The fraction of heavy vector mesons produced in a heavy ion collision, as
compared to a proton proton collision, serves as an important indication of the
formation of a thermal medium, the quark gluon plasma. This sort of analysis
strongly depends on understanding the thermal effects of a medium like the
plasma on the states of heavy mesons. In particular, it is crucial to know the
temperature ranges where they undergo a thermal dissociation, or melting.
AdS/QCD models are know to provide an important tool for the calculation of
hadronic masses, but in general are not consistent with the observation that
decay constants of heavy vector mesons decrease with excitation level. It has
recently been shown that this problem can be overcome using a soft wall
background and introducing an extra energy parameter, through the calculation
of correlation functions at a finite position of anti-de Sitter space. This
approach leads to the evaluation of masses and decay constants of S wave
quarkonium states with just one flavor dependent and one flavor independent
parameters. Here we extend this more realistic model to finite temperatures and
analyse the thermal behavior of the states 1S,2S and 3S of bottomonium
and charmonium. The corresponding spectral function exhibits a consistent
picture for the melting of the states where, for each flavor, the higher
excitations melt at lower temperatures. We estimate for these six states, the
energy ranges in which the heavy vector mesons undergo a transition from a well
defined peak in the spectral function to complete melting in the thermal
medium. A very clear distinction between the heavy flavors emerges, with
bottomonium state Υ(1S) surviving deconfinemet transition at
temperatures much larger than the critical deconfinement temperature of the
medium.Comment: 20 pages, 7 figure
