Number-of-constituent-quark scaling of elliptic flow: a quantitative study

TL;DR

This paper quantitatively investigates the number-of-constituent-quark scaling of elliptic flow in heavy-ion collisions using empirical fits to experimental data from RHIC and LHC, introducing variables to measure the scaling's validity.

Contribution

It introduces a quantitative method with variables to assess NCQ scaling of elliptic flow, moving beyond qualitative visual inspection.

Findings

Identifies the approximate region where NCQ scaling holds.

Provides a new quantitative framework for studying scaling phenomena.

Applicable to future experimental analyses.

Abstract

The number-of-constituent-quark (NCQ) scaling behavior of the elliptic flow of identified particles produced in A+A collisions is studied quantitatively using an empirical function that fits the experimental $v_2$ data available from the RHIC and LHC. The most common approach for NCQ scaling involves (1) doing a scaling of the experimental $v_2$ data of an identified particle with its NCQ, (2) doing the same to its transverse momentum or energy, then (3) combining all the scaled data and identifying the NCQ behavior by intuitively looking (since the measured experimental data are discrete). We define two variables $(d_1, d_2)$ to describe NCQ scaling quantitatively and simultaneously, and identify the approximate region where the NCQ scaling holds. This approach could be applied to study NCQ or other scaling phenomena in future experiments.