2003/02/03 by M. Ide, Ide, M., M. Biyajima +4
Mathematics · Physics and Astronomy · #High-Energy Particle Collisions Research #Markov Chains and Monte Carlo Methods #Stochastic processes and statistical mechanics #nucl-th
paper · pdf · doi:10.48550/arxiv.nucl-th/0302003
12 pages, 8 figures, Latex2e
arxiv created 2003/02/03 · arxiv updated 2009/12/01
Interesting data on dN\rm ch/dη in Au-Au collisions (η=-ln tan (θ/2)) with the centrality cuts have been reported by BRAHMS Collaboration. Using the total multiplicity N\rm ch = ∫ (dN\rm ch/dη)dη, we find that there are scaling phenomena among (N\rm ch)-1dN\rm ch/dη= dn/dη with different centrality cuts at √sNN = 130 GeV and 200 GeV, respectively. To explain these scaling behaviors of dn/dη, 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 + \frac 12\fracσ2γ(∂2)/(∂ x2)] P(x, t) where x means the rapidity (y) or pseudo-rapidity (η). t, γ and σ2 are the evolution parameter, the frictional coefficient and the variance, respectively. Introducing a variable of zr = η/η\rm rms (η\rm rms=√(< η2 >)) we explain the dn/d zr 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-1(dn)/(d η), where J-1=√(M(1+\sinh2 y))/√(1+M\sinh2 y) with M = 1 + (m/p\rm t)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.