Internal cumulants for femtoscopy with fixed charged multiplicity

TL;DR

This paper develops a refined method for analyzing higher-order correlations in femtoscopy, accounting for nonpoissonian multiplicity distributions and fixed charged multiplicity, improving accuracy over previous approaches.

Contribution

It introduces internal cumulants with an averaging approach that correctly handles nonpoissonian multiplicity distributions and fixed-N samples, with revised variance calculations.

Findings

Internal cumulants correctly nullify in uncorrelated fixed-N samples.

Revised variance and covariance formulas improve error estimation.

Implementation via a multiple event buffer algorithm enhances analysis efficiency.

Abstract

A detailed understanding of all effects and influences on higher-order correlations is essential. At low charged multiplicity, the effect of a nonpoissonian multiplicity distribution can significantly distort correlations. Evidently, the reference samples with respect to which correlations are measured should yield a null result in the absence of correlations. We show how the careful specification of desired properties necessarily leads to an average-of-multinomials reference sample. The resulting internal cumulants and their averaging over several multiplicities fulfil all requirements of correctly taking into account nonpoissonian multiplicity distributions as well as yielding a null result for uncorrelated fixed-N samples. Various correction factors are shown to be approximations at best. Careful rederivation of statistical variances and covariances within the frequentist approach yields errors for cumulants that differ from those used so far. We finally briefly discuss the implementation of the analysis through a multiple event buffer algorithm.