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Here we develop a model equation of state which successfully parameterizesthe thermodynamic functions of hadron resonance gas model at chemicalfreeze-out and which allows us to naturally explain the adiabatic chemicalfreeze-out criterion. The present model enables us to clearly demonstrate thatat chemical freeze-out the resulting hadronic mass spectrum used in the hadronresonance gas model is not an exponential-like, but a power-like. We argue thatsuch a property of hadronic mass spectrum at chemical freeze-out can beexplained by the two new effects found here for wide resonances existing in athermal environment: the near threshold thermal resonance enhancement and thenear threshold resonance sharpening. The effect of resonance sharpening isstudied for a sigma meson and our analysis shows that for the temperatures wellbelow 92 MeV the effective width of sigma meson is about 50 to 70 MeV. Thus,the effect of resonance sharpening justifies the usage of the sigma-likefield-theoretical models for the strongly interacting matter equation of stateat such temperatures. Also we argue that the most optimistic hope to find thequark gluon bags experimentally may be related to their sharpening andenhancement in a thermal medium. In this case the wide quark gluon bags mayappear directly or in decays as narrow resonances that are absent in the tablesof elementary particles and that have the width about 50-150 MeV and the massabout or above 2.5 GeV.

Adiabatic Chemical Freeze-out and Wide Resonance Modification in a Thermal Medium