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, $L(T)\approx \frac{1}{2}\sum _{\alpha }{g}_{\alpha }{e}^{-{\Delta }_{\alpha }/T}$, 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 $150\mathrm{MeV}<T<190\mathrm{MeV}$ with conventional meson and baryon states from two different models. For temperatures below 150 MeV 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.

• Received 11 April 2012

DOI:https://doi.org/10.1103/PhysRevLett.109.151601