STRONGLY INTERACTING MATTER:ANALYSIS OF QCD PHASE DIAGRAM BY THERMODYNAMIC GEOMETRY

My PhD research focused on the study of the Quantum Chromodynamics (QCD) phase transition, both from a phenomenological and a theoretical point of view. Three main research lines have been considered: • The study of some phenomenological topics of the phase transition has been carried out. In particular, I studied universality in light and heavy particles collisions at high energy, by looking at some experimental observables: in fact, it is increasingly noticeable that, high energy, high multiplicity events produced in small colliding systems show dynamical behaviour very similar to that one observed in AA collisions. These experimental results can be understood by drawing different observables, like the strangeness suppression factor γs and the yields of multi-strange hadrons, the average transverse momentum, and the elliptic flow scaled by the participant eccentricity, in terms of the the initial entropy density, that is the parton density in the transverse plane. Moreover, the previous analysis clarifies that in e+e− annihilation at the LEP or lower energies there is no chance of observing the enhancement of the strangeness production, that is γs ≳ 0.95, because the parton density in the transverse plane is too small. • The second aspect I studied is the role of the QCD transition during the evolution of the Universe. Indeed, the fluctuations of the cosmological parameters at the QCD transition originate from the combined effect of the equation of state and of the calculation of higher-order derivatives of the relevant physical parameters, that is, in early Universe, of the scale factor. We have shown, by a complete treatment of the thermodynamics of the whole system (strong and electroweak contributions), that after about 100 μs the cosmological parameters return to the typical values of a radiation dominated era, i.e. to their values before the transition. Therefore the possible signature of the deconfinement transition in early Universe is restricted to the modification of the primordial gravitational wave spectrum. • The main line of my research regards the study of the phase transition in field theory, and in QCD in particular, in the framework of thermodynamic geometry: the thermodynamic theory of fluctuations allows to define a manifold spanned by intensive thermodynamic variables, {θk} with k = 1, 2, . . . , N, and to equip this with the notion of a distance, dℓ2 = gμν(θ1, θ2, · · · θN) dθμ dθν, where gμν is the metric tensor. The metric tensor is defined as gμν = ∂2 logZ/∂θμ ∂θν, Z being the partition function, and measures the probability of fluctuation between two equilibrium states. I applied this method to LATTICE QCD and HRG models, to Nambu-Jona Lasinio model, and to study the effect of fluctuations in Quark-Meson model, and it is the first application of thermodynamic geometry to field theory at finite temperature and density. The phase transition has been studied evaluating the scalar curvature, R, of the thermo-metric, gμν. In all the studied models, R is positive (like for statistical repulsive) for temperature well above the transition one, and becomes negative around the transition. This suggests that around the chiral crossover, the interaction changes at mesoscopic level and there is a rearrangement of the collective interactions in the hot medium, from statistically repulsive (due to the fermionic nature of the bulk) to attractive. Our results concerning the NJL model and QM model show that thermodynamic geometry reliably describes the phase diagram. We notice that in both cases, R develops a peak structure around the chiral crossover. This is expected due to the relation between R and the correlation volume around a phase transition: as a matter of fact, at a second order phase transition R diverges due to the divergence of the correlation volume, while at a crossover the correlation length increases but remains finite. We have also found that in the region of small values of μ, the mesonic fluctuations enhance the magnitude of the curvature, and we understand this in terms of the stability of the phase with broken chiral symmetry. Indeed, fluctuations reduce the value of the determinant of the metric, g, meaning that fluctuations make the chiral broken phase less stable.