Non-perturbative improvement of composite operators with Wilson fermions

We propose a method to improve lattice operators composed of Wilson fermions which allows the removal of all corrections of $O(a)$, including those proportional to the quark mass, leaving only errors of $O(a^2)$. The method exploits the fact that chiral symmetry is restored at short distances. By imposing this requirement on correlation functions of improved lattice operators at short distances, the coefficients which appear in these operators can be determined. The method is an extension of the improvement program of the ALPHA collaboration, which, up to now, has only been applicable in the chiral limit. The extension to quarks with non-zero masses is particularly important for applications in heavy quark physics.Comment: 15 pages, Late

New issues for Numerical Stochastic Perturbation Theory

First attempts in the application of Numerical Stochastic Perturbation Theory (NSPT) to the problem of pushing one loop further the computation of SU(3) (SU(2)) pertubative beta function (in different schemes) are reviewed and the relevance of such a computation is discussed. Other issues include the proposal of a different strategy for gauge-fixed NSPT computations in lattice QCD.Comment: 3 pages, Latex, LATTICE98(algorithms

The Sub-leading Magnetic Deformation of the Tricritical Ising Model in 2D as RSOS Restriction of the Izergin-Korepin Model

We compute the $S$-matrix of the Tricritical Ising Model perturbed by the subleading magnetic operator using Smirnov's RSOS reduction of the Izergin-Korepin model. We discuss some features of the scattering theory we obtain, in particular a non trivial implementation of crossing-symmetry, interesting connections between the asymptotic behaviour of the amplitudes, the possibility of introducing generalized statistics, and the monodromy properties of the OPE of the unperturbed Conformal Field Theory.Comment: (13 pages

QCD on Coarse Lattices

We show that the perturbatively-improved gluon action for QCD, once it is tadpole-improved, gives accurate results even with lattice spacings as large as 0.4~fm. {\em No\/} tuning of the couplings is required. Using this action and lattice spacing, we obtain a static potential that is rotationally invariant to within a few percent, the spin-averaged charmonium spectrum accurate to within 30--40~MeV, and scaling to within 5--10\%. We demonstrate that simulations on coarse lattices are several orders of magnitude less costly than simulations using current methods.Comment: 4 page

Two-body non-leptonic decays on the lattice

We show that, under reasonable hypotheses, it is possible to study two-body non-leptonic weak decays in numerical simulations of lattice QCD. By assuming that final-state interactions are dominated by the nearby resonances and that the couplings of the resonances to the final particles are smooth functions of the external momenta, it is possible indeed to overcome the difficulties imposed by the Maiani-Testa no-go theorem and to extract the weak decay amplitudes, including their phases. Under the same assumptions, results can be obtained also for time-like form factors and quasi-elastic processes.Comment: 15 pages, 1 Postscript figur

Nonperturbative definition of the pole mass and short distance expansion of the heavy quark potential in QCD

We show that the O(Lambda) ambiguity in the pole mass can be fixed in a natural way by introducing a modified nonperturbative V-scheme momentum space coupling tilde-alphaV(q) where the confining contributions have been subtracted out. The method used is in the spirit of the infrared finite coupling approach to power corrections, and gives a non perturbative definition of the `potential subtracted' mass. The short distance expansion of the static potential is derived, taking into account an hypothetical short distance linear term. The magnitude of the standard OPE contributions are estimated in quenched QCD, based on results of Luscher and Weisz. It is observed that the expansion is not yet reliable at the shortest distances presently measured on the lattice.Comment: 10 pages, JHEP3.cls style; a few misprints corrected. To appear in Physics Letters

A simple construction of fermion measure term in U(1) chiral lattice gauge theories with exact gauge invariance

In the gauge invariant formulation of U(1) chiral lattice gauge theories based on the Ginsparg-Wilson relation, the gauge field dependence of the fermion measure is determined through the so-called measure term. We derive a closed formula of the measure term on the finite volume lattice. The Wilson line degrees of freedom (torons) of the link field are treated separately to take care of the global integrability. The local counter term is explicitly constructed with the local current associated with the cohomologically trivial part of the gauge anomaly in a finite volume. The resulted formula is very close to the known expression of the measure term in the infinite volume with a single parameter integration, and would be useful in practical implementations.Comment: 25 pages, uses JHEP3.cls, the version to appear in JHE

The gradient flow running coupling with twisted boundary conditions

We study the gradient flow for Yang-Mills theories with twisted boundary conditions. The perturbative behavior of the energy density $\langle E(t)\rangle$ is used to define a running coupling at a scale given by the linear size of the finite volume box. We compute the non-perturbative running of the pure gauge $SU(2)$ coupling constant and conclude that the technique is well suited for further applications due to the relatively mild cutoff effects of the step scaling function and the high numerical precision that can be achieved in lattice simulations. We also comment on the inclusion of matter fields.Comment: 27 pages. LaTe

The quark propagator in momentum space

The quark propagator is calculated in the Landau gauge at beta=6.0. A method for removing the dominant, tree-level lattice artefacts is presented, enabling a calculation of the momentum-dependent dynamical quark mass.Comment: LATTICE 99(spectrum), 3 pages, 3 figure

Non-perturbatively Renormalized Light-Quark Masses with the Alpha Action

We have computed the light quark masses using the O(a^2) improved Alpha action, in the quenched approximation. The renormalized masses have been obtained non-perturbatively. By eliminating the systematic error coming from the truncation of the perturbative series, our procedure removes the discrepancies, observed in previous calculations, between the results obtained using the vector and the axial-vector Ward identities. It also gives values of the quark masses larger than those obtained by computing the renormalization constants using (boosted) perturbation theory. Our main results, in the RI (MOM) scheme and at a renormalization scale \mu=2 GeV, are m^{RI}_s= 138(15) MeV and m^{RI}_l= 5.6(5) MeV, where m^{RI}_s is the mass of the strange quark and m^{RI}_l=(m^{RI}_u+m^{RI}_d)/2 the average mass of the up-down quarks. From these results, which have been obtained non-perturbatively, by using continuum perturbation theory we derive the \bar{MS} masses, at the same scale, and the renormalization group invariant (m^{RGI}) masses. We find m^{NLO \bar{MS}}_s= 121(13)$ MeV and m^{NLO\bar{MS}}_l= 4.9(4) MeV at the next-to-leading order; m^{N^2LO \bar{MS}}_s= 111(12) MeV, m^{N^2LO \bar{MS}}_l= 4.5(4) MeV, m_s^{RGI}= 177(19) MeV and m^{RGI}_l= 7.2(6) MeV at the next-to-next-to-leading order.Comment: 13 pages, 1 figur