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

الأصل · EN

Interesting data on dN ch/dη in Au-Au collisions (η=- (θ/2)) with the centrality cuts have been reported by BRAHMS Collaboration. Using the total multiplicity N ch = ∫ (dN ch/dη)dη, we find that there are scaling phenomena among (N ch)⁻¹dN 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[∂/∂ xx + 12σ²γ∂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 rms (η 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⁻¹dn/d η, where J⁻¹=√M(1+² y)/√1+M² y with M = 1 + (m/p 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.