Interpretation of the First Data on Central Au + Au Collisions at √ s = 56 and 130 A GeV

We compare three semi-microscopic theories to the first data on particle production in central Au+Au collisions taken at RHIC by the PHOBOS collaboration as well as to existing data on central Pb+Pb collisions taken at the SPS by the NA49 collaboration. LEXUS represents the SPS data quite well but not the RHIC data, whereas the wounded nucleon model does the opposite. The collective tube model fails to describe any of the data. This suggests a transition in the dynamics of particle production between √ s = 17 and 56 A GeV as one goes from the SPS to RHIC. Typeset using REVTEX [email protected] [email protected] 1 The first data from the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory has been presented by the PHOBOS collaboration [1]. Their result is that the numbers of electrically charged hadrons per unit of pseudo-rapidity, dNch/dη, produced in the 6% most central Au+Au collisions at √ s = 56 and 130 A GeV and averaged over the interval |η| < 1, are 408±12(stat)±30(syst) and 555±12(stat)±35(syst), respectively. Pseudo-rapidity is defined as η = 1 2 ln [(1 + cos θ)/(1− cos θ)], where the angle θ is measured with respect to the beam axis. The previous maximum energy for heavy ion collisions was √ s = 17 A GeV for Pb+Pb collisions at the SPS at CERN. Particle production in a high energy heavy ion collision is one of the fundamental observables. In this paper we report on a comparison of three semi-microscopic theories with both the RHIC and the SPS data in an attempt to understand the basic dynamics of these collisions. These theories are (1) a Linear EXtrapolation of Ultrarelativistic nucleon-nucleon Scattering to nucleus-nucleus collisions (LEXUS) [3], (2) the Wounded Nucleon Model (WNM) [5], and (3) the Collective Tube Model (CTM) [4]. We refer to these as semi-microscopic theories because they are based on input from nucleon-nucleon collisions but are not computed with QCD. Below we briefly describe these theories; for details the reader should consult the original papers. The LEXUS assumes that the nucleons follow straight-line trajectories, striking nucleons from the other nucleus that lie in their path and interacting with them exactly as in free space. Hadrons are produced in every nucleon-nucleon collision according to the parametrization N ch (s) = 1.568 (√ s−Mmin )3/4 /s ∼ 1.568s (1) with √ s being the center-of-mass energy in that nucleon-nucleon collision and is measured in GeV. With Mmin = 2mN + mπ this simple function represents particle production in nucleon-nucleon collisions up to √ s = 62 GeV, excluding single diffractive events, as well as proton-antiproton collisions at 200 GeV. It is also known that in nucleon-nucleon collisions the hadrons are produced with a Gaussian rapidity distribution centered at mid-rapidity and with a dispersion given by the formula 2 D NN(s) = ln ( √ s 2mN ) . (2) Unlike pseudo-rapidity, rapidity requires knowledge of the mass of the particle and is defined as y = 1 2 ln [(E + pz)/(E − pz)], where E is the energy and pz is the momentum along the beam axis. When the mass goes to zero η and y coincide; for pions their difference is typically very small. As a nucleon cascades through the other nucleus it loses energy, and this is taken into account via an evolution equation which is solved numerically. All parameters in LEXUS are fit to nucleon-nucleon data and nothing should be adjusted to fit nucleus-nucleus data. The above information is folded together with a constant inelastic nucleon-nucleon cross section σinel and with a realistic density distribution for the colliding nuclei. The WNM defines a nucleon to be wounded the first time it undergoes an inelastic collision with a nucleon from the other nucleus. A wounded nucleon is assumed to produce 1/2 of the average charged hadrons in a nucleon-nucleon collision at the same energy. Once it is wounded it cannot produce any more, although it can strike an unwounded nucleon and that one can produce particles. The total number of charged hadrons produced by nP wounded projectile nucleons and nT wounded target nucleons is Nch(nP , nT ) = nP + nT 2 N ch (s) . (3) These hadrons are assumed to be distributed in rapidity in a Gaussian way, centered at the nucleon-nucleon rest frame, and with a dispersion given by eq. (2). There is no energy loss assigned to the nucleons as they strike and wound other nucleons. Otherwise the geometrical folding to compute the number of wounded nucleons is standard and is done in exactly the same way as LEXUS. The CTM describes a nucleus-nucleus collision as a set of aligned tube-tube collisions. One tube is taken from the projectile nucleus and one from the target. The cross sectional area of the tubes is σinel. If one tube contains nP and the other tube nT participants then the center-of-mass energy available for particle production is s(nP , nT ) = 4nPnTp 2 cm + (nP + nT ) 2m2N , (4) 3 where pcm is the beam momentum of an individual nucleon in the nucleus-nucleus frame. The number of charged hadrons produced in this tube-tube collision is the same as that produced in an elementary nucleon-nucleon collision with the same available energy (baryon masses subtracted). That is, eq. (1) is applied with Mmin = (nP + nT )mN + mπ. This means that knowledge of particle production in nucleon-nucleon collisions at energies much higher than 200 GeV is required for RHIC! There is no experimental information on nucleonnucleon collisions above √ s = 62 GeV; higher energies should be measured in the future at RHIC. There is data on proton-antiproton collisions from the UA5 collaboration at CERN [6]. The average multiplicity, exclusive of single diffractive events, may be represented by the function N ch (s) = 22 + 1.7 ln (√ s/200 )