Charge and isospin fluctuations in a 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 $a=\pm,0$, i.e. for $T>\max T_{\rm cr}^a$. 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 $T\to T_{\rm cr}=T_{\rm cr}^a$, 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, $\mbox{max}T_{\rm cr}^{{a}}$ is found, above which the pion system exists in the non-condensed phase. Various pion cross variances are calculated for $T>\mbox{max}T_{\rm cr}^{{a}}$, 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 $Q/N$.