Several methods of generating three constituent-quarks in a nucleon are evaluated which explicitly maintain the nucleon's center of mass and desired radial distribution and can be used within Monte Carlo Glauber frameworks. The geometric models provided by each method are used to generate distributions over the Number of Constituent Quark Participants (Nqp) in p + p, d+Au and Au+Au collisions. The results are compared with each other and to a previous result of Nqp calculations, without this explicit constraint, used in measurements of √ s N N =200 GeV p + p, d+Au and Au+Au collisions at RHIC.PACS numbers: 25.75.Dw
I. GLAUBER MODELS FOR A+B COLLISIONSIn order to calculate the nuclear geometry, i.e. the number of participating nucleons (and more recently constituent-quark participants) in the collision of two nuclei, the Glauber Monte Carlo approach is widely used [1]. The nucleons in the two nuclei are taken to be frozen in position in their respective nucleus during the collision where it is also assumed that the nucleons travel along straight line trajectories which are not affected by any nucleon-nucleon (N+N) collisions. This enables a highenergy nucleus-nucleus (A+B) collision to be simulated in two steps:(i) Each beam and target nucleus, composed of A and B nucleons respectively is generated by placing the nucleons at random about the position of the nucleus, uniform in cos θ, φ and r 2 × ρ N (r) for spherical nuclei, where the nuclear density, ρ N (r), is typically taken as a Fermi (Woods-Saxon) density function [2]:r 2 dr sinθdθ dφ = ρ N (r) = ρ 0 1 + exp( r−c a0 )(1) with c = {1.18A 1/3 − 0.48} fm and the diffusivity a 0 = 0.545 fm for Au.(ii) The coordinates of the two nuclei are then shifted at random relative to each other in a plane transverse to the beam axis by a vector b, the impact parameter, sampling an area much larger than the range of possible impact parameters for the A+B collision. A pair of nucleons, one from each nucleus, interact with each other if their projected distance d in the plane transverse to the beam axis satisfies the condition:where σ inel N +N is the inelastic nucleon-nucleon cross section.The nuclear geometrical parameters such as N part , the number of participating nucleons, N coll , the number of binary N + N collisions, etc., can be computed for each trial.
A. Constituent QuarksThe approach can be extended one level further down with an additional step:(iii) modeling each nucleon by generating the positions of the three constituent-quarks (q) within it [3][4][5], effectively creating a constituent-quark structure of each nucleus. The A+B collision represented as a sum of q + q collisions is then obtained by changing the word "nucleon" to "quark" and N + N to q + q in step (ii) above.
II. ET AND NCH DISTRIBUTIONS AND EXTREME INDEPENDENT MODELS (EIM)Measurements of mid-rapidity transverse energy distributions dE T /dη in p+p, d+Au and Au+Au collisions at √ s N N =200 GeV were recently presented by the PHENIX collaboration [6]. The transverse energy E T , a multiparticle ...