Generalisation of the identity method for determination of high-order moments of multiplicity distributions with a software implementation

TL;DR

This paper extends the identity method to calculate high-order moments of multiplicity distributions in particle physics, providing a general solution and an open-source software tool for accurate analysis despite incomplete particle identification.

Contribution

It generalizes the identity method for arbitrary order moments and offers an open-source software implementation for practical use.

Findings

Generalized the identity method for n-th order moments.

Provided an open-source software tool, Idhim.

Enables accurate multiplicity analysis with incomplete identification.

Abstract

The incomplete particle identification limits the experimentally-available phase space region for identified particle analysis. This problem affects ongoing fluctuation and correlation studies including the search for the critical point of strongly interacting matter performed on SPS and RHIC accelerators. In this paper we provide a procedure to obtain $n$-th order moments of the multiplicity distribution using the identity method, generalising previously published solutions for $n=2$ and $n=3$. Moreover, we present an open source software implementation of this computation, called \textit{Idhim}, that allows one to obtain the true moments of identified particle multiplicity distributions from the measured ones provided the response function of the detector is known.