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Register a new userA Simple Statistical Model for Analysis of QGP-droplet (Fireball) Formation
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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.
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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 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
A Comparative study of the strengths and weakness of the models of fireball formation namely the statistical model of Ramanathan et.al (Physical Review C 70, 027903, 2004) and the approximation schemes of Kapusta et. al (Physical Review D 46, 1379, 1992) and its subsequent improved variants is made. The way to complement the various approximation schemes, in order to enhance their utility in the phenomenological analysis of QGP data that are expected from ongoing URHIC experiments, is suggested. The calculations demonstrate a striking QCD behaviour of the surface tension of the QGP droplet resulting in its increase with temperature, which is due to the confining nature of QCD forces at the surface and the interface surface tension varies as the cube of the transition temperature which is in conformity with the results of Lattice QCD simulations.
Quark-gluon plasma (QGP) droplet formation is re-considered with the addition of three loop correction to the earlier loop factors in the mean field potential. The correction of the three loop factor increases stability in the droplet formations of QGP at different parametrization factors of the QGP fluid and it is in better agreement in comparison to the lattice results of pressure, energy density and other thermodynamic relations. This implies that the contribution of the three loop enhances in showing the characteristic features of the QGP fluid. It shows that increasing the loop increased the strength of parametrization value which we defined earlier as a number parameter of fluid dynamics. It indicates that the model with the loop correction boosts in explaining about the formation of QGP droplet in the expansion of early universe
The effect of two loop correction in the formation of quark-gluon plasma (QGP) droplet is studied with the introduction of the two loop correction factor in the mean field potential. Due to the correction factor it shows stability in the droplet formation of QGP indicating at different parametrization factors of the QGP fluid. The correction factor in the potential also shows gluon parameter factor shifts to a larger value from its earlier value of gluon factor of one loop correction in obtaining the stable droplets. The results show decreasing in the observable QGP droplets and droplet sizes are found to be $1.5-2.0$ fm radii with the two loop correction. It indicates that there is parameter like Reynolds number which can control the dynamics of QGP droplet formation and the stability of droplet in the case of droplet formation with the two loop correction factor.
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