Mutual derivation between arbitrary distribution forms of momenta and momentum components

TL;DR

This paper systematically explores the relationship between different distribution forms of particle momenta and their components, using probability theory, with applications to high-energy collision data analysis.

Contribution

It introduces a framework for mutual derivation of momentum distributions and applies it to analyze experimental spectra with a flexible multi-component relativistic gas model.

Findings

Distributions of rapidities and pseudorapidities are effectively studied.

Analytic and Monte Carlo methods are used to model ideal gas distributions.

Experimental spectra are successfully analyzed using the proposed multi-component model.

Abstract

The mutual derivation between arbitrary distribution forms of momenta and momentum components of particles produced in an isotropic emission source are systematically studied in terms of probability theory and mathematical statistics. The distributions of rapidities and pseudorapidities are expediently studied. As an example, the classical and relativistic ideal gas models are used to show these distributions by the analytic and Monte Carlo methods. As an application, the experimental rapidity and transverse momentum spectra of light flavor particles produced in high energy collisions are analyzed by a multi-component relativistic ideal gas model in which the single model can be replaced by other models and distributions.