Susceptibilities and the Phase Structure of an Effective Chiral Model with Polyakov Loops

Quantum Chromodynamics (QCD) exhibits dynamical chiral symmetry breaking and confinement. Both features are related with global symmetries of the QCD Lagrangian. While the chiral symmetry is exact in the limit of massless quarks the Z(3) center symmetry, which governs confinement, is exact in the opposite limit, i.e., for infinitely heavy quarks. The susceptibilities of the corresponding order parameters were calculated in lattice gauge theory (LGT) with finite quark masses 1 and hence both symmetries are explicitly broken. Nevertheless, the susceptibilities show a peak structure. Thus, the global symmetries of the Lagrangian are still relevant even for finite quark masses. Based on this consideration one can construct an effective Lagrangian in terms of the order parameters, the Ginzburg-Landau effective theory. Recently, gluon degrees of freedom were introduced in the Nambu–Jona-Lasinio (NJL) Lagrangian 2,3 through an effective gluon potential expressed in terms of Polyakov loops (PNJL model) 4,5. The model has a non-vanishing coupling of the constituent quarks to the Polyakov loop and mimics confinement in the sense that only three-quark states contribute to the thermodynamics in the low-temperature phase. Hence, the PNJL model yields a better description of QCD thermodynamics near the phase transition than the NJL model. Furthermore, due to the symmetries of the Lagrangian, the model belongs to the same universality class as that expected