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Register a new userThe phase structure of QGP-Hadron in a statistical model using Cornell, Richardson and Peshier potentials
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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 effective 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.
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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 first 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
We propose a simple statistical model for the density of states for quarks and gluons in a QGP droplet, making the Thomas-Fermi model of the atom and the Bethe-model for the nucleons as templates for constructing the density of states for the quarks and gluons with due modifications for the `hot relativistic QGP state as against the `cold non-relativistic atom and nucleons, which were the subject of the earlier `forebears of the present proposal.We introduce `flow-parameters $gamma_{q,g}$ for the quarks and the gluons to take care of the hydrodynamical (plasma) flows in the QGP system as was done earlier by Peshier in his thermal potential for the QGP. By varying $gamma_{g}$ about the `Peshier-Value of $gamma_{q} = 1/6$, we find that the model allows a window in the parametric space in the range $8gamma_{q} leq gamma_{g} leq 12gamma_{q}$, with $gamma_{q} =1/6$ (Peshier-Value), when stable QGP droplets of radii $sim$ $6 fm$ appear at transition temperatures $100 MeV leq T leq 250 MeV$. The smooth cut at the phase boundary of the Free energy vs. droplet radius suggests a First - Order phase transition .On the whole the model offers a robust tool for studying QGP phenomenology as and when data from various ongoing experiments are available .
We construct the density of states for quarks and gluons using the `Thomas - Fermi model for atoms and the `Bethe model for nucleons as templates. With parameters to take care of the plasma (hydrodynamical) features of the QGP with a thermal potential for the interaction, we find a window in the parametric space of the model where observable QGP droplets of $ sim $ 5 fm radius can occur with transition temperature in the range 140 MeV to 250 MeV. By matching with the expectations of Lattice Gauge estimates of the QGP-hadron transitions, we can further narrow the window, thereby restricting the allowed values of the flow-parameters of the model.
We describe how the abundance and distribution of hyperon resonances can be used to probe freeze-out conditions. We demonstrate that resonance yields allow us to measure the time scales of chemical and thermal freeze-outs. This should permit a direct differentiation between the explosive sudden, and staged adiabatic freeze-out scenarios.
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.
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