In this work, we study the thermodynamic behavior of heavy-flavored meson matter in the framework of $(sigma,omega)$-meson-exchange model in relativistic mean field theory. We find a decreasing of the effective masses of $D$ and $B$ mesons as the tem
perature increases. By using the effective mass and maximum value of dissociation temperatures available from lattice QCD, the masses of the bound states $D bar{D}$ and $B bar{B}$ are estimated in 2 MeV for both molecules. For the $B$-meson matter, the pressure presents an exotic behavior, being negative for temperatures above 6.6 times the deconfinement transition temperature $T_c$. In addition, the ratio of pressure to energy density is similar to the value predicted for systems that behave as dark energy matter.
We use the method of double pole QCD sum rule which is basically a fit with two exponentials of the correlation function, where we can extract the masses and decay constants of mesons as a function of the Borel mass. We apply this method to study the
mesons: $rho(1S,2S)$, $psi(1S,2S)$, $Upsilon(1S,2S)$ and $psi_t(1S,2S)$. We also present predictions for the toponiuns masses $psi_t(1S,2S)$ of m(1S)=357 GeV and m(2S)=374 GeV.
We study the mesons matter D-bar{D} in the framework of sigma and omega meson exchange model using Waleckas mean field theory. We choose the equal number of D and anti-D meson then we get <omega^0>=0 and the field sigma exhibits a critical temperatur
e around 1.2 GeV. We investigate effective mass, pressure, energy density and energy per pair. We conclude that this matter is a gas and these results are not favorable for the existence of D-bar{D} bound state. Note: in arXiv:1211.5505 this interpretation has been updated where these results are favorable for the existence of $D-bar{D}$ bound state.
