Temperature Dependence of Heavy Meson Masses

Using a previously derived QCD effective hamiltonian we find the masses of heavy quarkonia states. Non perturbative effects are included through temperature dependent gluonic condensates. We find that even a moderate change in these condensates in a hot hadronic environment (below the deconfining transition) is sufficient to significantly change the heavy meson masses. The study of hadronic matter at high temperatures and densities has direct relevance for heavy-ion experiments. Apart from the search of quark gluon plasma, serious attention has been given to signatures of a hot system composed by hadrons below the deconfining transition. Among these signatures, changes in the masses due to medium effects play a major role. They have been extensively studied with the Nambu-JonaLasinio model [1], with non-relativistic potential models [2] , with QCD sum-rules [3] and in lattice QCD [4]. The experimental detection of medium effects on the masses is a very difficult problem. On the other hand, from the theoretical point of view the situation is not quite clear. Some calculations predict a significant decrease (∼ 400 MeV) of the ηc, J/ψ and ψ masses. Some others suggest that the masses stay constant. We will argue that they may increase. The approach to this problem adopted in the present work is in many aspects similar to QCD sum-rules at finite temperature. In particular, our results for the heavy quarkonium spectrum depend primarily on perturbation theory (which is related to the value of αs) and on the gluon condensate. The same conclusion is found in ref. [3]. The main difference between this work and the above mentioned spectrum calculations is that we give special emphasys to vacuum changes with temperature. It has been known since the late seventies that the QCD (physical) vacuum is full of soft gluons or, equivalently, contains chromoelectric (E) and magnetic (B) fields. Such a state, |Ω〉, has lower energy than a state without any fields, the perturbative vacuum, |0〉. This picture is supported by the existence of non-vanishing gluon condensates, i.e., 〈Ω| αs π Fμν F μν |Ω〉 = φ 6= 0 (1) where Fμν is the usual QCD field tensor.