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

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

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

Quantum Interactions Between Non-Perturbative Vacuum Fields

We develop an approach to investigate the non-perturbative dynamics of quantum field theories, in which specific vacuum field fluctuations are treated as the low-energy dynamical degrees of freedom, while all other vacuum field configurations are explicitly integrated out from the path integral. We show how to compute the effective interaction between the vacuum field degrees of freedom both perturbatively (using stochastic perturbation theory) and fully non-perturbatively (using lattice field theory simulations). The present approach holds to all orders in the couplings and does not rely on the semi-classical approximation.Comment: 15 pages, 4 figure

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 strategy to tackle finite size effects which can be quite sizeable in the computation of logarithmically divergent renormalization constants. Our first high loop determination of quark bilinears for Wilson fermions was limited to finite constants and finite ratios. A precise determination of Z_P and Z_S (and hence of Z_m) 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 computations for the Lattice QCD regularization defined by tree level Symanzik improved gauge action and Wilson 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.Comment: 7 pages, poster presented at the XXV International Symposium on Lattice Field Theory, July 30 - August 4 2007, Regensburg, German

Metropolis Monte Carlo on the Lefschetz thimble: application to a one-plaquette model

We propose a new algorithm based on the Metropolis sampling method to perform Monte Carlo integration for path integrals in the recently proposed formulation of quantum field theories on the Lefschetz thimble. The algorithm is based on a mapping between the curved manifold defined by the Lefschetz thimble of the full action and the flat manifold associated with the corresponding quadratic action. We discuss an explicit method to calculate the residual phase due to the curvature of the Lefschetz thimble. Finally, we apply this new algorithm to a simple one-plaquette model where our results are in perfect agreement with the analytic integration. We also show that for this system the residual phase does not represent a sign problem

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

Quantum field theories on the Lefschetz thimble

In these proceedings, we summarize the Lefschetz thimble approach to the sign problem of Quantum Field Theories. In particular, we review its motivations, and we summarize the results of the application of two different algorithms to two test models.Comment: contributions to 31st International Symposium on Lattice Field Theory - LATTICE 2013, July 29 - August 3, 2013, Mainz, Germany and QCD-TNT-III, 2-6 September, 2013, European Centre for Theoretical Studies in Nuclear Physics and Related Areas (ECT*), Villazzano, Trento (Italy