375 research outputs found
Effects of Nonperturbative Improvement in Quenched Hadron Spectroscopy
We discuss a comparative analysis of unimproved and nonperturbatively
improved quenched hadron spectroscopy, on a set of 104 gauge configurations, at
beta=6.2. We also present here our results for meson decay constants, including
the constants f_D and f_Ds in the charm-quark region.Comment: LATTICE98(spectrum
SU(2) lattice gluon propagators at finite temperatures in the deep infrared region and Gribov copy effects
We study numerically the SU(2) Landau gauge transverse and longitudinal gluon
propagators at non-zero temperatures T both in confinement and deconfinement
phases. The special attention is paid to the Gribov copy effects in the
IR-region. Applying powerful gauge fixing algorithm we find that the Gribov
copy effects for the transverse propagator D_T(p) are very strong in the
infrared, while the longitudinal propagator D_L(p) shows very weak (if any)
Gribov copy dependence. The value D_T(0) tends to decrease with growing lattice
size; however, D_T(0) is non-zero in the infinite volume limit, in disagreement
with the suggestion made in [1]. We show that in the infrared region D_T(p) is
not consistent with the pole-type formula not only in the deconfinement phase
but also for T < T_c. We introduce new definition of the magnetic infrared mass
scale ('magnetic screening mass') m_M. The electric mass m_E has been
determined from the momentum space longitudinal gluon propagator. We study also
the (finite) volume and temperature dependence of the propagators as well as
discretization errors.Comment: 11 pages, 14 figures, 3 tables. Few minor change
The Minimal Landau Background Gauge on the Lattice
We present the first numerical implementation of the minimal Landau
background gauge for Yang-Mills theory on the lattice. Our approach is a simple
generalization of the usual minimal Landau gauge and is formulated for general
SU(N) gauge group. We also report on preliminary tests of the method in the
four-dimensional SU(2) case, using different background fields. Our tests show
that the convergence of the numerical minimization process is comparable to the
case of a null background. The uniqueness of the minimizing functional employed
is briefly discussed.Comment: 5 pages, 1 tabl
Infrared-suppressed gluon propagator in 4d Yang-Mills theory in a Landau-like gauge
The infrared behavior of the gluon propagator is directly related to
confinement in QCD. Indeed, the Gribov-Zwanziger scenario of confinement
predicts an infrared vanishing (transverse) gluon propagator in Landau-like
gauges, implying violation of reflection positivity and gluon confinement.
Finite-volume effects make it very difficult to observe (in the minimal Landau
gauge) an infrared suppressed gluon propagator in lattice simulations of the
four-dimensional case. Here we report results for the SU(2) gluon propagator in
a gauge that interpolates between the minimal Landau gauge (for gauge parameter
lambda equal to 1) and the minimal Coulomb gauge (corresponding to lambda = 0).
For small values of lambda we find that the spatially-transverse gluon
propagator D^tr(0,|\vec p|), considered as a function of the spatial momenta
|\vec p|, is clearly infrared suppressed. This result is in agreement with the
Gribov-Zwanziger scenario and with previous numerical results in the minimal
Coulomb gauge. We also discuss the nature of the limit lambda -> 0 (complete
Coulomb gauge) and its relation to the standard Coulomb gauge (lambda = 0). Our
findings are corroborated by similar results in the three-dimensional case,
where the infrared suppression is observed for all considered values of lambda.Comment: 5 pages, 2 figures, one figure with additional results and extended
discussion of some aspects of the results added and some minor
clarifications. In v3: Various small changes and addition
Numerical Study of Gluon Propagator and Confinement Scenario in Minimal Coulomb Gauge
We present numerical results in SU(2) lattice gauge theory for the
space-space and time-time components of the gluon propagator at equal time in
the minimal Coulomb gauge. It is found that the equal-time would-be physical
3-dimensionally transverse gluon propagator vanishes at
when extrapolated to infinite lattice volume, whereas the
instantaneous color-Coulomb potential is strongly enhanced at
. This has a natural interpretation in a confinement scenario in
which the would-be physical gluons leave the physical spectrum while the
long-range Coulomb force confines color. Gribov's formula provides an excellent fit to our data
for the 3-dimensionally transverse equal-time gluon propagator
for relevant values of .Comment: 23 pages, 12 figures, TeX file. Minor modifications, incorporating
referee's suggestion
Numerical Study of the Ghost-Ghost-Gluon Vertex on the Lattice
It is well known that, in Landau gauge, the renormalization function of the
ghost-ghost-gluon vertex \widetilde{Z}_1(p^2) is finite and constant, at least
to all orders of perturbation theory. On the other hand, a direct
non-perturbative verification of this result using numerical simulations of
lattice QCD is still missing. Here we present a preliminary numerical study of
the ghost-ghost-gluon vertex and of its corresponding renormalization function
using Monte Carlo simulations in SU(2) lattice Landau gauge. Data were obtained
in 4 dimensions for lattice couplings beta = 2.2, 2.3, 2.4 and lattice sides N
