Bayesian reconstruction of impact parameter distributions from two observables for intermediate energy heavy ion collisions

TL;DR

This paper develops a Bayesian method combined with K-means clustering to reconstruct impact parameter distributions from two observables in intermediate energy heavy ion collisions, enhancing understanding of collision centrality and fragmentation.

Contribution

It introduces a model-independent Bayesian approach utilizing two observables and machine learning to accurately reconstruct impact parameter distributions and analyze their correlations.

Findings

Impact parameter fluctuations follow a Gaussian distribution due to microscopic stochasticity.

The combined use of multiplicity and transverse momentum improves impact parameter reconstruction.

Reconstructed distributions reveal correlations useful for understanding fragmentation mechanisms.

Abstract

To reconstruct the impact parameter distributions from the selected events sample or centrality, which is defined by two-observables, at intermediate energy heavy ion collisions, we extend the approach proposed by Das \textit{et al.} [Phys. Rev. C 97, 014905 (2018)], Rogly \textit{et al.} [Phys. Rev. C 98, 024902 (2018)], and Frankland \textit{et al.} [Phys. Rev. C 104, 034609 (2021)]. Based on deep investigations of the fluctuation mechanism, we found that the intrinsic fluctuations are mainly generated in the microscopic stochasticity of initialization and nucleon-nucleon collisions in the nonequilibrium process of heavy ion collisions, and this leads the observables to fluctuate with respect to impact parameter in a Gaussian form. In this work, the multiplicity of the charged particles and the total transverse momentum of the light charged particles are used simultaneously to model-independently reconstruct the impact parameter distributions for selected events or centrality based on the Bayesian method. For sorting the centrality with two observables, we propose to use the $K$-means clustering method (an unsupervised machine learning algorithm), which can automatically sort events when the class number is given. Furthermore, the reconstructed impact parameter distributions from data of the two observables can be used to learn the correlation between multiplicity and transverse momentum at different centralities, which may be useful for understanding the fragmentation mechanism.