# Azimuthal harmonics in small and large collision systems at RHIC top energies

## TL;DR

This study measures azimuthal harmonic coefficients in various collision systems at RHIC energies, revealing system-independent behavior for some harmonics and scaling laws that shed light on initial geometry and viscous effects.

## Contribution

It provides the first comprehensive comparison of azimuthal harmonics across small and large collision systems at RHIC, highlighting scaling behaviors and initial-geometry effects.

## Key findings

- $v_1^{ ext{even}}$ and $v_3$ are system-independent at fixed multiplicity.
- $v_2$ scales with initial eccentricity $ ext{and}$ multiplicity.
- $ ext{ln}(v_2/ ext{eccentricity})$ scales linearly with $ ext{N}_{ch}^{-1/3}$.

## Abstract

The first ($v_1^{\text{even}}$), second ($v_2$) and third ($v_3$) harmonic coefficients of the azimuthal particle distribution at mid-rapidity, are extracted for charged hadrons and studied as a function of transverse momentum ($p_T$) and mean charged particle multiplicity density $\langle \mathrm{N_{ch}} \rangle$ in U+U ($\roots =193$~GeV), Au+Au, Cu+Au, Cu+Cu, $d$+Au and $p$+Au collisions at $\roots = 200$~GeV with the STAR Detector. For the same $\langle \mathrm{N_{ch}} \rangle$, the $v_1^{\text{even}}$ and $v_3$ coefficients are observed to be independent of collision system, while $v_2$ exhibits such a scaling only when normalized by the initial-state eccentricity ($\varepsilon_2$). The data also show that $\ln(v_2/\varepsilon_2)$ scales linearly with $\langle \mathrm{N_{ch}} \rangle^{-1/3}$. These measurements provide insight into initial-geometry fluctuations and the role of viscous hydrodynamic attenuation on $v_n$ from small to large collision systems.