Minimizing statistical and systematic bias in transverse momentum correlations for relativistic heavy-ion collisions

TL;DR

This paper investigates how to minimize biases in transverse momentum correlation measurements in relativistic heavy-ion collisions, providing mathematical forms, simulation-based guidelines, and applicability ranges for accurate analysis.

Contribution

It derives correlation forms from mean-$p_t$ fluctuations, analyzes bias sources, and offers practical conditions to reduce biases in measurements.

Findings

Certain correlation forms reproduce input correlations accurately.

Bias effects depend on multiplicity and bin widths.

Guidelines for minimizing biases in practical data analysis.

Abstract

Two-particle correlation measurements and analysis are an important component of the relativistic heavy-ion physics program. In particular, particle pair-number correlations on two-dimensional transverse momentum ($p_t$) allow unique access to soft, semi-hard and hard-scattering processes in these collisions. Precise measurements of this type of correlation are essential for understanding the dynamics in heavy-ion collisions. However, transverse momentum correlation measurements are especially vulnerable to statistical and systematic biases. In this paper the origins of these large bias effects are explained and mathematical correlation forms are derived from mean-$p_t$ fluctuation quantities in the literature. Monte Carlo simulations are then used to determine the conditions, e.g. multiplicity and collision centrality bin widths, where each correlation form is minimally biased. The ranges of applicability for each correlation quantity are compared. Several are found to reproduce the assumed input correlations with reasonable fidelity over a wide range of conditions encountered in practical analysis of data.