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

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 $G=SU(2)$.

38 pages, 13 figures (26 sub-figures), uses REVTeX4

References in corpus (14)

• Color superconductivity in dense quark matter
• Infrared Properties of QCD from Dyson-Schwinger equations
• Pinch Technique: Theory and Applications
• Confining Solution of the Dyson-Schwinger Equations in Coulomb Gauge
• Chiral and deconfinement transition from correlation functions: SU(2) vs. SU(3)
• Chiral and deconfinement transition from Dyson-Schwinger equations
• Coulomb gauge gluon propagator and the Gribov formula
• Subcritical solution of the Yang-Mills Schroedinger equation in the Coulomb gauge
• The 't Hooft loop in the Hamiltonian approach to Yang-Mills theory in Coulomb gauge
• A novel background field approach to the confinement-deconfinement transition
• Revised variational approach to QCD in Coulomb gauge
• Finite-temperature Yang-Mills theory in the Hamiltonian approach in Coulomb gauge from a compactified spatial dimension
• Covariant variational approach to Yang-Mills Theory: Thermodynamics
• Polyakov loop, gluon mass, gluon condensate and its asymmetry near deconfinement