303 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

### 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 $D^{tr}(\vec{k})$ vanishes at
$\vec{k} = 0$ when extrapolated to infinite lattice volume, whereas the
instantaneous color-Coulomb potential $D_{44}(\vec{k})$ is strongly enhanced at
$\vec{k} = 0$. 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 $D^{tr}(\vec{k}) =
(|\vec{k}|/2)[(\vec{k}^2)^2 + M^4]^{1/2}$ provides an excellent fit to our data
for the 3-dimensionally transverse equal-time gluon propagator
$D^{tr}(\vec{k})$ for relevant values of $\vec{k}$.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

### 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

### 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 $D(k)$ in SU(N) gauge theory satisfies the bound ${d-1 \over d} {1
\over (2 \pi)^d} \int d^dk {D(k) \over k^2} \leq N$. This holds for Landau
gauge, in which case $d$ is the dimension of space-time, and for Coulomb gauge,
in which case $d$ is the dimension of ordinary space and $D(k)$ is the
instantaneous spatial gluon propagator. This bound implies that $\lim_{k \to
0}k^{d-2} D(k) = 0$, where $D(k)$ is the gluon propagator at momentum $k$, and
consequently $D(0) = 0$ in Landau gauge in space-time $d = 2$, and in Coulomb
gauge in space dimension $d = 2$, 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, ${1 \over d (2 \pi)^d}
\int_{- \pi}^{\pi} d^dk {\sum_\mu \cos^2(k_\mu/2) D_{\mu \mu}(k) \over 4
\sum_\lambda \sin^2(k_\lambda/2)} \leq N$. Here we have taken the
infinite-volume limit of lattice gauge theory at fixed lattice spacing, and the
lattice momentum componant $k_\mu$ is a continuous angle $- \pi \leq k_\mu \leq
\pi$. 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

### Magnetic Screening in Hot Non-Abelian Gauge Theory

We analyze the large distance and low-momentum behavior of the magnetic gluon
propagator of the SU(2) gauge theory at finite temperature. Lattice
calculations within the 4-dimensional as well as the effective, dimensionally
reduced 3-dimensional gauge theories in generalized Landau gauges and MAG show
that the magnetic propagator is strongly infrared suppressed in Landau gauges
but stays large and finite in MAG. Despite these differences in the
low-momentum behavior of the propagator calculated in different gauges the
magnetic fields are exponentially screened in all gauges considered. From the
propagator calculated in maximally Abelian gauge we find for the screening
mass, m_M = (1.48 +/- 0.17) T at T=2 T_c.Comment: 11 pages, LaTeX2e, new data added, conclusions unchanged. The final
version to appear in Phys. Lett.

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