V. Miccio

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.

3-d lattice Yang-Mills free energy to four loops

We compute the expansion of the 3-d Lattice Yang-Mills free energy to four-loop order by means of Numerical Stochastic Perturbation Theory. The first and second order are already known and are correctly reproduced. The third- and fourth-order coefficients are new results. The known logarithmic divergence in the fourth order is correctly identified. We comment on the relevance of our computation in the context of dimensionally reduced finite temperature QCD.

Four loop stochastic perturbation theory in 3d SU(3)

Abstract Dimensional reduction is a key issue in finite temperature field theory. For example, when following the QCD Free Energy from low to high scales across the critical temperature, ultrasoft degrees of freedom can be captured by a 3d SU(3) pure gauge theory. For such a theory a complete perturbative matching requires four loop computations, which we undertook by means of Numerical Stochastic Perturbation Theory. We report on the computation of the pure gauge plaquette in 3d, and in particular on the extraction of the logarithmic divergence at order g 8 , which had already been computed in the continuum.

Four-loop plaquette in 3d with a mass regulator

The QCD free energy can be studied by dimensional reduction to a three-dimensional (3d) effective theory, whereby non-perturbative lattice simulations become less demanding. To connect to the original QCD a perturbative matching computation is required, which is conventionally carried out in dimensional regularization. Therefore the 3d lattice results need to be converted to this regularization scheme as well. The conversion must be carried up to 4-loop order, where the free energy displays an infrared (IR) singularity. We therefore need a regulator which can be implemented both on the lattice and in the continuum computation. We introduce a mass regulator to perform Numerical Stochastic Perturbation Theory computations. Covariant gauge is fixed in the Faddeev-Popov scheme without introducing any ghost fields.

Unquenched numerical stochastic perturbation theory

The inclusion of fermionic loops contribution in Numerical Stochastic Perturbation Theory (NSPT) has a nice feature: it does not cost so much (provided only that an FFT can be implemented in a fairly efficient way). Focusing on Lattice SU(3), we report on the performance of the current implementation of the algorithm and the status of first computations undertaken.

Two and three loops computations of renormalization constants for lattice QCD

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.

3-d lattice SU(3) free energy to four loops

We report on the perturbative computation of the 3d lattice Yang-Mills free energy to four loops by means of Numerical Stochastic Perturbation Theory. The known first and second orders have been correctly reproduced; the third and fourth order coefficients are new results and the known logarithmic IR divergence in the fourth order has been correctly identified. Progress is being made in switching to the gluon mass IR regularization and the related inclusion of the Faddeev-Popov determinant.

Preliminary results in unquenched numerical stochastic perturbation theory

Abstract Introducing fermionic loops contributions in Numerical Stochastic Perturbation Theory was mainly motivated by the proposal to compute 2–3 loops for renormalization constants (and improvement coefficients). This is feasible because the computational overhead of unquenching NSPT is by far lower than for non perturbative simulations. We report on first, preliminary results for the quark propagator (basically the third loop for the critical mass) and discuss the status of the computation of other quantities.