System Size, Energy, Centrality and Pseudorapidity Dependence of Charged Particle Density in Nucleus-Nucleus Collisions at RHIC
By Rachid Nouicer
In ultrarelativistic heavy ion collisions, the charged particle multiplicities have been studied extensively because of the intrinsic interest in understanding the production mechanism. More recent interest comes in the context of searching for and studying new forms of matter that are expected to be created in heavy ion collisions at these energies. A key quantity that contains information about the longitudinal aspects of the multiparticle production process, and that has provided valuable input for discriminating between phenomenological models in the past, is the rapidity distribution of identified particles.
When particle identification is not available, the almost equivalent pseudorapidity density distribution of charged particles (dNch/dh) suffices. For this reason, such distributions have been studied in detail in hadron + proton, hadron + nucleus, proton + proton and nucleus + nucleus collisions. The PHOBOS experiment has performed a comprehensive set of measurements in Au+Au, Cu+Cu and d+Au collisions at several energies, ÖsNN = 19.6, 22.4, 62.4, 130 and 200 GeV, as well in p+p collisions at ÖsNN = 200 and 410 GeV, covering a span of an order of magnitude in the same detector, allowing for a reliable systematic study of particle production as a function of energy in these collisions [1,2,3,4,5]. The measured dNch/dh distributions were corrected for particles which were absorbed or produced in the surrounding material and for feed-down products from weak decays of neutral strange particles.
Once corrected, dNch/dh is a conceptually well-defined quantity that reflects most effects that contribute to particle production in heavy-ion collisions. It is sensitive to the initial conditions of the system, i.e. parton saturation, and also to the effects of rescattering and hadronic final-state interactions. In short, the full distribution of dNch/dh represents a time-integral of particle production throughout the entire heavy-ion collision. The advent of Cu+Cu collisions from RHIC at energies similar to those of the earlier Au+Au collisions presents a new opportunity to measure the system size dependence of important observables using different collision geometries.
New Cu+Cu results, reported in a recent paper by the PHOBOS collaboration  are expected to provide critical tests of the parametric dependence of dNch/dh, observed previously in Au+Au collisions. They significantly extend the range of measurements to a lower number of participant nucleons, Npart , compared to Au+Au and also allow for a direct comparison at the same Npart.
Making a global comparison of Cu+Cu and Au+Au results of charged particle density distributions, we find that the particle density per nucleon participant pair in the midrapidity region at given energy is similar in both systems. This implies that for the most central events in symmetric nucleus-nucleus collisions the particle density per nucleon participant pair does not depend on the size of the two colliding nuclei but only on the collision energy. The phenomenon of extended longitudinal scaling in Cu+Cu and Au+Au collisions holds independent of colliding energy and system size. The number of participants, Npart , is the scaling variable unifying the centrality dependence in Cu+Cu and Au+Au collisions for the total number of produced charged particles, NTotch [5,6].
A dependence on the size of the colliding nuclei is observed in the pseudorapidity distributions in the fragmentation regions (i.e. high |h|) at low energies, 22.4 and 62.4 GeV, when the collision centrality of the two systems is selected for similar Npart as it is presented in Figure 1a), 1b) and 1c). This may be attributed to the two excited nuclear remnants being bigger in Au+Au than in Cu+Cu collisions. This effect is most visible at the lowest energies where the broad h coverage gives access to |h| > ybeam, where yAuAubeam (200 GeV) = 5.36, yAuAubeam (62.4 GeV) = 4.20 and yAuAubeam (19.6 GeV) = 3.04. More detailed studies presented in Figure 1d), 1e) and 1f) reveal that a more precise matching of the shape (height and width) of the Cu+Cu and Au+Au pseudorapidity density distributions occurs for the same Npart /2A value rather than the same Npart value, where A is the mass number of the colliding nuclei. In other words, it is the collision geometry rather than just the number of nucleon participants that drives the detailed shape of the pseudorapidity distribution and its centrality dependence at RHIC energies. It should be noted that systems with matching Npart /2A values will also have matching Nspec /Npart values, where Nspec = 2A - Npart is the number of non-participating nucleons (spectators).
To investigate the precise matching of dNch/dh shapes between the two systems, Cu+Cu and Au+Au, over the full range h, Figure 2 shows the scaled pseudorapidity particle densities, dNch/dh¢/áNpart/2 ñ (where h¢ º h- ybeam corresponds effectively to the rest frame of one of the colliding nuclei) for centrality bins with a) the same fraction of total inelastic cross section 0-6% and b) similar value of Npart /2A. The best agreement of the shapes over the full range of h in Cu+Cu and Au+Au central collisions is obtained for centrality bins selected to yield similar value of Npart /2A in both systems. For centrality bins more peripheral than 25-30% (Fractional Cross Section < 0.7), the shapes-matching of dNch/dh¢/áNpart/2 ñ distributions in the two systems is similar when the centrality bins selected for the same fraction of total cross section or for the same Npart /2A. This observation can be explain by Figure 2c); for the same fraction of total inelastic cross section, the Cu+Cu and Au+Au collisions have similar Npart /2A for peripheral collisions but differ for more central collisions.
In summary, global comparison of Cu+Cu and Au+Au results shows that the particle density per nucleon participant pair in the midrapidity region at a given energy is similar in both systems. The phenomenon of extended longitudinal scaling in the two systems holds independent of colliding energy and system size. The number of participants is the scaling variable unifying the centrality dependence in Cu+Cu and Au+Au collisions for the total number of produced charged particles. More detailed studies reveal that the best matching of the dNch/dh shapes (height and width) between Cu+Cu and Au+Au collisions over the full range of h occurs when the collision centrality of the two systems is selected for similar Npart /2A. The essential role of collision geometry when comparing charged-particle density pseudorapidity distributions between nuclear species is clearly demonstrated at RHIC by the PHOBOS experiment.
 B. B. Back et al., Phys. Rev. Lett. 91, 052303
 B. B. Back et al., Phys. Rev. Lett. 93, 082301 (2004).
 B. B. Back et al., Phys. Rev. C 72, 031901(R) (2005).
 B. B. Back et al., Phys. Rev. C 74, 021901 (2006).
 B. B. Back et al. Phys. Rev. C 74, 021901(R) (2006)
 B. Alver et al., Submitted to Phys. Rev. Lett. (2007), arXiv: nucl-ex/0709.4008.