Fluctuations in non-ideal pion gas with dynamically fixed particle number

Abstract

We study the behavior of the non-ideal pion gas with the dynamically fixed number of particles, formed on an intermediate stage in ultra-relativistic heavy-ion collisions. The pion spectrum is calculated within the self-consistent Hartree approximation. General expressions are derived for cross-covariances of the number of various particle species in the pion gas of an arbitrary isospin composition. The behavior of the cross-variances is analyzed for the temperature approaching from above the maximal critical temperature of the Bose-Einstein condensation for the pion species a = ±, 0, i.e. for T > max T a cr . It is shown that in case of the system with equal averaged numbers of isospin species, the variance of the charge, Q = N+ − N−, diverges at T → Tcr = T a cr , whereas variances of the total particle number, N = N+ + N− + N0, and of a relative abundance of charged and neutral pions, G = (N+ + N−)/2 − N0, remain finite in the critical point. Then fluctuations are studied in the pion gas with small isospin imbalance 0 < |G| ≪ N and 0 < |Q| ≪ N and shifts of the effective masses, chemical potentials and values of critical temperatures are calculated for various pion species, and the highest critical temperature, maxT a cr is found, above which the pion system exists in the non-condensed phase. Various pion cross variances are calculated for T > maxT a cr , which prove to be strongly dependent on the isospin composition of the system, whereas the variances of N and G are found to be independent on the isospin imbalance up to the term linear in G/N and Q/N .

Large- N kinetic theory for highly occupied systems

“…For instance, for a relativistic scalar field theory describing interacting pions in the context of heavy-ion collisions, conditions for a conserved particle number density and the time interval where this approximation can be trusted have been discussed in Refs [58][59][60]…”

Nonequilibrium Pion Distribution within the Zubarev Approach

“…This is facilitated by extending the set of Lagrangian multipliers by the additional non-equilibrium chemical potentials for the hadrons will appear in the NSO. If the non-equilibrium chemical potential for the pions coincides with the pion effective mass, Bose-Einstein condensation will occur, and strong effects are expected on the measured pion spectra [19,20].…”