Multiplicity fluctuations due to the temperature fluctuations in high-energy nuclear collisions

Abstract

We investigate the multiplicity fluctuations observed in high-energy nuclear collisions attributing them to intrinsic fluctuations of temperature of the hadronizing system formed in such processes. To account for these fluctuations, we replace the usual Boltzmann-Gibbs (BG) statistics by the nonextensive Tsallis statistics characterized by the nonextensivity parameter $q$, with $|q\ensuremath{-}1|$ being a direct measure of fluctuation. In the limit of vanishing fluctuations, $q\ensuremath{\rightarrow}1$ and Tsallis statistics converge to the usual BG. We evaluate the nonextensivity parameter $q$ and its dependence on the hadronizing system size from the experimentally observed collision centrality dependence of the mean multiplicity $\ensuremath{\langle}N\ensuremath{\rangle}$ and its variance Var$(N)$. We attribute the observed system size dependence of $q$ to the finiteness of the hadronizing source, with $q=1$ corresponding to an infinite, thermalized source with a fixed temperature, and with $q>1$ (which is observed) corresponding to a finite source in which both the temperature and energy fluctuate.