Heavy quark-antiquark free energy and thermodynamics of string-hadron avoided crossings

The correlation function between two Polyakov loops encodes the free-energy shift due to a pair of separated colour conjugated sources in the hot QCD medium. This is analyzed in terms of a novel K\"all\'en-Lehmann spectral representation for the separating distance, implying an increasing and concave free-energy at all temperatures. We express the heavy $\bar{Q} Q$ free-energy shift below the phase transition in QCD in terms of colour neutral purely hadronic states with no explicit reference to quarks and gluons. Good agreement with lattice data is achieved when considering the avoided crossing mechanism underlying string breaking and with standard quenched values of the string tension known from charmonium and bottomonium phenomenology. We also address the role of the corresponding entropy shift and its renormalization group properties.