Application of Principal Component Analysis to establish proper basis for flow studies in heavy-ion collisions

TL;DR

This paper demonstrates that applying Principal Component Analysis to heavy-ion collision data identifies optimal bases for flow analysis, matching Fourier and Legendre polynomial series, and enables studying flow-structure coupling.

Contribution

It introduces PCA as a data-driven method to determine optimal basis functions for flow analysis in heavy-ion collisions, replacing manual selection.

Findings

PCA coefficients match Fourier coefficients in azimuthal analysis.

PCA in longitudinal dimension aligns with Legendre polynomial basis.

Simultaneous analysis reveals coupling between longitudinal structure and azimuthal anisotropy.

Abstract

It is shown that Principal Component Analysis (PCA) applied to event-by-event single-particle distributions in A-A collisions allows establishing the most optimal basis for anisotropic flow studies from data itself, in contrast to manual selection of the basis functions. PCA coefficients for azimuthal particle distributions are identical to Fourier coefficients from a conventional analysis techniques. PCA applied in longitudinal dimension reveals optimal basis that is similar to Legendre polynomial series. Analysis in both dimensions simultaneously allows studying the coupling of the longitudinal structure of events with the azimuthal anisotropy of particle emission.