The effective potential of the Polyakov loop in the Hamiltonian approach to QCD

TL;DR

This paper studies the effective potential of the Polyakov loop in finite temperature QCD using a Hamiltonian approach, including dynamical quarks and two-loop gluon contributions, to better understand the deconfinement phase transition.

Contribution

It extends the Hamiltonian Coulomb gauge approach by incorporating dynamical quarks and two-loop gluon effects to improve the description of the deconfinement transition.

Findings

One-loop approximation poorly describes the phase transition for full QCD.

Two-loop corrections strengthen gluon confinement and reduce unphysical effects.

Critical temperature increases to about 340 MeV with parameter tuning.

Abstract

We investigate the effective potential of the Polyakov loop, which is the order parameter for the deconfinement phase transition in finite temperature QCD. Our work is based on the Hamiltonian approach in Coulomb gauge where finite temperature $T$ is introduced by compactifying one space direction. We briefly review this approach and extend earlier work in the Yang-Mills sector by including dynamical quarks. In a first approximation, we follow the usual functional approach and include only one-loop contributions to the energy, with the finite temperature propagators replaced by their $T=0$ counter parts. It is found that this gives a poor description of the phase transition, in particular for the case of full QCD with $N_f = 3$ light flavours. The physical reasons for this unexpected result are discussed, and pinned down to a relative weakness of gluon confinement compared to the deconfining tendency of the quarks. We attempt to overcome this issue by including the relevant gluon contributions from the two-loop terms to the energy. We find that the two-loop corrections have indeed a tendency to strengthen the gluon confinement and weaken the unphysical effects in the confining phase, while slightly increasing the (pseudo-)critical temperature $T^\ast$ at the same time. To fully suppress artifacts in the confining phase, we must tune the parameters to rather large values, increasing the critical temperature to $T^\ast \approx 340\,\mathrm{MeV}$ for $G=SU(2)$.