  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.
