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 $$T>\max T_\mathrm{cr}^a$$ . 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 $$T\rightarrow T_\mathrm{cr}=T_\mathrm{cr}^a$$ , 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, $$\text{ max }T_\mathrm{cr}^{{a}}$$ is found, above which the pion system exists in the non-condensed phase. Various pion cross variances are calculated for $$T>\text{ max }T_\mathrm{cr}^{{a}}$$ , 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.