Modifications in clusterization procedures for heavy-ion collisions: minimum spanning tree, simulated annealing, coalescence

TL;DR

The paper presents the open-source Common Clusterization Library (CCL) for flexible cluster identification in transport models of heavy-ion collisions, implementing MST via DSU, SACA/SA, a two-pass SA chain (CCL SA), stable-cluster tracking (sMST), box-like coalescence, and a mixed coalescence with negative binding-energy criteria. Through systematic comparisons against ALADiN and NA49 data, it shows that DSU-based MST matches full MST results with reduced computation time, SA-based methods improve early-time binding-energy behavior, and the coalescence variants complemented by sMST yield improved agreement across observables. The results highlight the importance of time-dependent parameter choices and online tracking for accurate cluster yields, and demonstrate the utility of CCL as a portable, extensible framework across transport codes. Overall, CCL provides fast, open-access tools for robust cluster reconstruction and parameter studies in heavy-ion collision simulations, with practical implications for isotope and hypernuclei production modeling.

Abstract

A new open-source cluster finding library ''Common Clusterization Library'' (CCL) is proposed to describe the clusters production when applied to the transport codes. The new library was applied to the Parton-Hadron-Quantum-Molecular Dynamics approach to be comparable with the established and well known MST and SACA implementations on the exactly same set of the events. The presented procedures were tested with rapidity density distributions and complex observables like $\langle M_{imf} \rangle$ and $\langle Z_{\text{max}} \rangle$ vs $Z_{bound}2$ at the energies of ALADiN and NA49 experiments. An improvement to the simulated annealing chain is proposed to reduce the computational time. The new stable clusters tracking algorithm for the ''lost'' cluster recovering is presented. The results of the ''box-like'' coalescence procedure and a mixed method which incorporates the coalescence algorithm steps and the negative binding energy criteria are presented. The difference between the Helium-3 found by the MST-based cluster finding procedure and the coalescence algorithm applied on the exactly same set of events and baryons is shown for the first time.

Figures (9)

• Figure 1: Upper panel: $\langle M_{imf} \rangle$ vs $Z_{bound}2$; Lower panel: $\langle Z_{\text{max}} \rangle$ vs $Z_{bound}2$; Black solid lines -- PHQMD MST at $t = 50$ fm/c. Red dashed lines -- PHQMD MST at $t = 100$ fm/c. Orange dash-dotted lines -- CCL MST at $t = 50$ fm/c. Blue dotted lines -- CCL MST at $t = 100$ fm/c. ALADiN experimental data (black circles) are taken from LeFevre:2019wuj.
• Figure 2: $\langle M_{imf} \rangle$ (top panel) and $\langle E_{\text{bind}} \rangle$ (bottom) vs $Z_{bound}2$ for CCL MST. Black solid lines -- $t = 50$ fm/c, red dashed lines -- at $t = 100$ fm/c, orange dash-dotted lines -- $t = 150$ fm/c, blue dotted lines -- $t = 200$ fm/c. Black circles -- ALADiN experimental data LeFevre:2019wuj.
• Figure 3: $\langle M_{imf} \rangle$ (top panel), $\langle Z_{\text{max}} \rangle$ (middle panel) and $\langle E_{bind} \rangle$ (bottom panel) as a function of $Z_{bound}2$. Black solid lines and orange dash-dotted lines are PHQMD SACA at $t = 50$ and $t = 100$ fm/c. Red dashed lines and blue dotted lines -- CCL SA at $t = 50$ and $t = 100$ fm/c. Black circles -- ALADiN experimental data taken from LeFevre:2019wuj.
• Figure 4: Rapidity density distribution of deuterons and $^3He$ with and without stable clusters tracking procedure with several parameters sets for the MST edges (\ref{['tab:tracking']}): black solid lines -- T1 set, T2 -- red dashed lines, T3 set -- orange dash-dotted lines. Black circles -- NA49 experimental dataNA49:2016qvu.
• Figure 5: Rapidity density distribution. Black solid lines and orange dash-dotted lines -- $d$ and $^{4}He$ from UrQMD, red dashed lines and blue dotted lines -- same from CCL coalescence. Probabilities to form nuclei are taken from the UrQMD model source code.