Model independent shape analysis of correlations in 1, 2 or 3 dimensions

TL;DR

This paper introduces a versatile, model-independent approach for analyzing two-particle short-range correlations in various dimensions, utilizing orthonormal function expansions to accurately describe correlation functions.

Contribution

It presents a novel, data-driven method employing orthonormal expansions like Edgeworth and Laguerre for detailed correlation analysis across multiple dimensions.

Findings

Applicable to Bose-Einstein, statistical, and dynamical correlations.

Provides systematic correction terms for shape deviations.

Extends to multi-dimensional correlation functions.

Abstract

A generic, model-independent method for the analysis of the two-particle short-range correlations is presented, that can be utilized to describe e.g. Bose-Einstein (HBT or GGLP), statistical, dynamical or other short-range correlation functions. The method is based on a data-motivated choice for the zero-th order approximation for the shape of the correlation function, and on a systematic determination of the correction terms with the help of complete orthonormal set of functions. The Edgeworth expansion is obtained for approximately Gaussian, the Laguerre expansion for approximately exponential correlation functions. Multi-dimensional expansions are also introduced and discussed.