Power Law in Micro-Canonical Ensemble with Scaling Volume Fluctuations

Volume fluctuations are introduced in a statistical modelling of relativistic particle collisions. The micro-canonical ensemble is used, and the volume fluctuations are assumed to have the specific scaling properties. This leads to the KNO scaling of the particle multiplicity distributions as measured in p+p interactions. A striking prediction of the model is a power law form of the single particle momentum spectrum at high momenta. Moreover, the mean multiplicity of heavy particles also decreases as a function of the particle mass according to a power law. Finally, it is shown that the dependence of the momentum spectrum on the particle mass and momentum reduces to the dependence on the particle energy. These results resemble the properties of particle production in collisions of high energy particles.