Principal component analysis of the nonlinear coupling of harmonic modes in heavy-ion collisions

TL;DR

This paper introduces a principal component analysis method for studying nonlinear harmonic mode couplings in heavy-ion collisions, providing a new way to analyze flow correlations and their momentum dependence.

Contribution

It generalizes the correlation matrix to include multiple flow vectors and applies PCA to reveal dominant nonlinear coupling modes in heavy-ion collision data.

Findings

Identified dominant nonlinear coupling modes in simulated Pb+Pb collisions.

Demonstrated the method's ability to analyze momentum-dependent flow correlations.

Provided a framework for detailed study of harmonic mode interactions.

Abstract

The principal component analysis of flow correlations in heavy-ion collisions is studied. The correlation matrix of harmonic flow is generalized to correlations involving several different flow vectors. The method can be applied to study the nonlinear coupling between different harmonic modes in a double differential way in transverse momentum or pseudorapidity. The procedure is illustrated with results from the hydrodynamic model applied to Pb+Pb collisions at $\sqrt{s}=2760$GeV. Three examples of generalized correlations matrices in transverse momentum are constructed corresponding to the coupling of $v_2^2$ and $v_4$, of $v_2v_3$ and $v_5$, or of $v_2^3$, $v_3^3$, and $v_6$. The principal component decomposition is applied to the correlation matrices and the dominant modes are calculated.