Excitation Function of the Longitudinal Expansion in Central Nuclear Collisions

Longitudinal hadron spectra from Proton-Proton (pp) and nucleusnucleus (AA) collisions from Elab = 2 AGeV to √ s = 200 AGeV are investigated. The widths of the rapidity spectra for various particle species increases monotonously with energy. The present calculation indicates no sign of a step like behaviour as excepted from the Kaon transverse mass systematics. For Pions, the transport simulation is consistent with a Landau type scaling of the rapidity widths, both in central AA reactions and in pp collisions. However, other hadron species do not follow the Landau scaling. The present model predicts a decreasing rapidity width with particle mass for newly produced particles, not supporting a Landau type flow interpretation. Excitation Function of the Longitudinal Expansion in Central Nuclear Collisions 2 Based on recent lattice QCD (lQCD) calculations it has been speculated that partonic degrees of freedom might already lead to visible effects at ∼ 5 A·GeV [1]. Especially the hardening of the measured transverse mass (mt) spectra in central Au+Au collisions relative to pp interactions [2, 3] around AGS energies obtained great interest and was studied in detail [4]. This increase of the inverse slope parameter T is commonly attributed to strong collective flow, which is absent in the respective pp or pA collisions. It has also been proposed [5] to interpret the high and approximately constantK slopes above ∼ 30 AGeV – the ’step’ – as an indication of the phase transition. This interpretation seems supported by microscopic transport simulations • directly indicating the importance of sub-hadronic degrees of freedom above AGS energies [6] and • from the comparison of the thermodynamic parameters T and μB extracted from the transport models in the central overlap region [7] with the experimental systematics on chemical freeze-out configurations [8] in the T, μB plane. Let us now explore whether a similar ’step’ is also present in the excitation function of longitudinal observables. For the present study we employ the UrQMD model (v2.2) [9, 10]. It takes into account the formation and multiple rescattering of hadrons and dynamically describes the generation of pressure in the hadronic expansion phase. It involves also interactions of (di-)quarks, however gluonic degrees of freedom are not treated explicitly, but are implicitly present in strings. This simplified treatment is generally accepted to describe Proton-Proton and Proton-nucleus interactions. It became popular to interpret relativistic heavy ion reactions with Landau’s hydrodynamical model [11, 12, 13, 14, 15, 16] (for recent applications of this model to relativistic nucleus-nucleus interactions see [17, 18, 19]). Therefore we will use this simple hydrodynamical picture as a baseline for the model and data comparison. The main physics assumptions of Landau’s picture are: The collision of two Lorentzcontracted hadrons or nuclei leads to full thermalization in a volume of size Vmp/ √ s. This justifies the use of thermodynamics and establishes the system size and energy dependence. A simple equation of state p = ǫ/3 is assumed. Chemical potentials are usually assumed to vanish. The main results derived from these assumptions are: A universal formula for the produced entropy, determined mainly by the initial Lorentz contraction and Gaussian rapidity distributions, at least for newly produced particles. The results can be summarised in the energy dependent rapidity density [15]: dN dy = Ks √ 2πL exp(− y 2L ) with L = σ y = ln( √ s/2mp). (1) As depicted in Fig. 1 (left) the UrQMD predictions (full circles) for the rapidity widths of negatively charged Pions in Au+Au (Pb+Pb) reactions are in line with the experimental data [19] (full diamonds) and Landau’s hydrodynamical model (full line). A rather surprising observation is that the calculated rapidity widths of π in pp interactions (open squares) are identical to the AA results. Excitation Function of the Longitudinal Expansion in Central Nuclear Collisions 3 10 0 2 5 10 1 2 5 10 2 2 5 Ecm (GeV) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 (d N /d y ) o f Landau data p+p Au+Au/Pb+Pb