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arXiv 2207.03563nucl-thnucl-ex
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中能重离子反应方位流的主成分分析

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

Bao-An Li, Jake Richter

备注：
Significant revisions with additional results and discussions. Nuclear Physics A in press
发表信息：
Nuclear Physics A1034 (2023) 122640
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摘要：

通过奇异值分解（SVD）的大型数据集的主成分分析（PCA）是一种自适应的探索性方法，可以揭示数据背后的自然模式。最近的几个应用程序的PCA SVD事件的单粒子方位角分布矩阵在超相对论重离子碰撞在RHIC-LHC能量表明，正弦和余弦函数选择{ \it先验}在传统的傅立叶分析自然是最佳的基础，方位流研究根据数据本身。我们使用同位旋相关的Boltzmann-Uehling-Uhlenbeck（IBUU）输运模型对$E_{\rm beam}/A$ =1.23 GeV的中心Au+Au碰撞进行了PCA-SVD分析，以解决以下两个问题：（1）如果在1GeV/核子附近的重离子反应中核子方位角分布协方差矩阵的主成分是自然的正弦和/或余弦函数，以及（2）在研究致密核物质物态方程时，PCA SVD与传统的傅立叶展开流动分析相比有何优势。我们发现：（1）在我们的分析中，没有一个主成分是自然的正弦和/或余弦函数;（2）虽然协方差矩阵的特征向量和特征值都明显依赖于物态方程，但在研究重离子碰撞中方位角集体流稠密核物质物态方程时，PCA SVD并没有比传统Fourier分析更明显的优势。

英文摘要：

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.

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