2,102 research outputs found
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
Thimble regularization at work for Gauge Theories: from toy models onwards
A final goal for thimble regularization of lattice field theories is the
application to lattice QCD and the study of its phase diagram. Gauge theories
pose a number of conceptual and algorithmic problems, some of which can be
addressed even in the framework of toy models. We report on our progresses in
this field, starting in particular from first successes in the study of one
link models.Comment: 7 pages, 2 figures. Talk given at the Lattice2015 Conferenc
One-dimensional QCD in thimble regularization
QCD in 0+1 dimensions is numerically solved via thimble regularization. In
the context of this toy model, a general formalism is presented for SU(N)
theories. The sign problem that the theory displays is a genuine one, stemming
from a (quark) chemical potential. Three stationary points are present in the
original (real) domain of integration, so that contributions from all the
thimbles associated to them are to be taken into account: we show how
semiclassical computations can provide hints on the regions of parameter space
where this is absolutely crucial. Known analytical results for the chiral
condensate and the Polyakov loop are correctly reproduced: this is in
particular trivial at high values of the number of flavors N_f. In this regime
we notice that the single thimble dominance scenario takes place (the dominant
thimble is the one associated to the identity). At low values of N_f
computations can be more difficult. It is important to stress that this is not
at all a consequence of the original sign problem (not even via the residual
phase). The latter is always under control, while accidental, delicate
cancelations of contributions coming from different thimbles can be in place in
(restricted) regions of the parameter space.Comment: 20 pages, 5 figures (many more pdf files) (one reference added
Thimble regularization at work besides toy models: from Random Matrix Theory to Gauge Theories
Thimble regularization as a solution to the sign problem has been
successfully put at work for a few toy models. Given the non trivial nature of
the method (also from the algorithmic point of view) it is compelling to
provide evidence that it works for realistic models. A Chiral Random Matrix
theory has been studied in detail. The known analytical solution shows that the
model is non-trivial as for the sign problem (in particular, phase quenched
results can be very far away from the exact solution). This study gave us the
chance to address a couple of key issues: how many thimbles contribute to the
solution of a realistic problem? Can one devise algorithms which are robust as
for staying on the correct manifold? The obvious step forward consists of
applications to gauge theories.Comment: 7 pages, 1 figure. Talk given at the Lattice2015 Conferenc
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
Power corrections and perturbative coupling from lattice gauge thoeries
From the analysis of the perturbative expansion of the lattice regularized
gluon condensate, toghether with MC data, we present evidence of OPE-unexpected
dim-2 power corrections in the scaling behaviour of the Wilson loop. These can
be interpreted as an indication that in lattice gauge theories the running
coupling at large momentum contains contributions of order Q^2.Comment: 3 pages, 2 figures. Talk given at the Lattice97 conference,
Edinburgh, U
Numerical Stochastic Perturbation Theory for full QCD
We give a full account of the Numerical Stochastic Perturbation Theory method
for Lattice Gauge Theories. Particular relevance is given to the inclusion of
dynamical fermions, which turns out to be surprisingly cheap in this context.
We analyse the underlying stochastic process and discuss the convergence
properties. We perform some benchmark calculations and - as a byproduct - we
present original results for Wilson loops and the 3-loop critical mass for
Wilson fermions.Comment: 35 pages, 5 figures; syntax revise
Four Loop Result in Lattice Gauge Theory by a Stochastic Method: Lattice Correction to the Condensate
We describe a stochastic technique which allows one to compute numerically
the coefficients of the weak coupling perturbative expansion of any observable
in Lattice Gauge Theory. The idea is to insert the exponential representation
of the link variables into the
Langevin algorithm and the observables and to perform the expansion in
\beta^{-1/2}. The Langevin algorithm is converted into an infinite hierarchy of
maps which can be exactly truncated at any order. We give the result for the
simple plaquette of SU(3) up to fourth loop order (\beta^{-4}) which extends by
one loop the previously known series.Comment: 9 pages. + 5 figures (postscript) appended at the end, (University of
Parma, Dept.of Physics, report uprf-397-1994
New issues for Numerical Stochastic Perturbation Theory
First attempts in the application of Numerical Stochastic Perturbation Theory
(NSPT) to the problem of pushing one loop further the computation of SU(3)
(SU(2)) pertubative beta function (in different schemes) are reviewed and the
relevance of such a computation is discussed. Other issues include the proposal
of a different strategy for gauge-fixed NSPT computations in lattice QCD.Comment: 3 pages, Latex, LATTICE98(algorithms
B Physics on the Lattice: , , , , mixing, \fb and all that
We present a short review of our most recent high statistics lattice
determinations in the HQET of the following important parameters in B physics:
the B--meson binding energy, and the kinetic energy of the
b quark in the B meson, , which due to the presence of power
divergences require a non--perturbative renormalization to be defined; the
running mass of the b quark,
; the -- mass splitting, whose
value in the HQET is determined by the matrix element of the chromo--magnetic
operator between B meson states, ; the B parameter of the
-- mixing, , and the decay constant of the B meson,
. All these quantities have been computed using a sample of gauge
field configurations on a lattice at . For
and , we obtain our
estimates by combining results from three independent lattice simulations at
, and on the same volume.Comment: 3 latex pages, uses espcrc2.sty (included). Talk presented at
LATTICE96(heavy quarks
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