Maria Luigia Paciello

Problems on lattice gauge fixing

We review many topics and results about numeric gauge fixing in lattice QCD.

Gribov Noise on the Lattice Axial Current Renormalisation Constant

Abstract We study the influence of Gribov copies, in the Landau gauge, on the lattice renormalisation constant Z A of the axial current, obtained from a Ward identity on quark state correlation functions, with the Clover action, in quenched SU(3) gauge theory. A comparison between the gauge invariant determination of Z A and the gauge dependent one is discussed. On a 16 3 ×32 lattice at β =6.0 and with K = 0.1425, the values, on a sample of 36 configurations, are Z A =1.08(5) (gauge dependent calculation) and Z A =1.06(2) (gauge independent calculation). We find that the residual gauge freedom associated to Gribov copies induces observable effects, which, at the level of numerical accuracy of our simulation, are included in the statistical uncertainty inherent in a Monte Carlo simulation. Doubling the statistics suggests that the fluctuation due to the lattice Gribov ambiguity scales down at least as fast as a pure statistical error.

SU (3) lattice gauge fixing with overrelaxation and Gribov copies

Abstract We report on the phenomenology of SU (3) lattice Landau gauge fixing as obtained by using an overrelaxation algorithm. An interesting result obtained using this very efficient algorithm is that distinct Gribov copies are generated by simply modifying the value ω of the overrelaxation parameter for a fixed starting configuration. By generating random gauge equivalent configurations, we study the variation of the number of copies with the lattice volume and gauge coupling.

On the definition of gauge field operators in lattice gauge fixed theories

Abstract We address the problem of defining the four-potential, A a μ ( x ), on the lattice, in terms of the natural link variables, U μ ( x ). Different regularized definitions are shown, through non perturbative numerical computation, to converge towards the same continuum renormalized limit.

Gribov copies and smeared correlation functions in lattice QCD

Abstract We study the influence of Gribov copies in the Coulomb gauge on the smeared hadronic correlation functions that are involved in the determination of the B meson decay constant. We find that the residual gauge freedom associated to Gribov copies induces observable noise effects, though at the level of numerical accuracy of our simulation these effects are not relevant to the final determination of ƒ B . Our results indicate that such effects may become important on bigger lattices.

Phase transition analysis in Z2 and U(1) lattice gauge theories

Abstract The transition region of Z 2 lattice gauge theory is investigated by inverting the strong coupling series of the average plaquette energy E P ( J ). We find a clear evidence for a first-order transition and the existence of a metastable phase. In the U(1) case we confirm a second-order phase transition even if there is a little discrepancy on the critical point position as indicated by Monte Carlo simulations.

Glueballs and the superfluid phase of Two-Color QCD

We present the first results on scalar glueballs in cold, dense matter using lattice simulations of two-color QCD. The simulations are carried out on a 63×12 lattice and use a standard hybrid molecular dynamics algorithm for staggered fermions for two values of quark mass. The glueball correlators are evaluated via a multi-step smearing procedure. The amplitude of the glueball correlator peaks in correspondence with the zero temperature chiral transition, μc=mπ/2, and the propagators change in a significant way in the superfluid phase, while the Polyakov loop is nearly insensitive to the transition. Standard analysis suggest that lowest mass in the 0++ gluonic channel decreases in the superfluid phase, but these observations need to be confirmed on larger and more elongated lattices. These results indicate that a non-zero density induces non-trivial modifications of the gluonic medium.

The string tension in gauge theories. A suggestion for a new measurement method

Abstract We discuss a new method for testing confinement and measuring the string tension (in the Coulomb gauge). Our numerical simulations demonstrate that the problems related to Gribov copies are not harmful and that the method is effective in the case of pure gauge QCD. We discuss the relevance of the method for studying gauge theories coupled to fermionic matter.

STRING TENSION IN GAUGE THEORIES

A review article on string tension concept and their relevance as non-perturbative quantity on the study of quark confinement in lattice gauge theories. A detailed description of a variety of methods to measure the string tension on the lattice and an indication of the most promising developments is proposed.

Glue ball masses and the chameleon gauge

Abstract We introduce a new numerical technique to compute mass spectra, based on the difference method and on a new gauge fixing procedure. We show that the method is very effective by test runs on a SU (2) lattice gauge theory.