Scaling Behavior of (Nch)-1dNch/d at by the PHOBOS Collaboration and Its Implication: A Possible Explanation Employing the Ornstein-Uhlenbeck Process

Recently, interesting data concerning $dN_{ch}/d\eta$ in Au-Au collisions[$\eta=-\ln \tan (\theta/2)$] with centrality cuts have been reported from thePHOBOS Collaboration. In most treatment these data are divided by the number ofparticipants (nucleons) in collisions. Instead of this method, we use the totalmultiplicity $N_{ch} = \int (dN_{ch}/d\eta)d\eta$ and find that there isscaling phenomenon among $(N_{ch})^{-1}dN_{ch}/d\eta = dn/d\eta$ with differentcentrality cuts at $\sqrt{s_{NN}} = 130$ GeV. To explain this scaling behaviorof $dn/d\eta$, we employ a stochastic approach using the Ornstein-Uhlenbeckprocess 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. Apossible method fot the detection of the quark-gluon plasma (QGP) through$dN_{ch}/d\eta$ is presented.Comment: 15 pages, 9 figures, PTPTe