We propose an algebraic form for the density of states of quarks and gluons in a Quark-Gluon Plasma (QGP) fireball in quasi-equilibrium with a hadronic medium as $rho(k)= frac {alpha}{k} + {beta}k + {delta}k^{2}$, and determine the parameters $alpha$
, $beta$ and $delta$ using Lattice Gauge results on the velocity of sound in QGP. The behaviour of the resulting $rho(k)$ can be easily compared with the thermodynamic data on QGP that is expected from LHC and other RHIC experiments. Our numerical result shows a linear rise of the value of $rho(k)$ for $ksim T approx 160 to 180 MeV$, which is significant, and throws light on the evolution of the QGP phase.
We study the phase structure of the QGP-Hadron system under quasi-static equilibrium using the Ramanathan et al. statistical model for the QGP fireball formation in a hadronic medium. While in the earlier published studies we had used the Peshier eff
ective potential which is appropriate for the deconfined QGP phase but could be extrapolated to the transition region from the higher momentum regime, in this paper we study the same system using the Cornell and Richardson potentials which are more relevant for the low momentum confinement regime, but could again be extrapolated to the transition region from below. Surprisingly, the overall picture in both the cases are quite similar with minor divergences,(though,the results with the Richardson potential shows a sizable deviation from the other two potentials), thus indicating the robustness of the model and its self-consistency. The result of our numerical results pertaining to the variation of the velocity of sound in the QGP-Hadron medium with temperature in the various scenarios considered by us, is that, the phase transition seems to be a gentle roll-over of phases rather than a sharp transition of either the first or second order, a result in conformity with recent lattice calculations, but with much less effort.
We study the effect of finite chemical potential for the QGP constituents in the Ramanathan et al. statistical model (Phys.Rev.C70, 027903,2004). While the earlier computations using this model with vanishing chemical potentials indicated a weakly fi
rst order phase transition for the system in the vicinity of 170 MeV (Pramana, 68, 757, 2007), the introduction of finite values for the chemical potentials of the constituents makes the transition a smooth roll over of the phases, while allowing fireball formation with radius of a few fermi to take place. This seems to be in conformity with the latest consensus on the nature of the QGP-Hadron phase transition. Keywords: Quark Gluon Plasma, Quark Hadron Phase Transition
