Relativistic diffusion model and analysis of large transverse momentum distributions

In order to describe large transverse momentum ($p_T$) distributions observed in high energy nucleus-nucleus collisions, a stochastic model in the three dimensional rapidity space is introduced. The fundamental solution of the radial symmetric diffusion equation is Gaussian-like in radial rapidity. We can also derive a $p_T$ or radial rapidity distribution function, where a distribution of emission center is taken into account. It is applied to the analysis of observed large $p_T$ distributions of charged particles. It is shown that our model approaches to a power function of $p_T$ in the high transverse momentum limit.