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

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 $E_{\mathrm{beam}}/A$=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.

Significant revisions with additional results and discussions. Nuclear Physics A in press

References in corpus (8)

• Transverse momentum analysis of collective motion in relativistic nuclear collisions
• Suppression of elliptic flow in a minimally viscous quark-gluon plasma
• Directed, elliptic and higher order flow harmonics of protons, deuterons and tritons in Au+Au collisions at $\sqrt{s_{NN}}=2.4$ GeV
• Principal component analysis of event-by-event fluctuations
• Transport approaches for the Description of Intermediate-Energy Heavy-Ion Collisions
• Collision dynamics at medium and relativistic energies
• Principal-component analysis of two-particle azimuthal correlations in PbPb and pPb collisions at CMS
• Application of Principal Component Analysis to establish proper basis for flow studies in heavy-ion collisions

Cited by in corpus (3)

• Bayesian inference of in-medium baryon-baryon scattering cross sections from HADES proton flow data
• A Neural Network Approach for Orienting Heavy-Ion Collision Events
• Evolutions of in-medium baryon-baryon scattering cross sections and stiffness of dense nuclear matter from Bayesian analyses of FOPI proton flow excitation functions