Abstract
While the Polyakov loop is an order parameter of the deconfinement transition in the heavy quark mass regime of QCD, its sensitivity to the deconfinement of light, dynamical quarks in QCD is not apparent. On the other hand, the quark mass dependence of the Polyakov loop is sensitive to the appearance of a chiral phase transition. Using lattice QCD calculations in the staggered fermion discretization scheme at finite values of the lattice spacing, $aT = 1/8$, we show here, for the first time, that the Polyakov loop expectation value, and the heavy quark free energy extracted from it, behave like energy-like observables in the vicinity of the chiral phase transition temperature $T_c$. Consistent with scaling behavior of energy-like observables in the 3-$d$, O(2) universality class, the quark mass derivatives diverge in the chiral limit at $T_c$ while the temperature derivatives stay finite. The latter will develop a characteristic spike at $T_c$. This, however, may be resolved only in calculations with quark masses being two orders of magnitude smaller than those currently accessible in lattice QCD calculations.
Highlights
The Lagrangian of quantum chromodynamics (QCD), the theory describing interactions controlled by the strong force, possesses exact global symmetries only in the massless and infinite quark mass limits
Errors are large for the results obtained with the smallest light quark mass, H 1⁄4 1=160, it is evident that ∂ðFq=TÞ=∂H has maxima at T ∼ 145–150 MeV which are close to the chiral phase transition temperature on lattices with temporal extent
We have examined the quark mass dependence of the Polyakov loop expectation value and the heavy quark free energy extracted from it
Summary
The Lagrangian of quantum chromodynamics (QCD), the theory describing interactions controlled by the strong force, possesses exact global symmetries only in the massless (chiral) and infinite quark mass (pure gauge) limits. The latter case has been extensively exploited in lattice QCD calculations to discuss the deconfinement phase transition in pure gauge theories [1,2,3] and its imprint in the heavy quark sector of QCD. We present results on the temperature and quark mass dependence of hPi and Fq=T close to the chiral limit We show that both of them reflect properties of energylike observables in the vicinity of Tc and discuss the resulting chiral limit behavior. As will become clear in the following, none of the qualitative features that will arise from the energylike behavior of the Polyakov loop in theories with global OðNÞ symmetry will depend on this difference
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