Levy distributions for one-dimensional analysis of the Bose-Einstein correlations

TL;DR

This paper explores the relationships between parameters of Levy distributions used in analyzing Bose-Einstein correlations, accounting for finite momentum differences, and verifies the formalism with experimental data across various collision processes.

Contribution

It provides the first comprehensive analysis of Levy distribution parameters in Bose-Einstein correlation studies, including special cases and experimental validation.

Findings

Relations between correlation strength and emission region radius are established.

Mathematical formalism is validated with experimental data.

Good agreement observed across different collision energies and processes.

Abstract

A general study of relations between the parameters of two centrally-symmetric Levy distributions, often used for one-dimensional investigation of Bose - Einstein correlations, is given for the first time. These relations of the strength of correlations and of the radius of the emission region take into account possible various finite ranges of the Lorentz invariant four-momentum difference for two centrally-symmetric Levy distributions. In particular, special cases of the relations are investigated for Cauchy and normal (Gaussian) distributions. The mathematical formalism is verified using the recent measurements given a generalized centrally-symmetric Levy distribution is used. The reasonable agreement is observed between estimations and experimental results for all available types of strong interaction processes and collision energies.