Equation of State for Hot and Dense Matter: $\sigma$-$\omega$-$\rho $   Model with Scaled Hadron Masses and Couplings
  The proposed earlier relativistic mean-field model with hadron masses and coupling constants depending on the $\sigma$-meson field is generalized to finite temperatures. Within this approach we simulate the in-medium behavior of the hadron masses motivated by the Brown-Rho scaling. The high-lying baryon resonances and boson excitations as well as excitations of the $\sigma$, $\omega$ and $\rho$ fields interacting via mean fields are incorporated into this scheme. Thermodynamic properties of hot and dense hadronic matter are elaborated with the constructed equation of state. Even at zero baryon density, effective masses of $\sigma$-$\omega$-$\rho$-$N$ excitations abruptly drop down for $T\gsim 170$ MeV and reach zero at a critical temperature $T=T_{c\sigma}\sim 210$ MeV. Below $T_{c\sigma}$ (at $T\sim 190$ MeV) the specific heat gets a peak like at crossover. We demonstrate that our EoS can be matched with that computed on the lattice for high temperatures provided the baryon resonance couplings with nucleon are partially suppressed. In this case the quark liquid would masquerade as the hadron one. The model is applied to description of heavy ion collisions in a broad collision energy range. It might be especially helpful for studying phase diagram in the region near possible phase transitions. 
A. S. Khvorostukhin, V. D. Toneev and D.N. Voskresensky