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|$\ll$ N and 0<|Q|$\ll$ 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${}_{cr}^a$ is found, above which the pion system exists in the non-condensed phase. Various pion cross variances are calculated for T>maxT${}_{cr}^a$, 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.