Fractal diffusion processes in particle physics

Abstract

A series of consistent measurements of kinematic variables for pion diffraction production processes by pions with an initial momentum of about 4 GeV/c were analyzed: π+ + p → p + 2π+ + π− and π− + p → p + 2π− + π+. The Hurst method analysis discovered the presence of the memory effect for both data arrays. The distributions of the transition probability density appeared to seek some equilibrium shape, characteristic of the fractal Brownian motion (FBM). The process can be defined by the special diffusion Fokker-Planck equation (FPE). The obtained values of Hurst coefficient 0.5 < H < 1, which is a parameter of FPE, mean that the processes explored are realized in fractal generalized phase space with fractional dimension.