Gluon propagators in $$2+1$$ lattice QCD with nonzero isospin chemical potential

The static longitudinal and transverse gluon propagators in the Landau gauge are studied in $$2+1$$ 2 + 1 lattice QCD with nonzero isospin chemical potential $$\mu _I$$ μ I . Parameterization of the momentum dependence of the propagators is provided for all values of the chemical potential under study. We find that the longitudinal propagator is infrared suppressed at nonzero $$\mu _I$$ μ I with suppression increasing with increasing $$\mu _I$$ μ I . It is found, respectively, that the electric screening mass is increasing with increasing $$\mu _I$$ μ I . Additionally, we analyze the difference between two propagators as a function of the momentum and thus compare interactions in chromoelectric and chromomagnetic sectors.

Gluons in two-color QCD at high baryon density

Landau gauge longitudinal and transverse gluon propagators are studied in lattice QCD with gauge group [Formula: see text] at varying temperature and quark density. In particular, it is found that the longitudinal propagator decreases with increasing quark chemical potential at all temperatures under study, whereas the transverse propagator increases with increasing quark chemical potential at [Formula: see text] MeV and does not depend on it at higher temperatures. The relative strength of chromoelectric and chromomagnetic interactions is also discussed.

CONFINING TIME-LIKE GLUON AND CONFINED SPATIAL GLUONS IN COULOMB GAUGE QCD

We investigate the Gribov-Zwanziger scenario in Coulomb gauge QCD using a SU(3) quenched lattice gauge simulation. The ghost propagator diverges in the infrared limit stronger than the free ghost propagator, and the ghost degree of freedom plays a central role in the confinement mechanism in the Coulomb gauge. The infrared divergent ghost dressing function results in the confining color-Coulomb instantaneous interaction. The equal-time transverse gluon propagator is suppressed in the infrared region. Therefore, in the Coulomb gauge, the instantaneous interaction mediated by time-like gluons is responsible for the confining force, and the would-be physical gluons are confined in hadrons.

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 λ equal to 1) and the minimal Coulomb gauge (corresponding to λ = 0). For small values of λ we find that the spatially-transverse gluon propagator D tr (0, |p|), considered as a function of the spatial momenta |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 λ→0 (complete Coulomb gauge) and its relation to the standard Coulomb gauge (λ = 0). Our findings are corroborated by similar results in the three-dimensional case, where the infrared suppression is observed for all considered values of λ.

EQUIVALENCE OF THE β-FUNCTION OF THE VARIATIONAL APPROACH TO THAT OF QCD

The variational ansatz for the ground state wavefunctional of QCD is found to capture the antiscreening behaviour that contributes the dominant "-4" to the β-function and leads to asymptotic freedom. By considering an SU (N) purely gauge theory in the Hamiltonian formalism and choosing the Coulomb gauge, the origins of all screening and antiscreening contributions in gluon processes are found in terms of the physical degrees of freedom. The overwhelming antiscreening contribution of "-4" is seen to originate in the renormalisation of a Coulomb interaction by a transverse gluon. The lesser screening contribution of " [Formula: see text]" is seen to originate in processes involving transverse gluon interactions. It is thus apparent how the variational ansatz must be developed to capture the full running of the QCD coupling constant.