Particle multiplicities and ratios in excluded volume models

Abstract

One of the most surprising results is to find that a consistent description of all the experimental results on particle multiplicities and ratios obtained from the lowest Alternating Gradient Synchrotron to the highest Relativistic Heavy Ion Collider energies is possible within the framework of a thermal statistical model. We explore here the utility of a thermodynamically consistent excluded volume model recently proposed by us in explaining the above experimental results and we further compare our results with those obtained from an ideal gas model and other excluded-volume model that are often used in describing a grand canonical statistical system consisting of hot, dense hadron gas. We find that the energy dependence of the total multiplicities of strange and nonstrange hadrons in general shows close agreement with the experimental data, although slight deviation is observed for some multistrange hadrons, e.g., $\ensuremath{\Omega}+\overline{\ensuremath{\Omega}},\ensuremath{\Xi}$, and \ensuremath{\Phi}. The difference observed in these cases does not clearly support our assumption of the same freeze-out volume of the fireball that homogeneously emit all kinds of particles. Similarly we have calculated the ratios for particles and antiparticles such as ${K}^{\ensuremath{-}}/{K}^{+},\phantom{\rule{0.3em}{0ex}}\overline{p}/p,\phantom{\rule{0.3em}{0ex}}\overline{\ensuremath{\Lambda}}/\ensuremath{\Lambda},\phantom{\rule{0.3em}{0ex}}\overline{\ensuremath{\Xi}}/\ensuremath{\Xi}$, and $\overline{\ensuremath{\Omega}}/\ensuremath{\Omega}$, as well as the ratios of the unequal mass particles $\ensuremath{\langle}{K}^{+}\ensuremath{\rangle}/\ensuremath{\langle}{\ensuremath{\pi}}^{+}\ensuremath{\rangle},\ensuremath{\langle}{K}^{\ensuremath{-}}\ensuremath{\rangle}/\ensuremath{\langle}{\ensuremath{\pi}}^{\ensuremath{-}}\ensuremath{\rangle}, \ensuremath{\langle}\ensuremath{\Lambda}\ensuremath{\rangle}/\ensuremath{\langle}\ensuremath{\pi}\ensuremath{\rangle},\phantom{\rule{0.3em}{0ex}}\ensuremath{\langle}{\ensuremath{\Xi}}^{\ensuremath{-}}\ensuremath{\rangle}/\ensuremath{\langle}\ensuremath{\pi}\ensuremath{\rangle},\phantom{\rule{0.3em}{0ex}}\ensuremath{\langle}\ensuremath{\Omega}+\overline{\ensuremath{\Omega}}\ensuremath{\rangle}/\ensuremath{\langle}\ensuremath{\pi}\ensuremath{\rangle}$, and $\ensuremath{\langle}\ensuremath{\Phi}\ensuremath{\rangle}/\ensuremath{\langle}\ensuremath{\pi}\ensuremath{\rangle}$ and studied their variations with respect to the center-of-mass energy in the excluded-volume models and, finally, the results are compared with the experimental data. We find that in some cases, although the calculated results show close agreements with the experimental data, the deviations between theory and experiment in cases of unequal mass and multistrange particle ratios, like $\ensuremath{\langle}\ensuremath{\Lambda}\ensuremath{\rangle}/\ensuremath{\langle}\ensuremath{\pi}\ensuremath{\rangle},\phantom{\rule{0.3em}{0ex}}\ensuremath{\langle}{\ensuremath{\Xi}}^{\ensuremath{-}}\ensuremath{\rangle}/\ensuremath{\langle}\ensuremath{\pi}\ensuremath{\rangle},\phantom{\rule{0.3em}{0ex}}\ensuremath{\langle}\ensuremath{\Omega}+\overline{\ensuremath{\Omega}}\ensuremath{\rangle}/\ensuremath{\langle}\ensuremath{\pi}\ensuremath{\rangle},\ensuremath{\langle}\ensuremath{\Phi}\ensuremath{\rangle}/\ensuremath{\langle}\ensuremath{\pi}\ensuremath{\rangle},$ etc., appear to be quite large and thus warrant further investigations on the suitability of thermal hadron gas models.