Source Function from Two-Particle Correlation Through Deblurring

TL;DR

This paper introduces a novel application of the Richardson-Lucy deblurring algorithm to extract particle emission sources from two-particle correlation functions in heavy-ion collision experiments, offering an alternative to traditional Gaussian fitting methods.

Contribution

It proposes using the Richardson-Lucy deblurring algorithm to directly infer the emission source from correlation data, bypassing the need for parametric Gaussian models.

Findings

RL algorithm effectively reconstructs the source from correlation functions.

The method provides a non-parametric imaging approach.

Potential for improved accuracy over traditional fitting methods.

Abstract

In heavy-ion collisions, low relative-velocity two-particle correlations have been a tool for assessing space-time characteristics of particle emission. Those characteristics may be cast in the form of a relative emission source related to the correlation function through the Koonin-Pratt (KP) convolution formula that involves the relative wave-function for the particles in its kernel. In the literature, the source has been most commonly sought by parametrizing it in a Gaussian form and fitting to the correlation function. At times the source was more broadly imaged from the function, still employing a fitting. Here, we propose the use of the Richardson-Lucy (RL) optical deblurring algorithm for deducing the source from a correlation function. The RL algorithm originally follows from probabilistic Bayesian considerations and relies on the intensity distributions for the optical object and its image, as well as the convolution kernel, being positive definite, which is the case for the corresponding quantities of interest within the KP formula.