Error Estimation for Moments Analysis in Heavy-Ion Collision Experiments

TL;DR

This paper derives statistical error formulas for moments analysis of conserved quantities in heavy-ion collisions, crucial for understanding QCD phase structure, validated through Monte Carlo simulations.

Contribution

It introduces a new error estimation method for moments analysis based on the Delta theorem, enhancing accuracy in experimental data interpretation.

Findings

Derived limit distributions for moments analysis

Validated error formulas with Monte Carlo simulations

Improved accuracy in fluctuation measurements

Abstract

Fluctuations of conserved quantities are predicted to be sensitive to the correlation length and connected to the thermodynamic susceptibility. Thus, moments of net-baryon, net-charge and net-strangeness have been extensively studied theoretically and experimentally to explore phase structure and bulk properties of QCD matters created in heavy ion collision experiment. As the moments analysis is statistics hungry study, the error estimation is crucial to extract physics information from the limited experimental data. In this paper, we will derive the limit distributions and error formula based on Delta theorem in statistics for various order moments used in the experimental data analysis. The Monte Carlo simulation is also applied to test the error formula.