The Polyakov loop and the hadron resonance gas model

TL;DR

This paper proposes a hadronic representation of the Polyakov loop in the confined phase of QCD, demonstrating its effectiveness in describing lattice data and exploring the potential role of exotic hadrons.

Contribution

It introduces a sum rule linking the Polyakov loop to hadronic states with one heavy quark, extending the hadron resonance gas model to the Polyakov loop in QCD.

Findings

The sum rule accurately describes lattice data between 150MeV and 190MeV.

Different lattice results below 150MeV suggest the possible existence of exotic hadrons.

The model's agreement depends on the inclusion of exotic states in the spectrum.

Abstract

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 for temperatures in the range 150MeV<T<190MeV with conventional meson and baryon states from two different models. For temperatures below 150MeV different lattice results disagree. One set of data can be described if exotic hadrons are present in the QCD spectrum while other sets do not require such states.