Principal Component Analysis of Azimuthal Flow in Intermediate-Energy Heavy-Ion Reactions

TL;DR

This study applies PCA-SVD to simulated heavy-ion collision data at 1.23 GeV/nucleon to investigate if natural basis functions align with traditional Fourier analysis and to compare their effectiveness in studying nuclear matter EOS.

Contribution

It demonstrates that principal components do not naturally correspond to sine or cosine functions and finds no clear advantage of PCA-SVD over Fourier analysis in this context.

Findings

Principal components are not naturally sine or cosine functions.

Eigenvalues and eigenvectors depend on the EOS.

No advantage of PCA-SVD over Fourier analysis for EOS studies.

Abstract

Principal Component Analysis (PCA) via Singular Value Decomposition (SVD) of large datasets is an adaptive exploratory method to uncover natural patterns underlying the data. Several recent applications of the PCA-SVD to event-by-event single-particle azimuthal angle distribution matrices in ultra-relativistic heavy-ion collisions at RHIC-LHC energies indicate that the sine and cosine functions chosen {\it a priori} in the traditional Fourier analysis are naturally the most optimal basis for azimuthal flow studies according to the data itself. We perform PCA-SVD analyses of mid-central Au+Au collisions at $E_{\rm beam}/A$=1.23 GeV simulated using an isospin-dependent Boltzmann-Uehling-Uhlenbeck (IBUU) transport model to address the following two questions: (1) if the principal components of the covariance matrix of nucleon azimuthal angle distributions in heavy-ion reactions around 1 GeV/nucleon are naturally sine and/or cosine functions and (2) what if any advantages the PCA-SVD may have over the traditional flow analysis using the Fourier expansion for studying the EOS of dense nuclear matter. We find that (1) in none of our analyses the principal components come out naturally as sine and/or cosine functions, (2) while both the eigenvectors and eigenvalues of the covariance matrix are appreciably EOS dependent, the PCA-SVD has no apparent advantage over the traditional Fourier analysis for studying the EOS of dense nuclear matter using the azimuthal collective flow in heavy-ion collisions.