= 4, 8, 16.Comment: 3 pages, 1 figure, presented by A. Mihara at the IX Hadron Physics
and VII Relativistic Aspects of Nuclear Physics Workshops, Angra dos Reis,
Rio de Janeiro, Brazil (March 28--April 3, 2004
Modeling the Gluon Propagator in Landau Gauge: Lattice Estimates of Pole Masses and Dimension-Two Condensates
We present an analytic description of numerical results for the Landau-gauge
SU(2) gluon propagator D(p^2), obtained from lattice simulations (in the
scaling region) for the largest lattice sizes to date, in d = 2, 3 and 4
space-time dimensions. Fits to the gluon data in 3d and in 4d show very good
agreement with the tree-level prediction of the Refined Gribov-Zwanziger (RGZ)
framework, supporting a massive behavior for D(p^2) in the infrared limit. In
particular, we investigate the propagator's pole structure and provide
estimates of the dynamical mass scales that can be associated with
dimension-two condensates in the theory. In the 2d case, fitting the data
requires a non-integer power of the momentum p in the numerator of the
expression for D(p^2). In this case, an infinite-volume-limit extrapolation
gives D(0) = 0. Our analysis suggests that this result is related to a
particular symmetry in the complex-pole structure of the propagator and not to
purely imaginary poles, as would be expected in the original Gribov-Zwanziger
scenario.Comment: 21 pages, 5 postscript figure
The No-Pole Condition in Landau gauge: Properties of the Gribov Ghost Form-Factor and a Constraint on the 2d Gluon Propagator
We study the Landau-gauge Gribov ghost form-factor sigma(p^2) for SU(N)
Yang-Mills theories in the d-dimensional case. We find a qualitatively
different behavior for d=3,4 w.r.t. d=2. In particular, considering any
(sufficiently regular) gluon propagator D(p^2) and the one-loop-corrected ghost
propagator G(p^2), we prove in the 2d case that sigma(p^2) blows up in the
infrared limit p -> 0 as -D(0)\ln(p^2). Thus, for d=2, the no-pole condition
\sigma(p^2) 0) can be satisfied only if D(0) = 0. On the
contrary, in d=3 and 4, sigma(p^2) is finite also if D(0) > 0. The same results
are obtained by evaluating G(p^2) explicitly at one loop, using fitting forms
for D(p^2) that describe well the numerical data of D(p^2) in d=2,3,4 in the
SU(2) case. These evaluations also show that, if one considers the coupling
constant g^2 as a free parameter, G(p^2) admits a one-parameter family of
behaviors (labelled by g^2), in agreement with Boucaud et al. In this case the
condition sigma(0) <= 1 implies g^2 <= g^2_c, where g^2_c is a 'critical'
value. Moreover, a free-like G(p^2) in the infrared limit is obtained for any
value of g^2 < g^2_c, while for g^2 = g^2_c one finds an infrared-enhanced
G(p^2). Finally, we analyze the Dyson-Schwinger equation (DSE) for sigma(p^2)
and show that, for infrared-finite ghost-gluon vertices, one can bound
sigma(p^2). Using these bounds we find again that only in the d=2 case does one
need to impose D(0) = 0 in order to satisfy the no-pole condition. The d=2
result is also supported by an analysis of the DSE using a spectral
representation for G(p^2). Thus, if the no-pole condition is imposed, solving
the d=2 DSE cannot lead to a massive behavior for D(p^2). These results apply
to any Gribov copy inside the so-called first Gribov horizon, i.e. the 2d
result D(0) = 0 is not affected by Gribov noise. These findings are also in
agreement with lattice data.Comment: 40 pages, 2 .eps figure
SU(2) Landau gluon propagator on a 140^3 lattice
We present a numerical study of the gluon propagator in lattice Landau gauge
for three-dimensional pure-SU(2) lattice gauge theory at couplings beta = 4.2,
5.0, 6.0 and for lattice volumes V = 40^3, 80^3, 140^3. In the limit of large V
we observe a decreasing gluon propagator for momenta smaller than p_{dec} =
350^{+ 100}_{- 50} MeV. Data are well fitted by Gribov-like formulae and seem
to indicate an infra-red critical exponent kappa slightly above 0.6, in
agreement with recent analytic results.Comment: 5 pages with 2 figures and 3 tables; added a paragraph on
discretization effect
Some exact properties of the gluon propagator
Recent numerical studies of the gluon propagator in the minimal Landau and
Coulomb gauges in space-time dimension 2, 3, and 4 pose a challenge to the
Gribov confinement scenario.
We prove, without approximation, that for these gauges, the continuum gluon
propagator in SU(N) gauge theory satisfies the bound . This holds for Landau
gauge, in which case is the dimension of space-time, and for Coulomb gauge,
in which case is the dimension of ordinary space and is the
instantaneous spatial gluon propagator. This bound implies that , where is the gluon propagator at momentum , and
consequently in Landau gauge in space-time , and in Coulomb
gauge in space dimension , but D(0) may be finite in higher dimension.
These results are compatible with numerical studies of the Landau-and
Coulomb-gauge propagator.
In 4-dimensional space-time a regularization is required, and we also prove
an analogous bound on the lattice gluon propagator, . Here we have taken the
infinite-volume limit of lattice gauge theory at fixed lattice spacing, and the
lattice momentum componant is a continuous angle . Unexpectedly, this implies a bound on the {\it high-momentum} behavior of
the continuum propagator in minimum Landau and Coulomb gauge in 4 space-time
dimensions which, moreover, is compatible with the perturbative renormalization
group when the theory is asymptotically free.Comment: 13 page
- …