The medium dependent finite width is introduced into an exactly solvable model with the general mass-volume spectrum of the QGP 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. 25.75.Nq Keywords: Hagedorn spectrum, finite width of quark-gluon bags, subthreshold suppression of bags

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The influence of the medium dependent finite width of quark gluon plasma (QGP) bags on their equation of state is analyzed within an exactly solvable model. It is argued that the large width of the QGP bags not only explains the observed deficit in the number of hadronic resonances, but also clarifies the reason why the heavy QGP bags cannot be directly observed as metastable states in a hadronic phase. The model allows us to estimate the minimal value of the width of QGP bags being heavier than 2 GeV from a variety of the lattice QCD data and get that the minimal resonance width at zero temperature is about 600 MeV, whereas the minimal resonance width at the Hagedorn temperature is about 2000 MeV. As shown, these estimates are almost insensitive to the number of the elementary degrees of freedom. The recent lattice QCD data are analyzed and it is found that besides σT 4 term the lattice QCD pressure contains T -linear and T 4 ln T terms in the range of temperatures between 240 MeV and 420 MeV. The presence of the last term in the pressure bears almost no effect on the width estimates. Our analysis shows that at high temperatures the average mass and width of the QGP bags behave in accordance with the upper bound of the Regge trajectory asymptotics (the linear asymptotics), whereas at low temperatures they obey the lower bound of the Regge trajectory asymptotics (the square root one). Since the model explicitly contains the Hagedorn mass spectrum, it allows us to remove an existing contradiction between the finite number of hadronic Regge families and the Hagedorn idea of the exponentially growing mass spectrum of hadronic bags.PACS: 25.75.-q,25.75.Nq Keywords: Hagedorn spectrum, finite width of quark-gluon bags, subthreshold suppression of bags

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We develop a novel model of the QCD matter critical endpoint by matching the deconfinement phase transition curve with the nil line of the bag surface tension coefficient. As a result, this leads to a new structure of the leading singularities of isobaric partition, and in contrast to all previous studies of such mod els, the deconfined phase in our approach is defined not by an essential singularity of the isobaric partition function but its simple pole. As an unexpected result, we find out that the first order phase transition in this model is the surface tension induced transition. The sufficient conditions of its existence are analyzed and the possible physical consequences are discussed.