Fluctuating initial conditions in heavy ion collisions from the Glauber approach

Abstract

In the framework of the Glauber approach applied to the initial stage of ultra-relativistic heavy-ion collisions we analyze the shape parameters of the early-formed system (fireball) and their event-by-event fluctuations. We test a variety of models: the conventional wounded-nucleon model, a model admixing binary collisions to the wounded nucleons, a model with hot spots, and the hot-spot model where the deposition of energy occurs with a superimposed probability distribution. We look in detail at the so-called participant harmonic moments, {epsilon}*, obtained by an averaging procedure where in each event the system is translated to its center of mass and aligned with the major principal axis of the ellipse of inertia. Quantitative comparisons indicate substantial relative effects for {epsilon}* in variants of Glauber models. However, the dependence of the scaled standard deviation {delta}{epsilon}*/, {epsilon}* on the chosen model is weak. For all models the values range from about 0.5 for the central collisions to about 0.3-0.4 for peripheral collisions, for both gold-gold and copper-copper collisions. They are dominated by statistics and change only by 10-15% from model to model. We provide an approximate analytic expansion for the harmonic moments and their fluctuations given in terms of the fixed-axes moments. For centralmore » collisions and in the absence of correlations the expansion gives the simple formula {delta}{epsilon}*/{epsilon}*{approx_equal}{radical}(4/{pi}-1)=0.52. Similarly, we obtain expansions for the radial profiles of the higher harmonics. We investigate the relevance of the shape-fluctuation effects for jet quenching and find them important only for very central events. Finally, we make some comments of relevance for hydrodynamics, the elliptic flow, and its fluctuations. We argue how smooth hydrodynamics leads to the known result v{sub 4}{approx}v{sub 2}{sup 2} and, further, to the prediction {delta}v{sub 4}/v{sub 4}=2{delta}v{sub 2}/v{sub 2}.« less