Quasi normal modes for Heavy Vector Mesons in a Finite Density Plasma
There are strong indications that ultra-relativistic heavy ion collisions, produced in accelarators, lead to the formation of a new state of matter: the quark gluon plasma (QGP). This deconfined QCD matter is expected to exist just for very short times after the collision. All the information one can get about the plasma is obtained from the particles that reach the detectors. Among them, heavy vector mesons are particularly important. The abundance of $ c {\bar c}$ and $b {\bar b}$ states produced in a heavy ion collision is a source of information about the plasma. In contrast to the light mesons, that completely dissociate when the plasma is formed, heavy mesons presumably undergo a partial thermal dissociation. The dissociation degree depends on the temperature and also on the presence of magnetic fields and on the density (chemical potential). So, in order to get information about the plasma out of the quarkonium abundance data, one needs to resort to models that provide the dependence of the dissociation degree on these factors. Holographic phenomenological models provide a nice description for charmonium and bottomonium quasi-states in a plasma. In particular, quasi-normal modes associated with quarkonia states have been studied recently for a plasma with magnetic fields. Here we extend this analysis of quasinormal models to the case when charmonium and bottomonium are inside a plasma with finite density. The complex frequencies obtained are then compared with a Breit Wigner approximation for the peaks of the corresponding thermal spectral functions, in order to investigate the quantitative agreement of the different descriptions of quarkonium quasi-states.