Power Law in Micro-Canonical Ensemble with Scaling Volume Fluctuations

TL;DR

This paper introduces volume fluctuations with scaling properties into a micro-canonical ensemble model of relativistic particle collisions, predicting power-law behaviors in particle spectra and multiplicities consistent with high-energy collision data.

Contribution

It presents a novel statistical model incorporating scaling volume fluctuations that explains observed power-law distributions in high-energy particle collisions.

Findings

KNO scaling of multiplicity distributions

Power-law form of high-momentum spectra

Mass-dependent multiplicity decrease

Abstract

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.