Levy Flight &TGD

Abstract

This article was motivated by an interesting Science Daily popular article about the finding that in high energy heavy ion collisions in which quark-gluon plasma is created. What is studied is the distribution for the distances of hadrons travelled between two collisions during the re-scattering phase during which hadrons collide, fuse and long-lived resonances decay. This distribution is studied for pions. It is found that the distribution does not obey Gaussian distribution as in Brownian motion but has a long tail obeying a power law. This distribution is associated with Levy flight for which the distribution parameter corresponds to a Levy walk for which the second moment of the distribution is finite. Levy walk is the analog of Brownian motion for the distances travelled during the period of final state interactions. The physical origin of the tail would be the slow decay of resonances decaying eventually to mesons and pions. The tail obeys a power law, which suggests a scaling symmetry and fractality associated with criticality. The new physics predicted by TGD suggests an identification for the origin the analog of Brownian motion and of quantum criticality implying Levy walk.