C. Torrero

The leading non-perturbative coefficient in the weak-coupling expansion of hot QCD pressure

Using Numerical Stochastic Perturbation Theory within three-dimensional pure SU(3) gauge theory, we estimate the last unknown renormalization constant that is needed for converting the vacuum energy density of this model from lattice regularization to the MS scheme. Making use of a previous non-perturbative lattice measurement of the plaquette expectation value in three dimensions, this allows us to approximate the first non-perturbative coefficient that appears in the weak-coupling expansion of hot QCD pressure.

High-loop perturbative renormalization constants for lattice QCD (I): finite constants for Wilson quark currents

We present a high order perturbative computation of the renormalization constants ZV, ZA and of the ratio ZP/ZS for Wilson fermions. The computational setup is the one provided by the RI’-MOM scheme. Three- and four-loop expansions are made possible by numerical stochastic perturbation theory. Results are given for various numbers of flavors and/or (within a finite accuracy) for generic nf up to three loops. For the case nf=2 we also present four-loop results. Finite-size effects are well under control, and the continuum limit is taken by means of hypercubic symmetric Taylor expansions. The main indetermination comes from truncation errors, which should be assessed in connection with the convergence properties of the series. The latter is best discussed in the framework of boosted perturbation theory, whose impact we try to assess carefully. Final results and their uncertainties show that high-loop perturbative computations of lattice QCD renormalization constants (RCs) are feasible and should not be viewed as a second choice. As a by-product, we discuss the perturbative expansion for the critical mass, for which results are also for generic nf up to three loops, while a four-loop result is obtained for nf=2.

Two-point functions of quenched lattice QCD in Numerical Stochastic Perturbation Theory. (II) The gluon propagator in Landau gauge

Abstract This is the first of a series of two papers on the perturbative computation of the ghost and gluon propagators in SU ( 3 ) Lattice Gauge Theory. Our final aim is to eventually compare with results from lattice simulations in order to enlight the genuinely non-perturbative content of the latter. By means of Numerical Stochastic Perturbation Theory we compute the ghost propagator in Landau gauge up to three loops. We present results in the infinite volume and a → 0 limits, based on a general strategy that we discuss in detail.

High loop renormalization constants by NSPT: a status report

We present an update on Numerical Stochastic Perturbation Theory projects for Lattice QCD, which are by now run on apeNEXT. As a first issue, we discuss a st rategy to tackle finite size effects which can be quite sizeable in the computation of logarithmically divergent renormalization constants. Our first high loop determination of quar k bilinears for Wilson fermions was limited to finite constants and finite ratios. A precise deter mination of ZP and ZS (and hence of Zm) now becomes possible. We also give an account of computations for actions different from the standard regularization we have taken into account so far (Wilson gauge action and Wilson fermions). In particular, we present the status of computat ions for the Lattice QCD regularization defined by tree level Symanzik improved gauge action and Wils on fermions, which became quite popular in recent times. We also take the chance to discuss the related topic of the computation of the gluon and ghost propagators (which we undertook in collaboration with another group). This is relevant in order to better understand non-perturbative computations of propagators aiming at qualitative/quantitative understanding of confinement.

The phase diagram of the three-dimensionalZ2 gauge Higgs system at zero and finite temperature

Abstract We study the effect of adding a matter field to theZ2 gauge model in three dimensions at zero and finite temperature. Up to a given value of the parameter regulating the coupling, the matter field produces a slight shift of the transition line without changing the universality class of the pure gauge theory, as seen by finite size scaling analysis or by comparison, in the finite temperature case, to exact formulas of conformal field theory. At zero temperature the critical line turns into a first-order transition. The fate of this kind of transition in the finite temperature case is discussed.

Computing the nucleon sigma terms at the physical point

Nucleon sigma terms are quantities that play an important role in various areas: among others, they connect the pion-nucleon and the kaon-nucleon amplitudes to the hadron spectrum and they are also relevant for the direct detection of Dark Matter. We present preliminary results for the up-down and strange sigma terms obtained from

The lattice ghost propagator in Landau gauge up to three loops using Numerical Stochastic Perturbation Theory

N_f=2+1

Two and three loops computations of renormalization constants for lattice QCD

lattice simulations that are performed at five lattice spacings and for pion masses all the way down to its physical value.

A new approach to the two-dimensional

We complete our high-accuracy studies of the lattice ghost propagator in Landau gauge in Numerical Stochastic Perturbation Theory up to three loops. We present a systematic strategy which allows to extract with sufficient precision the non-logarit hmic parts of logarithmically divergent quantities as a function of the propagator momentum squared in the infinite-volume and a → 0 limits. We find accurate coincidence with the one-loop resul t for the ghost self-energy known from standard Lattice Perturbation Theory and improve our previous estimate for the two-loop constant contribution to the ghost self-energy in Landau gauge. Our results for the perturbative ghost propagator are compared with Monte Carlo measurements of the ghost propagator performed by the Berlin Humboldt university group which has used the exponential relation between potentials and gauge links.

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Renormalization constants can be computed by means of Numerical Stochastic Perturbation Theory to two/three loops in lattice perturbation theory, both in the quenched approximation and in the full (unquenched) theory. As a case of study we report on the computation of renormalization constants of the propagator for Wilson fermions. We present our unquenched ( N f = 2) computations and compare the results with non perturbative determinations.