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.Comment: 3 pages, 3 figures, Lattice2002(algor

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.Comment: Lattice2004(improv), 3 pages, 4 figure

Numerical Stochastic Perturbation Theory. Convergence and features of the stochastic process. Computations at fixed (Landau) Gauge

Concerning Numerical Stochastic Perturbation Theory, we discuss the convergence of the stochastic process (idea of the proof, features of the limit distribution, rate of convergence to equilibrium). Then we also discuss the expected fluctuations in the observables and give some idea to reduce them. In the end we show that also computation of quantities at fixed (Landau) Gauge is now possible.Comment: 3 pages. Contributed to 17th International Symposium on Lattice Field Theory (LATTICE 99), Pisa, Italy, 29 Jun - 3 Jul 199

Beta-function, Renormalons and the Mass Term from Perturbative Wilson Loops

Several Wilson loops on several lattice sizes are computed in Perturbation Theory via a stochastic method. Applications include: Renormalons, the Mass Term in Heavy Quark Effective Theory and (possibly) the beta-function.Comment: 3 pages, 1 eps figure. Contributed to 17th International Symposium on Lattice Field Theory (LATTICE 99), Pisa, Italy, 29 Jun - 3 Jul 199

A consistency check for Renormalons in Lattice Gauge Theory: beta^(-10) contributions to the SU(3) plaquette

We compute the perturbative expansion of the Lattice SU(3) plaquette to beta^(-10) order. The result is found to be consistent both with the expected renormalon behaviour and with finite size effects on top of that.Comment: 15 pages, 5 colour eps figures. Axes labels added in the figures. A comment added in the appendi

The n_f=2 residual mass in lattice HQET to alpha^3 order

We compute the so called residual mass in Lattice Heavy Quark Effective Theory to alpha^3 order in the n_f=2 (unquenched) case. The control of this additive mass renormalization is crucial for the determination of the heavy quark mass from lattice simulations. We discuss the impact on an unquenched determination of the b-quark mass.Comment: Lattice2004(heavy), 3 pages, 1 figur

Fermionic Loops in Numerical Stochastic Perturbation Theory

We discuss the inclusion of fermionic loops contributions in Numerical Stochastic Perturbation Theory for Lattice Gauge Theories. We show how the algorithm implementation is in principle straightforward and report on the status of the project.Comment: Lattice 2000 (Perturbation Theory), 4 pages, (misprint corrected

High loop renormalization constants for Wilson fermions/Symanzik improved gauge action

We present the current status of our computation of quark bilinear renormalization constants for Wilson fermions and Symanzik improved gauge action. Computations are performed in Numerical Stochastic Perturbation Theory. Volumes range from 10^4 to 32^4. Renormalization conditions are those of the RI'-MOM scheme, imposed at different values of the physical scale. Having measurements available at several momenta, irrelevant effects are taken into account by means of hypercubic symmetric Taylor expansions. Finite volumes effects are assessed repeating the computations at different lattice sizes. In this way we can extrapolate our results to the continuum limit, in infinite volume.Comment: 8 pages, 3 figures, talk presented at the 27th International Symposium on Lattice Field Theory (Lattice 2009), Beijing, China, 26-31 Jul 200

Lattice gluodynamics at negative g^2

We consider Wilson's SU(N) lattice gauge theory (without fermions) at negative values of beta= 2N/g^2 and for N=2 or 3. We show that in the limit beta -> -infinity, the path integral is dominated by configurations where links variables are set to a nontrivial element of the center on selected non intersecting lines. For N=2, these configurations can be characterized by a unique gauge invariant set of variables, while for N=3 a multiplicity growing with the volume as the number of configurations of an Ising model is observed. In general, there is a discontinuity in the average plaquette when g^2 changes its sign which prevents us from having a convergent series in g^2 for this quantity. For N=2, a change of variables relates the gauge invariant observables at positive and negative values of beta. For N=3, we derive an identity relating the observables at beta with those at beta rotated by +- 2pi/3 in the complex plane and show numerical evidence for a Ising like first order phase transition near beta=-22. We discuss the possibility of having lines of first order phase transitions ending at a second order phase transition in an extended bare parameter space.Comment: 7 pages, 7 figures, uses revtex, Eqs. 15-17 corrected, minor change