Statistical theory of cumulant mapping in an imperfect apparatus

TL;DR

This paper provides a formal analysis of cumulant mapping in imperfect experimental setups, highlighting its robustness and limitations in observing multi-particle fragmentation amidst noise and false correlations.

Contribution

It offers a theoretical framework for understanding cumulant mapping under noise, identifying conditions for its effectiveness and potential issues with false signals.

Findings

Cumulant mapping remains effective for dominant processes.

False cumulant signals increase faster than linearly with event rate.

A simple test can identify false contributions in data.

Abstract

Cumulant mapping has been recently suggested [Frasinski, Phys. Chem. Chem. Phys. 24, 207767 (2022)] as an efficient approach to observing multi-particle fragmentation pathways, while bypassing the restrictions of the usual coincidence-measurement approach. We present a formal analysis of the cumulant-mapping technique in the presence of moderate external noise, which induces spurious correlations between the fragments. Suppression of false-cumulant signal may impose severe restrictions on the stability of the experimental setup and/or the permissible average event rate, which increase with the cumulant order. We demonstrate that cumulant mapping in an imperfect apparatus remains competitive for dominant processes and for pathways with a background-free marker fragment. We further show that the false-cumulant contributions increase faster than linearly with the average event rate, providing a simple test for the experimental data analysis.