Unified Description of Efficiency Correction and Error Estimation for Moments of Conserved Quantities in Heavy-Ion Collisions

TL;DR

This paper presents a unified framework for correcting efficiency effects and estimating errors in moments of conserved quantities in heavy-ion collisions, improving accuracy and consistency in statistical analysis.

Contribution

It introduces a method expressing moments via factorial moments for straightforward efficiency correction and derives a general error formula using covariance and the Delta theorem.

Findings

The error estimates from the Delta theorem and Bootstrap methods agree well.

The proposed correction method simplifies the analysis of moments in heavy-ion collision data.

Simulation tests validate the accuracy of the error estimation techniques.

Abstract

We provide a unified description of efficiency correction and error estimation for moments of conserved quantifies in heavy-ion collisions. Moments and cumulants are expressed in terms of the factorial moments, which can be easily corrected for the efficiency effect. By deriving the covariance between factorial moments, one can obtain the general error formula for the efficiency corrected moments based on the error propagation derived from the Delta theorem. The skellam distribution based Monto Carlo simulation is used to test the Delta theorem and Bootstrap error estimation methods. The statistical errors calculated from the two methods can well reflect the statistical fluctuations of the efficiency corrected moments.