Two-dimensional Bayesian Approach for Centrality Determination in Nucleus-Nucleus Collisions

TL;DR

This work tackles centrality determination in nucleus-nucleus collisions by introducing a two-dimensional Bayesian framework based on the observables $(N_{ ext{hits}}, E_{ ext{spec}})$. A two-dimensional Gamma distribution, decorrelated through a rotation, models the joint fluctuations at fixed $b$, with moments tied to centrality via polynomial fits in the centrality variable $c_b$ and calibrated for experimental effects using factors $oldsymbol{ ext{alpha}}$ and $oldsymbol{ extbeta}$ and an efficiency $oldsymbol{ extepsilon}$. The Bayes posterior $P(b|E_{ ext{spec}},N_{ ext{hits}})$ is computed to reconstruct impact-parameter distributions, and centrality classes are obtained via constrained clustering; applied to simulated Xe+CsI collisions at $3.8$ AGeV, the method reproduces model $b$ distributions within about 2% and reduces autocorrelation in proton multiplicity analyses. An appendix develops a two-parameter Glauber-type description of multiplicity fluctuations, separating volume and particle-production fluctuations and enabling parameter reduction when comparing data to simulations. Overall, the approach provides a robust, low-bias centrality estimator suitable for low-multiplicity heavy-ion systems and sets the stage for expanding the observable set in BM@N.

Abstract

The determination of centrality in nucleus-nucleus collisions is a crucial task as it enables the estimation of the impact parameter and hence allows for the comparison of experimental results with data from theoretical models and other experiments. In this work, we present a two-dimensional approach for centrality determination based on a Bayesian framework. The observables used were the number of track hits and the deposited energy of spectators in the forward hadronic calorimeter. A distribution is proposed to describe the fluctuations of these two observables at a fixed impact parameter value, which provides a significantly superior description of the observable distributions in both central and peripheral regions. The effectiveness of the proposed method was verified for the BM@N experiment using simulated data for Xe+CsI collisions at a beam energy of 3.8 AGeV.

Figures (10)

• Figure 1: Schematic view of the BM@N setup in the 2023 Xe run kapishin2020.
• Figure 2: Correlation between the deposited spectator energy in FHCal and the impact parameter for Xe+CsI collisions at a beam energy of 3.8 AGeV in DCM-QGSM-SMM model: a) for all modules, b) for large modules afanasiev2024.
• Figure 3: Fit results (red curves) of the track hit number distribution (upper panels, a-c) and the deposed energy in the FHCal (middle panels, d-f) for several fixed impact parameter values corresponding to central, semi-central, and peripheral collisions. The lower panels(g-i) show the results of fitting the two-dimensional distribution of observables using function \ref{['eq:2DFitFixb']}, see text.
• Figure 4: The left plot shows dependenc of the varianc of the energy of spectators in FHCal and the right plot shows varianc of the number of track hits, as well as their covariance on centrality.
• Figure 5: