Analysis of transverse momentum distributions observed at RHIC by a stochastic model in hyperbolic space

We are much intersted in events with high multiplicity at RHIC, where thousands of particles are produced per event. To describe such many particle system, a sort of collective approach will be useful. One-particle rapidity or pseudo-rapidity distributions observed at RHIC are well described by the Ornstein-Uhlenbeck process with two or three sources [1]. In this paper, we would extend our approach to include an expansion for transverse direction. We can derive the formula same with that proposed by Voloshin [2] from the three-dimensional Ornstein-Uhlenbeck process using the variables, longitudinal rapidity and two transverse momenta. The fundamental solution is gaussian in these variables. Even if the formula is integrated over the azimuthal angle in the transverse momentum plane, the distribution is only slightly modified from the gaussian. However, observed pt distributions at RHIC have long tails compared with an exponential distribution, and cannot be described by the formula.