Deconfinamento della materia adronica e suscettività nel modello PNJL

This work is focused on the study of the phase diagram of Quantum-Chromo Dynamics (QCD), aiming at the determination of chemical freeze-out parameters of the Quark Gluon Plasma (QGP) formed in relativistic heavy-ion collisions. The phase diagram of QCD is divided in two interesting regions. The first one, at low temperatures and/or chemical potential, is the so-called ¿confined region¿, where the color degrees of freedom are confined in hadrons and the chiral symmetry is spontaneously broken. At higher temperatures and/or baryon-chemical potential there is another phase called ¿deconfined phase¿ in which the colored degrees of freedom move freely on distances larger than the typical hadronic radius and chiral symmetry is restored. From lattice-QCD we know that at vanishing/small baryon chemical potential the phase transition is a cross-over, while at higher chemical potentials, it is argued that the transition is of first order, ending with a critical point. Unfortunately, lattice-QCD simulations cannot be extended to the region of high chemical potentials, due to sign problem, which prevents the Montecarlo sampling of gauge field configurations. The goal of this thesis is the determination of transition parameters and, possibly, the recognition of the critical end point. For this purpose it is used the chiral effective model called Nambo-Jona-Lasinio with Polyakov Loop (PNJL). This model describes quark/anti-quarks with point-like interaction (NJL) with the addition of an average gauge field expressed through the Polyakov loop (PNJL). The latter plays the role of the order parameter for the deconfinement phase transition. In this thesis two different versions of the PNJL model are considered, which differ in the effective potential for the Polyakov loop degree of freedom: the first one is a polynomial potential, the second one a logarithmic potential. In the first part of my thesis we discuss the phase diagram of QCD as well as the theoretical and experimental tools useful for the study the phase diagram (Lattice-QCD, Heavy-ion collissions, Effective Model and Fluctuations); we also show the main results obtained in the literature. In the second part of my thesis the PNJL model is described in details: the mean field equations are derived in the Hartree approximation and this are subsequently solved via numerical algorithms. From the Gran Potential of the PNJL model it is possible to obtain the thermodynamics quantities (pressure and quark density) and the fluctuations of system, in particular the generalized quark susceptibilities. The quark susceptibilities are useful to identify the parameters and the order of the phase transition. Indeed, near the phase transition the fluctuations are expected to grow and eventually, near the critical point, they might be discontinuous. Finally, in the last part of my thesis the coefficients of the Taylor expansion of the pressure around zero chemical potential as a function of the ratio chemical potential/temperature are calculated within the PNJL model and compared with the existent Lattice-QCD results.