Determining source cumulants in femtoscopy with Gram-Charlier and Edgeworth series

TL;DR

This paper compares Gram-Charlier and Edgeworth series for estimating source cumulants in femtoscopy, demonstrating that Edgeworth series offers more accurate results than Gram-Charlier, especially for non-Gaussian distributions.

Contribution

It introduces a method to determine fourth-order source cumulants from momentum space measurements using series expansions, highlighting the superiority of Edgeworth over Gram-Charlier.

Findings

Gram-Charlier series is highly inaccurate for this application.

Edgeworth series provides increasingly accurate estimates.

Ordering of terms according to the Central Limit Theorem is crucial.

Abstract

Lowest-order cumulants provide important information on the shape of the emission source in femtoscopy. For the simple case of noninteracting identical particles, we show how the fourth-order source cumulant can be determined from measured cumulants in momentum space. The textbook Gram-Charlier series is found to be highly inaccurate, while the related Edgeworth series provides increasingly accurate estimates. Ordering of terms compatible with the Central Limit Theorem appears to play a crucial role even for nongaussian distributions.