in discretizations based on the overlap operator. We discuss perturbative estimates for the renormalization factors and possible strategies for their non-perturbative evaluation. Our results can be used to isolate the long-distance contributions to the $\Delta I=1/2$ rule, coming from physics effects around the intrinsic QCD scale.
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ABSTRACT: Using quenched chiral perturbation theory we compute meson correlation functions at finite volume and fixed gauge field topology. We also present the corresponding analytical predictions for the unquenched theory at fixed gauge field topology. These results can be used to measure the low-energy parameters of the chiral Lagrangian from lattice simulations in volumes much smaller than one pion Compton wavelength.
Nuclear Physics B.
