Quark matter in the context of Quantum chromodynamics

The Hagedorn temperature, T_H, is the temperature in theoretical physics where hadronic matter (i.e. ordinary matter) is no longer stable, and must either "evaporate" or convert into quark matter; as such, it can be thought of as the "boiling point" of hadronic matter. It was discovered by Rolf Hagedorn. The Hagedorn temperature exists because the amount of energy available is high enough that matter particle (quark–antiquark) pairs can be spontaneously pulled from vacuum. Thus, naively considered, a system at Hagedorn temperature can accommodate as much energy as one can put in, because the formed quarks provide new degrees of freedom. However, if this phase is viewed as quarks instead, it becomes apparent that the matter has transformed into quark matter, which can be further heated.

The Hagedorn temperature, T_H, is about 150 MeV/k_B or about 1.7×10 K, little above the mass–energy of the lightest hadrons, the pion. Hagedorn was able not only to give a simple explanation for the thermodynamical aspect of high energy particle production, but also worked out a formula for the hadronic mass spectrum and predicted the limiting temperature for hot hadronic systems.

The QCD vacuum is the quantum vacuum state of quantum chromodynamics (QCD). It is an example of a non-perturbative vacuum state, characterized by non-vanishing condensates such as the gluon condensate and the quark condensate in the complete theory which includes quarks. The presence of these condensates characterizes the confined phase of quark matter.