THE HADRON TO QUARK GLUON TRANSITION

In this paper we are concerned with the hadron to quark/gluon transition. We describe the equilibrium states of hadronic matter by a Hagedorn spectrum; introducing scaling masses, as dictated by the restoration of chiral invariance with increasing temperature, we show that in the chiral SU(2)f limit there is a maximum hadron temperature (T(H))max congruent-to 128 MeV. Since the quark/gluon perturbative phase involves restoration of conformal invariance, we take the bag constant to be the conformal anomaly, i.e. the gluon condensate. The stability condition P(QG) > 0 for the pressure requires that there is a minimum temperature; we find (T(QG))min congruent-to 172 MeV for SU(2)f. According to the simple Hagedorn model, there appears to be a region of temperature between (T(H))max and (T(QG))min in which no admissible equilibrium states exist. Since the two phases cannot exist at a common temperature, in this model there is no QCD phase transition.