Geometric relation between centrality and the impact parameter in relativistic heavy-ion collisions

Details Geometric relation between centrality and the impact parameter in relativistic heavy-ion collisions Geometric relation between centrality and the impact parameter in relativistic heavy-ion collisions

2001-10-08

arxiv.org/abs/nucl-th/0110020v1

Phys.Rev. C65 (2002) 024905

Physics

Nuclear Physics

Nuclear Theory

4 pages, 2 figures, Revtex 3

Scientific paper

10.1103/PhysRevC.65.024905

We show, under general assumptions which are well satisfied in relativistic heavy-ion collisions, that the geometric relation of centrality c to the impact parameter b, namely c ~ pi b^2/sigma_inel, holds to a very high accuracy for all but most peripheral collisions. More precisely, if c(N) is the centrality of events with the multiplicity higer than N, then b is the value of the impact parameter for which the average multiplicity is equal to N. The corrections to this geometric formula are of the order (Delta n(b)/)^2, where Delta n(b) is the width of the multiplicity distribution at a given value of b, hence are very small. In other words, the centrality effectively measures the impact parameter.

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