Thermodynamics and fluctuations of conserved charges in a hadron resonance gas model in a finite volume

Abstract

The thermodynamics of hot and dense matter created in heavy-ion collision experiments are usually studied as a system of infinite volume. Here we report on possible effects for considering a finite system size for such matter in the framework of the Hadron Resonance Gas model. The bulk thermodynamic variables as well as the fluctuations of conserved charges are considered. We find that the finite size effects are insignificant once the observables are scaled with the respective volumes. The only substantial effect is found in the fluctuations of electric charge which may therefore be used to extract information about the volume of fireball created in heavy-ion collision experiments.PACS numbers: 12.38. Mh,21.65.Mn, Our present day universe contains a significant fraction of matter in hadronic form. In the very early universe − a few microseconds after the Big Bang [1] when the temperature was extremely high, the strongly interacting matter is expected to have existed in the partonic form. Similar exotic state of matter may exist inside compact stars due to extremely high matter density attained by gravitational compression [2]. For the last few decades various experimental efforts are being made to recreate such exotic matter through the collisions of heavy-ions at ultra-relativistic energies. Experimental facilities at CERN (France/Switzerland), BNL (USA) and the upcoming facility at GSI (Germany) are at the forefront of efforts taken to create these exotic states of matter. One of the major goals in the experiments is to study thermodynamic properties of strongly interacting matter at high temperatures and densities. Present experimental data as well as lattice QCD simulations seem to indicate a smooth cross over from hadronic to quark gluon matter at low density and high temperature [3,4]. At high density and low temperature a first order transition is expected [5][6][7][8][9][10].Usually any thermodynamic study assumes the system volume to be infinite. However the fireball created in the relativistic heavy ion collision experiments has a finite spatial volume. The size of such spatial volume critically depends on three parameters : the size of the colliding nuclei, the center of mass energy ( √ s) and the centrality of collisions. Analysis of experimental data could reveal the freeze out volume of the system. One way to carry out such an analysis is the study of HBT radii which has been done in Ref.[11]. The major finding of this study indicates that the freeze out volume increases as the √ s increases and the estimated freeze out volume varies from 2000 f m 3 to 3000 f m 3 . Another way of estimating the system size is through the comparison of simulation results with the experimental data as done in Ref. [12] where the UrQMD model [13] is used for this purpose. A study of the P b − P b collisions at different energies and centralities resulted in a freeze-out volume in the range 50 f m 3 to 250 f m 3 . We note that these volumes as quoted above, are the freeze out volumes and as one looks back to the early...

Thermalization in a small hadron gas system and high-multiplicity pp events

“…As has been pointed out in the Ref. [25], the variation with the system-size at high temperature disappears due to the dominant population of higher mass resonances, including the Hagedorn States, which, unlike the low mass resonances, are not affected on implementation of finite size effect. As can be seen in the Figure 5, though the mean free path of pions for the hadron gas of different sizes, constrained with the LQCD EoS, is different in the lower region of the temperature scale, it asymptotically approaches the same value of ∼ 1 fm at T ∼ 160 MeV.…”

“…[19], for the simultaneous consideration of Hagedorn states and the excluded volume effect. The finite size effect on volume and number of particles, considered infinite in the thermodynamic limit, can be implemented [24,25] by cutting off the low momentum regions in the integral over momentum space. We introduce the finite size effect [25], using the lower limit of momentum, p cutof f (M eV ) = 197 π/R(f m), where R is the characteristic system-size.…”

Reparametrizing the Polyakov–Nambu–Jona-Lasinio model

“…They may also be useful as signatures of a possible phase transition or crossover [16,59,[121][122][123][124][125][126][127][128][129]. The pressure of the system at a given temperature and arbitrary chemical potentials may be expanded as a Taylor series around zero chemical potentials.…”

Higher moments of net-proton multiplicity distributions in a heavy-ion event pile-up scenario

“…There have been speculations that the non-monotonic behavior of κσ 2 as a function of center-of-mass energy ( √ s N N ) in the netproton multiplicity (N diff = N p − Np) distribution measured by the STAR [16] experiment may be an indication of the QCD critical point. Several studies have been carried out to estimate the excess of dynamical fluctuations such as the effect of kinematical acceptance [20], inclusion of resonance decays [21][22][23], exact (local) charge conservation [24,25], excluded volume corrections [26,27] and so forth to provide a proper thermal baseline for experi-mental measurements [28][29][30][31][32].…”