Analyses of dNch/dη and dNch/dy distributions of BRAHMS Collaboration by means of the Ornstein-Uhlenbeck process

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Interesting data on dNch/dη in Au-Au collisions (η=-In tan(θ/2)) with the centrality cuts have been reported by BRAHMS Collaboration. Using the total multiplicity Nch=∫(dNch/dη)dη, we find that there are scaling phenomena among (Nch){ 1dNch/dη=dn/dη with different centrality cuts at √SNN=130 GeV and 200 GeV, respectively. To explain these scaling behaviors of dnl'drj, we consider the stochastic approach named the Ornstein-Uhlenbeck process with two sources. The following Fokker-Planck equation is adopted for the present analyses, ∂P(x,t)/∂t = γ[∂/∂x x+1/2 σ2/γ ∂2/∂x2]P(x,t) where x means the rapidity (y) or pseudo-rapidity (η). t, γ and σ2 and the evolution parameter, the frictional coefficient and the variance, respectively. Introducing a variable of zr=η/ηrms (ηrms=√<η2>) we explain the dn/dzr distributions in the present approach. Moreover, to explain the rapidity (y) distributions from η distributions at 200 GeV, we have derived the formula as dn/dy=J{ 1dn/dη' where J{ 1=√M(1+sinh2y)/√1+Msinh2y with M=1+(m/pt)2. Their data of pion and all hadrons are fairly well explained by the O-U process. To compare our approach with another one, a phenomenological formula by Eskola et al. is also used in calculations of dn/dη.
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