Holographic model for charmonium dissociation

Abstract

We present a holographic bottom up model for the thermal behavior of $ c \bar c$ vector mesons in a finite temperature and density plasma. There is a clear physical interpretation for the three imput energy parameters of the model. Two of them are related to the mass spectrum of the heavy meson. Namely the quark mass and the string tension of the quark anti-quark interaction. The third parameter is a large energy scale associated with the non-hadronic meson decay. In such a process the heavy meson is transformed into a much lighter state by electroweak processes. The corresponding transition amplitude is assumed to depend on the enegy scale associated with this large mass variation. With this three parameter model one can fit the masses and decay constants of $ J / \Psi $ and three radial excitations with an rms error of 20.7 %. Using the geometry of a charged black hole, one finds the spectral function for charmonium states inside a plasma at finite temperature and density. The charmonium dissociation in the medium is represented by the decrease in the height of the spectral function peaks.