A Measure for Isotropy-Equilibrium Degree of a Multi-Particle System

Aiming at using sphericity as a tool to study the isotropy-equilibrium property of a multi-particle system, in particular the hadronic final state IFS produced in
instanton-induced DIS events, we discuss in detail the dependence of sphericity on multiplicity and the multiplicity distribution, as well as on the isotropy degree of the system. A rotational symmetric model with a fluctuating isotropy-degree is constructed, which can fit the mean and width of sphericity of the Monte Carlo IFS-results simultaneously. The IFS from the Monte Carlo simulation is found to be not ideally isotropic but has a probability of 4.7% to be isotropic within error of 5%. The results provide us a description of how far the IFS departs from equilibrium. The method developed is applicable to any Monte Carlo generated multi-particle system, for which the isotropy-equilibrium property is significant.