Efficient and robust calculation of femtoscopic correlation functions in spherical harmonics directly from the raw pairs measured in heavy-ion collisions

TL;DR

This paper introduces a new formalism for calculating femtoscopic correlation functions directly in spherical harmonics, improving efficiency and robustness in heavy-ion collision data analysis.

Contribution

The paper develops a formalism to compute correlation functions directly in spherical harmonics from raw pair data, avoiding 3D histograms and enhancing stability.

Findings

Method is computationally efficient and robust against data holes.

Formalism successfully applied to simulated data example.

Provides a practical implementation guide for experimental analysis.

Abstract

We present the formalism for calculating the femtoscopic correlation function directly in spherical harmonics. The numerator and denominator are stored as a set of one-dimensional histograms representing the spherical harmonic decompositions of each. We present the formalism to calculate the correlation function from them directly, without going to any three-dimensional histogram. We discuss the practical implementation of the method and we provide an example of its use. We also discuss the stability of the method in the presence of $\theta$-$\phi$ holes in the underlying data (e.g. from experimental acceptance).