2,842 research outputs found
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
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.Comment: Lattice2004(non-zero), 3 pages, 2 figure
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 , where 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
Renormalization of infrared contributions to the QCD pressure
Thanks to dimensional reduction, the infrared contributions to the QCD
pressure can be obtained from two different three-dimensional effective field
theories, called the Electrostatic QCD (Yang-Mills plus adjoint Higgs) and the
Magnetostatic QCD (pure Yang-Mills theory). Lattice measurements have been
carried out within these theories, but a proper interpretation of the results
requires renormalization, and in some cases also improvement, i.e. the removal
of terms of O(a) or O(a^2). We discuss how these computations can be
implemented and carried out up to 4-loop level with the help of Numerical
Stochastic Perturbation Theory.Comment: 7 pages, 4 figures, talk presented at Lattice 2006 (High temperature
and density
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 MSbar 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.Comment: 16 pages. v2: published versio
3-d Lattice QCD Free Energy to Four Loops
We compute the expansion of the 3-d Lattice QCD 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.Comment: 8 pages, 3 figures, latex typeset with JHEP3.cl
Two-point functions of quenched lattice QCD in Numerical Stochastic Perturbation Theory. (I) The ghost propagator in Landau gauge
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
limits, based on a general strategy that we discuss in detail.Comment: 27 pages, 11 figure
Two-point functions of quenched lattice QCD in Numerical Stochastic Perturbation Theory
We summarize the higher-loop perturbative computation of the ghost and gluon
propagators in SU(3) Lattice Gauge Theory. Our final aim is to compare with
results from lattice simulations in order to expose the genuinely
non-perturbative content of the latter. By means of Numerical Stochastic
Perturbation Theory we compute the ghost and gluon propagators in Landau gauge
up to three and four loops. We present results in the infinite volume and limits, based on a general fitting strategy.Comment: 3 pages, 5 figures, talk at conference QCHS-IX, Madrid 201
An efficient method to compute the residual phase on a Lefschetz thimble
We propose an efficient method to compute the so-called residual phase that
appears when performing Monte Carlo calculations on a Lefschetz thimble. The
method is stochastic and its cost scales linearly with the physical volume,
linearly with the number of stochastic estimators and quadratically with the
length of the extra dimension along the gradient flow. This is a drastic
improvement over previous estimates of the cost of computing the residual
phase. We also report on basic tests of correctness and scaling of the code.Comment: New simulations, new plot, new appendix added. To appear in PRD. 9
pages, 3 figure
The lattice ghost propagator in Landau gauge up to three loops using Numerical Stochastic Perturbation Theory
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-logarithmic parts of logarithmically divergent quantities as a function
of the propagator momentum squared in the infinite-volume and limits.
We find accurate coincidence with the one-loop result 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.Comment: 8 pages, 6 figures, XXVII International Symposium on Lattice Field
Theory - LAT2009, Beijin
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