Fresh look at the Hagedorn mass spectrum as seen in the experiments

The medium-dependent finite width is introduced into an exactly solvable model with the general mass-volume spectrum of the QGP (Quark Gluon Plasma) bags. The model allows us to estimate the minimal value of the QGP bags' width from the lattice QCD data. The large width of the QGP bags not only explains the observed deficit in the number of hadronic resonances comparing to the Hagedorn mass spectrum, but also clarifies the reason why the heavy QGP bags cannot be directly observed as metastable states in a hadronic phase. (authors)