Charge and isospin fluctuations in a non-ideal pion gas with dynamically fixed particle number

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 cr a . It is shown that in the case of the system with equal averaged numbers of isospin species, the variance of the charge, Q = N + - N - , diverges at T → T cr = T cr a , whereas variances of the total particle number, N = N + + N - + N 0 , and of a relative abundance of charged and neutral pions, G = ( N + + N - ) / 2 - N 0 , 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, max T cr a is found, above which the pion system exists in the non-condensed phase. Various pion cross variances are calculated for T > max T cr a , 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 .