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

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.Comment: 38 pages, 9 figure

Weak low-energy couplings from topological zero-mode wavefunctions

We discuss a new method to determine the low-energy couplings of the $\Delta S=1$ weak Hamiltonian in the $\epsilon$-regime. It relies on a matching of the topological poles in $1/m^2$ of three-point functions of two pseudoscalar densities and a four-fermion operator computed in lattice QCD, to the same observables in the Chiral Effective Theory. We present the results of a NLO computation in chiral perturbation theory of these correlation functions together with some preliminary numerical results.Comment: 7 pages. Contribution to Lattice 200

Spatio-temporal pattern recognizers using spiking neurons and spike-timing-dependent plasticity.

It has previously been shown that by using spike-timing-dependent plasticity (STDP), neurons can adapt to the beginning of a repeating spatio-temporal firing pattern in their input. In the present work, we demonstrate that this mechanism can be extended to train recognizers for longer spatio-temporal input signals. Using a number of neurons that are mutually connected by plastic synapses and subject to a global winner-takes-all mechanism, chains of neurons can form where each neuron is selective to a different segment of a repeating input pattern, and the neurons are feed-forwardly connected in such a way that both the correct input segment and the firing of the previous neurons are required in order to activate the next neuron in the chain. This is akin to a simple class of finite state automata. We show that nearest-neighbor STDP (where only the pre-synaptic spike most recent to a post-synaptic one is considered) leads to "nearest-neighbor" chains where connections only form between subsequent states in a chain (similar to classic "synfire chains"). In contrast, "all-to-all spike-timing-dependent plasticity" (where all pre- and post-synaptic spike pairs matter) leads to multiple connections that can span several temporal stages in the chain; these connections respect the temporal order of the neurons. It is also demonstrated that previously learnt individual chains can be "stitched together" by repeatedly presenting them in a fixed order. This way longer sequence recognizers can be formed, and potentially also nested structures. Robustness of recognition with respect to speed variations in the input patterns is shown to depend on rise-times of post-synaptic potentials and the membrane noise. It is argued that the memory capacity of the model is high, but could theoretically be increased using sparse codes

Effective heavy-light meson energies in small-volume quenched QCD

We study effective energies of heavy-light meson correlation functions in lattice QCD and a small volume of (0.2 fm)^4 to non-perturbatively calculate their dependence on the heavy quark mass in the continuum limit. Our quenched results obtained here constitute an essential intermediate step of a first fully non-perturbative computation of the b-quark's mass in the static approximation that has recently been presented as an application of a new proposal to non-perturbatively renormalize the Heavy Quark Effective Theory. The renormalization constant and the improvement coefficients relating the renormalized current and subtracted quark mass are determined in the relevant parameter region at weak couplings, which allows to perform the numerical simulations at several, precisely fixed values of the renormalization group invariant heavy quark mass in a range from 3 GeV to 15 GeV.Comment: 24 pages including figures and tables, latex2e; version published in JHEP, small additions, results unchange

K-->pipi amplitudes from lattice QCD with a light charm quark

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 large 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.Comment: 4 pages, 1 figure. Minor modifications. Final version to appear on PR

Non-perturbative renormalisation of left-left four-fermion operators with Neuberger fermions

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 Delta S=1 and Delta S=2 effective Hamiltonians. Our results are an essential ingredient for the determination of the low-energy constants governing non-leptonic kaon decays.Comment: 14 pages, 3 figure

Correlation functions at small quark masses with overlap fermions

We report on recent work on the determination of low-energy constants describing Delta{S}=1 weak transitions, in order to investigate the origins of the Delta{I}=1/2 rule. We focus on numerical techniques designed to enhance the statistical signal in three-point correlation functions computed with overlap fermions near the chiral limit.Comment: Talk presented at Lattice2004(weak), Fermilab, 21-26 June 2004, 3 pages, 2 figure

On the determination of low-energy constants for ΔS=1\Delta S=1 transitions

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.Comment: 11 pages, 2 figures, talks presented at Lattice 2005 (Weak matrix elements

Opening the Rome-Southampton window for operator mixing matrices

We show that the running of operators which mix under renormalization can be computed fully non-perturbatively as a product of continuum step scaling matrices. These step scaling matrices are obtained by taking the "ratio" of Z matrices computed at different energies in an RI-MOM type scheme for which twisted boundary conditions are an essential ingredient. Our method allows us to relax the bounds of the Rome-Southampton window. We also explain why such a method is important in view of the light quark physics program of the RBC-UKQCD collaborations. To illustrate our method, using n_f=2+1 domain-wall fermions, we compute the non-perturbative running matrix of four-quark operators needed in K->pipi decay and neutral kaon mixing. Our results are then compared to perturbation theory.Comment: 8 pages, 7 figures. v2: PRD version, minor changes and few references adde