Scaling Behavior of $(N_{ch})^{-1}dN_{ch}/d\eta$ at $\sqrt{s_{NN}} = 130$ GeV by the PHOBOS Collaboration and Its Implication --A Possible Explanation Employing the Ornstein-Uhlenbeck Process--

Abstract

Recently, interesting data concerning $dN_{ch}/d\eta$ in Au-Au collisions [$\eta=-\ln \tan (\theta/2)$] with centrality cuts have been reported from the PHOBOS Collaboration. In most treatment these data are divided by the number of participants (nucleons) in collisions. Instead of this method, we use the total multiplicity $N_{ch} = \int (dN_{ch}/d\eta)d\eta$ and find that there is scaling phenomenon among $(N_{ch})^{-1}dN_{ch}/d\eta = dn/d\eta$ with different centrality cuts at $\sqrt{s_{NN}} = 130$ GeV. To explain this scaling behavior of $dn/d\eta$, we employ a stochastic approach using the Ornstein-Uhlenbeck process with two sources. A Langevin equation is adopted for this explanation. Moreover, comparisons of $dn/d\eta$ at $\sqrt{s_{NN}} = 130$ GeV with that at $\sqrt{s_{NN}} = 200$ GeV are made, and no significant difference is found. A possible method fot the detection of the quark-gluon plasma (QGP) through $dN_{ch}/d\eta$ is presented.