Quantum chromodynamics and the statistical hydrodynamical model of hadron production

Abstract

We analyze the Fermi-Landau statistical hydrodynamical model of hadron-hadron multiplicities in the framework of QCD, using the Pokorski---Van Hove model wherein the collision of preexisting glue dominates the multiplicity. It is noted that previous dismissal of the possibility of thermalization in the basis of nuclear "transparency" is circumvented in this picture because the valence quarks pass through, whereas the gluon clouds interact strongly. Assuming that the gluons equilibrate to a thermalized plasmoid within the Fermi-Landau (FL) Lorentz-contracted initial volume, we derive a simple formula for the multiplicity with the form ${N}_{\mathrm{ch}}\ensuremath{\approx}2.5{f}^{\frac{1}{4}}{{W}_{\mathrm{had}}}^{\frac{1}{2}}$ (three flavors excited), where $1\ensuremath{-}f$ is the fraction of energy carried away by the leading particles and ${W}_{\mathrm{had}}=fW$ is the energy left behind. If $f$ were fixed at a constant value of \textonehalf{}, the formula would agree extremely well with data up to and including $\overline{p}p$ collider energies. (The widely held belief that collider multiplicities rule out the Fermi power law was based on the use of $W$ rather than ${W}_{\mathrm{had}}$.) However, using the data of Basile et al., in which multiplicities are broken down as a function of ${W}_{\mathrm{had}}$ for different $W$ values, we find that the ${f}^{\frac{1}{4}}$ dependence is ruled out. We conclude that thermalization of the colliding gluon clouds in the FL volume is also ruled out, although thermalization in the gluon fragmentation and central regions remains a possibility.