Lévy Distributions for One-Dimensional Analysis of the Bose–Einstein Correlations

V A Okorokov

doi:10.1155/2017/5465398

Abstract

A general study of relations between the parameters of two centrally symmetric Lévy 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 Lévy 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 that a generalized centrally symmetric Lévy distribution is used. The reasonable agreement is observed between estimations and experimental results for all available types of strong interaction processes and collision energies.

Highlights

Correlations between two identical bosons, called Bose–Einstein correlations (BEC), are a well-known phenomenon in high-energy and nuclear physics
The case is investigated for smooth approximation of the one experimental 1D Bose–Einstein correlation function by two various centrally symmetric Levy parameterizations
It is shown that finite range of q should be taken into account and corresponding systems of equations should be used for derivation of set {λ, R} based on the a priori known values of corresponding parameters for both cases of the two general view centrally symmetric Levy parameterizations and the two specific functions most used in experimental studies

Summary

Introduction

Correlations between two identical bosons, called Bose–Einstein correlations (BEC), are a well-known phenomenon in high-energy and nuclear physics. The derivation of the relations between the sets of BEC parameters for two centrally symmetric Levy distributions is the important task for correct comparison of the results from different experiments, creation of the global kinematic (energy, pair transverse momentum, etc.) dependencies of BEC parameters, and so on Such studies are important for investigations of common features of softstage dynamics in various multiparticle production processes as well as for equation of state (EoS) of strongly interacting matter, in particular, search for phase transition to the quarkgluon deconfined matter. The experimental database is shown in Appendix for 1D BEC parameters

Relations between BEC Parameters in General Case

Relations between BEC Parameters in Specific Cases

Comparison with Experimental Results

1.89 CPLEAR

Summary