1204.2424 (E. Megias et al.)

The Polyakov loop and the hadron resonance gas model    [PDF]

E. Megias, E. Ruiz Arriola, L. L. Salcedo

The Polyakov loop has been used repeatedly as an order parameter in the deconfinement phase transition in QCD. We argue that, in the confined phase, its expectation value can be represented in terms of hadronic states, similarly to the hadron resonance gas model for the pressure. Specifically, L(T) \approx 1/2\sum_\alpha g_\alpha e^(-\Delta_\alpha/T), where g_\alpha are the degeneracies and \Delta_\alpha are the masses of hadrons with exactly one heavy quark (the mass of the heavy quark itself being subtracted). We show that this approximate sum rule gives a fair description of available lattice data with N_f=2+1 at low temperatures by using the spectrum of hadrons containing one charmed quark, and the \bar{MS}-scheme charmed quark mass. A direct fit to this latter quantity yields a close value, m_c=1280_{-44}^{+29}MeV. The lattice data are well reproduced by a simplified version of this formula, L(T)= N_f(2N_f+3)e^(-\Delta/T), for T < 200 MeV and Delta=913(2)MeV. We argue that this number should be Delta \sim 2 \sqrt(\sigma) with \sigma the string tension.

View original: http://arxiv.org/abs/1204.2424