Chemical Nonequilibrium in High Energy Nuclear Collisions

Strange particles produced in S–Au/W/Pb 200 A GeV and Pb–Pb 158 A GeV reactions are described invoking final hadronic phase space in thermal equilibrium, but allowing chemical non-equilibrium. Several sets of statistical freeze-out parameters are obtained for each system, invoking different models of dense matter. We show that only when allowing for strange and non-strange flavor abundance non-equilibrium, a statistically significant description of the experimental results is obtained. Physical properties of the fireball at chemical freeze-out condition are evaluated and considerable universality of hadron freezeout between the two different collision systems is established. The relevance of the Coulomb effect in the highly charged Pb–Pb fireballs for the chemical analysis are discussed. The influence of explosive collective matter flow is also described. Presented at the International Conference Strangeness in Quark Matter, held in Padova, July 1998 To appear in: Journal of Physics G 1. Chemical non-equilibrium statistical model 1.1. Introductory remarks We report here on the recent progress we made with the thermal model freezeout analysis of the CERN-SPS 200 A GeV Sulphur beam reactions with laboratory stationary ‘heavy’ targets, such as Gold, Tungsten or Lead nuclei [1], and we also present the current status of our ongoing effort to understand the results from CERN 158 A GeV Lead beam Pb–Pb collisions [2, 3]. These reactions occur at an energy ECM = √ s/B = 8–9GeV ≃ 9mNc per participating nucleon in the center of momentum frame. This high energy available materializes in form of high hadronic particle multiplicity which we are aiming to interpret. In this work we assume local thermal (i.e., energy equipartition) equilibrium [4, 5, 6, 7] reached in a relatively small and dense volume of highly excited hadronic matter, the ‘fireball’. One can argue that the accessibility of many degrees of freedom, as expressed by high specific entropy content, validates thermal equilibrium approach. As of now there is no established theoretical argument for the rapid kinetic equilibration process in highly excited, dense hadronic matter. However, this seems to be the case: consider that as seen in the results of the precise measurements made by experiments WA85/WA94/WA97 [8, 9], the transverse mass spectra are nearly identical for particle-antiparticle pairs where particles comprise some quarks brought into the reaction, e.g., Λ–Λ, Ξ–Ξ. When modeling the production of these particles in microscopic models, we encounter in general vastly different m⊥ spectra [10]. Chemical Nonequilirium 2 The fireball undergoes complex chemical evolution until at some stage final state particle abundances freeze-out. We refer here to the stage in evolution of the fireball at which density has dropped to the level that in subsequent collisions particle abundances remain unchanged. The mechanisms of chemical equilibration in which particle numbers change are today theoretically better understood than are mechanisms responsible for what is believed to be much faster to establish thermal (kinetic) equilibration, where momentum exchange between existent particles is the key mechanism. Recall that it has been the allowance of non-equilibrium chemical abundance for strange quarks which permitted to analyze accurately the experimental strange particle abundance data and to characterize the properties of the particle source [6, 11, 12, 13, 14]. Here our primary result, concluded from the success of the description of the experimental data, is that chemical non-equilibrium both for light and strange quarks is a necessary requisite for the understanding of the experimental particle abundances. The corresponding technical refinement not present in earlier work is that we introduce a parameter, the light quark phase space occupancy (see below) γq to describe the light quark chemical non-equilibrium[1, 22]. We did not previously consider simultaneously a interpretation of strange and non-strange particles and hence the need to allow for light quark chemical non-equilibrium was not visible to us: the strange quark phase space occupancy γs was determined relative to γq, which we now understand is also off-equilibrium. Since we now can accurately describe abundances of strange as well as non-strange hadrons, we combine in the present analysis the strangeness diagnostic tools of dense matter with the entropy enhancement [12, 15]. We side-step here initially, mainly to keep the number of parameters to a minimum, the need to study collective matter flows originating in both, the memory of the initial ‘longitudinal’ collision momentum, and the explosive disintegration driven by the internal pressure of compressed hadronic matter. However, we will present in section 5 a short account of the results obtained with such effects, and illustrate changes that arise in our present study. 1.2. Parameters and their physical meaning We employ the local thermal equilibrium method, and thus use a local freeze-out temperature Tf . Regarding chemical equilibration, we will recognize two different types, relative and absolute. We speak of relative chemical equilibration occurring through quark exchange reactions described in terms of fugacities λi, i = u, d, s. In general we will not distinguish between the two light q = u, d quarks, and thus we use two fugacities only. From the valance quark fugacities, the hadronic particle fugacities are reconstituted. However, the fugacities λi do not regulate the total number of s-s̄ valance quark-pairs present, and this number has to be controlled by a new parameter, the phase space occupancies γi, i = u, d, s — again, we shall not distinguish between the two light flavors. To understand the role of γi note that any compound particle comprising a particle-antiparticle pair is not controlled in abundance by a fugacity, since the formation of such particles does not impact the conservation laws. The abundance of, e.g., neutral pions comprises normally no (quark) fugacity at all. This abundance is thought to be regulated solely by temperature. This of course implies the tacit assumption of absolute chemical equilibrium. However, the effective fugacity of quarks is λiγi and antiquarks λ −1 i γi, and thus with the introduction of γi we can control pair abundance independently of other properties of the system. The proper Chemical Nonequilirium 3 statistical physics foundation of γi is obtained considering the maximum entropy principle for evolution of physical systems. In such a study it has been determined that while the equilibrium limit γi → 1 maximizes the specific chemical entropy, this maximum is very shallow [16], indicating that a system with dynamically evolving physical properties such as the occupied volume will in general find more effective paths to increase entropy, than offered by the establishment of the absolute chemical equilibrium. The dynamical theory for γs has been one of the early cornerstones of the proposal to use strangeness as signature of deconfinement [17, 18]. A time dependent build up of chemical abundance was first considered in the context of microscopic strangeness production in QGP, after it was realized that strange flavor production occurs at the same time scale as the collision process. More generally, one must expect, considering the time scales, that all quark flavors will not be able to exactly follow the rapid evolution in time of dense hadronic matter. Moreover, fragmentation of gluons in hadronizing QGP can contribute additional quark pair abundance, conveniently described by the factor γi. It is thus to be expected that also for light quarks the chemical phase space occupancy factor γq 6=