# $p_T$-Dependent Particle Number Fluctuations From Principal Component Analyses in Hydrodynamic Simulations of Heavy-Ion Collisions

## TL;DR

This study uses principal component analysis on hydrodynamic simulations of heavy-ion collisions to compare flow and multiplicity fluctuations with experimental data, revealing key differences in $p_T$ dependence.

## Contribution

It introduces a toy model to analytically understand PCA modes and their dependence on fluctuations, highlighting discrepancies in $p_T$ trends between simulations and experiments.

## Key findings

- Flow PCA components match experimental trends.
- Multiplicity PCA shows simulation-experiment $p_T$ trend differences.
- Hydrodynamic models exhibit larger transverse momentum fluctuations.

## Abstract

We carry out a principal component analysis of fluctuations in a hydrodynamic simulation of heavy-ion collisions, and compare with experimental data from the CMS collaboration. The leading and subleading principal components of elliptic and triangular flow reproduce the trends seen in data. By contrast, the principal components of multiplicity fluctuations show an interesting difference in their $p_T$ dependence for simulations compared to experimental data. Specifically, the leading component increases with $p_T$ in hydrodynamics, while it is constant in experiment. In order to understand how the leading and subleading modes arise, we construct a toy model where the principal components have a simple analytic form. We show how the PCA components depend on fluctuations of the average transverse momentum and of the total multiplicity, as well as correlations between the two, and we verify that hydrodynamic simulations agree with the predictions of the toy model. The difference in the momentum trend is likely due to the fact that hydrodynamic models typically have transverse momentum fluctuations that are larger than seen experimentally.