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

The Dirac operator spectrum: a perturbative approach

By computing the Dirac operator spectrum by means of Numerical Stochastic Perturbation Theory, we aim at throwing some light on the widely accepted picture for the mechanism which is behind the Bank-Casher relation. The latter relates the chiral condensate to an accumulation of eigenvalues in the low end of the spectrum. This can be in turn ascribed to the usual mechanism of repulsion among eigenvalues which is typical of quantum interactions. First results appear to confirm that NSPT can indeed enable us to inspect a huge reshuffling of eigenvalues due to quantum repulsion.Comment: 8 pages, 6 figures; talk presented at the 27th International Symposium on Lattice Field Theory (Lattice 2009), Beijing, China, 26-31 Jul 200

High-loop perturbative renormalization constants for Lattice QCD (III): three-loop quark currents for Iwasaki gauge action and n_f=4 Wilson fermions

This is the third of a series of papers on three-loop computation of renormalization constants for Lattice QCD. Our main point of interest are results for the regularization defined by Iwasaki gauge action and n_f=4 Wilson fermions. Our results for quark bilinears renormalized according to the RI'-MOM scheme can be compared to non-perturbative results. The latter are available for Twisted Mass QCD: being defined in the chiral limit, renormalization constants must be the same. We also address more general problems. In particular, we discuss a few methodological issues connected to summing the perturbative series such as the effectiveness of Boosted Perturbation Theory and the disentanglement of irrelevant and finite volume contributions. Discussing these issues we consider ont only the new results of this paper, but also those for the regularization defined by tree-level Symanzik improved gauge action and n_f=2 Wilson fermions, which we presented in a recent paper of ours. We finally comment to which extent the techniques we put at work in the NSPT context can provide a fresher look into the lattice version of the RI'-MOM scheme.Comment: 20 pages, 4 figures, pdflatex The Section on different ways of summing the series has been updated: a few extra informations have been provided and a clearer notation has been introduce

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

Developments and new applications of numerical stochastic perturbation theory

A review of new developments in numerical stochastic perturbation theory (NSPT) is presented. In particular, the status of the extension of the method to gauge fixed lattice QCD is reviewed and a first application to compact (scalar) QED is presented. Lacking still a general proof of the convergence of the underlying stochastic processes, a self-consistent method for testing the results is discussed.Comment: 3 pages, 1 figure. Poster presented at the Lattice97 conference, Edinburgh, U

Making Racing Fun Through Player Modeling and Track Evolution

This paper addresses the problem of automatically constructing tracks tailor-made to maximize the enjoyment of individual players in a simple car racing game. To this end, some approaches to player modeling are investigated, and a method of using evolutionary algorithms to construct racing tracks is presented. A simple player-dependent metric of entertainment is proposed and used as the fitness function when evolving tracks. We conclude that accurate player modeling poses some significant challenges, but track evolution works well given the right track representation

Four-loop lattice-regularized vacuum energy density of the three-dimensional SU(3) + adjoint Higgs theory

The pressure of QCD admits at high temperatures a factorization into purely perturbative contributions from "hard" thermal momenta, and slowly convergent as well as non-perturbative contributions from "soft" thermal momenta. The latter can be related to various effective gluon condensates in a dimensionally reduced effective field theory, and measured there through lattice simulations. Practical measurements of one of the relevant condensates have suffered, however, from difficulties in extrapolating convincingly to the continuum limit. In order to gain insight on this problem, we employ Numerical Stochastic Perturbation Theory to estimate the problematic condensate up to 4-loop order in lattice perturbation theory. Our results seem to confirm the presence of "large" discretization effects, going like $a\ln(1/a)$, where $a$ is the lattice spacing. For definite conclusions, however, it would be helpful to repeat the corresponding part of our study with standard lattice perturbation theory techniques.Comment: 35 pages. v2: minor corrections, published versio

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

An efficient flamelet progress-variable method for modeling non-premixed flames in weak electric fields

Combustion stabilization and enhancement of the flammability limits are mandatory objectives to improve nowadays combustion chambers. At this purpose, the use of an electric field in the flame region provides a solution which is, at the same time, easy to implement and effective to modify the flame structure. The present work describes an efficient flamelet progress-variable approach developed to model the fluid dynamics of flames immersed in an electric field. The main feature of this model is that it can use complex ionization mechanisms without increasing the computational cost of the simulation. The model is based on the assumption that the combustion process is not directly influenced by the electric field and has been tested using two chemi-ionization mechanisms of different complexity in order to examine its behavior with and without the presence of heavy anions in the mixture. Using a one- and two-dimensional numerical test cases, the present approach has been able to reproduce all the major aspects encountered when a flame is subject to an imposed electric field and the main effects of the different chemical mechanisms. Moreover, the proposed model is shown to produce a large reduction in the computational cost, being able to shorten the time needed to perform a simulation up to 40 times.Comment: 26 pages, 13 figures, paper accepted for publication on Computers and Fluid