We consider the potential-model approach for obtaining the spectrum of charmonium and bottomonium, replacing the usual gluon propagator by one obtained from lattice simulations. The resulting spectra are compared to the corresponding ones in the Corn
ell-potential case. We also estimate the interquark distance in both cases.
By evaluating the so-called Bose-ghost propagator, we present the first numerical evidence of BRST-symmetry breaking for Yang-Mills theory in minimal Landau gauge, i.e. due to the restriction of the functional integration to the first Gribov region i
n the Gribov-Zwanziger approach. Our data are well described by a simple fitting function, which can be related to a massive gluon propagator in combination with an infrared-free (Faddeev-Popov) ghost propagator. As a consequence, the Bose-ghost propagator, which has been proposed as a carrier of the confining force in minimal Landau gauge, displays a 1/p^4 singularity in the infrared limit.
The Bose-ghost propagator has been proposed as a carrier of the confining force in Yang-Mills theories in minimal Landau gauge. We present the first numerical evaluation of this propagator, using lattice simulations for the SU(2) gauge group in the s
caling region. Our data are well described by a simple fitting function, which is compatible with an infrared-enhanced Bose-ghost propagator. This function can also be related to a massive gluon propagator in combination with an infrared-free (Faddeev-Popov) ghost propagator. Since the Bose-ghost propagator can be written as the vacuum expectation value of a BRST-exact quantity and should therefore vanish in a BRST-invariant theory, our results provide the first numerical manifestation of BRST-symmetry breaking due to restriction of gauge-configuration space to the Gribov region.
We prove a lower bound for the smallest nonzero eigenvalue of the Landau-gauge Faddeev-Popov matrix in Yang-Mills theories. The bound is written in terms of the smallest nonzero momentum on the lattice and of a parameter characterizing the geometry o
f the first Gribov region. This allows a simple and intuitive description of the infinite-volume limit in the ghost sector. In particular, we show how nonperturbative effects may be quantified by the rate at which typical thermalized and gauge-fixed configurations approach the Gribov horizon. Our analytic results are verified numerically in the SU(2) case through an informal, free and easy, approach. This analysis provides the first concrete explanation of why the so-called scaling solution of the Dyson-Schwinger equations is not observed in lattice studies.
We present improved upper and lower bounds for the momentum-space ghost propagator of Yang-Mills theories in terms of the two smallest nonzero eigenvalues (and their corresponding eigenvectors) of the Faddeev-Popov matrix. These results are verified
using data from four-dimensional numerical simulations of SU(2) lattice gauge theory in minimal Landau gauge at beta = 2.2, for lattice sides N = 16, 32, 48 and 64. Gribov-copy effects are discussed by considering four different sets of numerical minima. We then present a lower bound for the smallest nonzero eigenvalue of the Faddeev-Popov matrix in terms of the smallest nonzero momentum on the lattice and of a parameter characterizing the geometry of the first Gribov region $Omega$. This allows a simple and intuitive description of the infinite-volume limit in the ghost sector. In particular, we show how nonperturbative effects may be quantified by the rate at which typical thermalized and gauge-fixed configurations approach the boundary of Omega, known as the first Gribov horizon. As a result, a simple and concrete explanation emerges for why lattice studies do not observe an enhanced ghost propagator in the deep infrared limit. Most of the simulations have been performed on the Blue Gene/P--IBM supercomputer shared by Rice University and S~ao Paulo University.
We propose to investigate infrared properties of gluon and ghost propagators related to the so-called Gribov-Zwanziger confinement scenario, originally formulated for Landau and Coulomb gauges, for other gauges as well. We present results of our inve
stigation of SU(2) lattice gauge theory in the maximally Abelian gauge (MAG), focusing on the behavior of propagators in the off-diagonal (i.e. non-Abelian) sector. We also comment on our preliminary results for general linear covariant gauges, in particular for Feynman gauge.
