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  • Open Access

Toward a topological data analysis for heavy-ion collisions

Federica Capellino1,*, Andrea Dubla1,†, Silvia Masciocchi1,2,‡, Govert Nijs3,§, and Daniel Spitz4,∥

  • *Contact author: f.capellino@gsi.de
  • †Contact author: a.dubla@gsi.de
  • ‡Contact author: s.masciocchi@gsi.de
  • §Contact author: govert.nijs@cern.ch
  • ∥Contact author: daniel.spitz@mis.mpg.de
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Phys. Rev. C 112, 054909 – Published 25 November, 2025

DOI: https://doi.org/10.1103/w5pw-prkv

Abstract

The collective expansion of the quark-gluon plasma (QGP) created in heavy-ion collisions suggests that geometry-inspired approaches can be useful in extracting information about the QGP. In this work, a systematic study of observables based on topological data analysis is provided for simulations of heavy-ion collisions. Specifically, we implement persistent homology observables for metric-based complexes in the heavy-ion model trajectum and provide predictions for Pb-Pb and O-O collisions, where the tunable model parameters are taken from a Bayesian analysis performed in Pb-Pb collisions. This, in particular, allows us to compute systematic uncertainties on our observables from the uncertainties in the model parameters. To bridge between new and already established observables, we build a dictionary linking the topological observables to traditional ones, such as particle multiplicities, momentum distributions, and the elliptic flow coefficient. While the persistent homology observables largely reflect known phenomenology and do not show enhanced sensitivity to the model's tunable parameters compared to conventional observables, this study demonstrates the viability and robustness of topological techniques in the context of heavy-ion physics. They may offer alternative perspectives and potential applications in heavy-ion physics.

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References (54)

  1. W. Busza, K. Rajagopal, and W. van der Schee, Annu. Rev. Nucl. Part. Sci. 68, 339 (2018).
  2. S. Acharya et al., Eur. Phys. J. C 84, 813 (2024).
  3. J. Adams et al., Nucl. Phys. A 757, 102 (2005).
  4. K. Adcox et al., Nucl. Phys. A 757, 184 (2005).
  5. G. Nijs, W. van der Schee, U. Gürsoy, and R. Snellings, Phys. Rev. C 103, 054909 (2021).
  6. G. Nijs, W. van der Schee, U. Gürsoy, and R. Snellings, Phys. Rev. Lett. 126, 202301 (2021).
  7. B. Schenke, C. Shen, and P. Tribedy, Phys. Rev. C 102, 044905 (2020).
  8. L. Vermunt, Y. Seemann, A. Dubla, S. Floerchinger, E. Grossi, A. Kirchner, S. Masciocchi, and I. Selyuzhenkov, Phys. Rev. C 108, 064908 (2023).
  9. P. Lu, R. Kavak, A. Dubla, S. Masciocchi, and I. Selyuzhenkov, Nucl. Sci. Tech. 36, 142 (2025).
  10. M. R. Heffernan, C. Gale, S. Jeon, and J.-F. Paquet, Phys. Rev. C 109, 065207 (2024).
  11. M. R. Heffernan, C. Gale, S. Jeon, and J.-F. Paquet, Phys. Rev. Lett. 132, 252301 (2024).
  12. D. Everett et al., Phys. Rev. Lett. 126, 242301 (2021).
  13. J. E. Parkkila, A. Onnerstad, S. F. Taghavi, C. Mordasini, A. Bilandzic, M. Virta, and D. J. Kim, Phys. Lett. B 835, 137485 (2022).
  14. M. Virta, J. Parkkila, and D. J. Kim, Phys. Rev. C 111, 044903 (2025).
  15. G. Giacalone et al., Phys. Rev. Lett. 134, 082301 (2025).
  16. G. Giacalone et al., Phys. Rev. Lett. 135, 012302 (2025).
  17. J. Brewer, A. Mazeliauskas, and W. van der Schee, arXiv:2103.01939.
  18. N. Otter, M. A. Porter, U. Tillmann, P. Grindrod, and H. A. Harrington, EPJ Data Sci. 6, 17 (2017).
  19. F. Chazal and B. Michel, Front. Artif. Intell. 4, 667963 (2021).
  20. G. Hamilton, T. Dore, and C. Plumberg, Phys. Rev. C 106, 064912 (2022).
  21. R. Wang, C. Qiu, C.-S. Hu, Z. Li, and Y. Wu, Phys. Lett. B 864, 139405 (2025).
  22. D. Thomas, S. Demers, S. Krishnaswamy, and B. Rieck, in Machine Learning and the Physical Sciences Workshop, NeurIPS 2022 (unpublished).
  23. T. Gaertner and J. Reiten, arXiv:2312.06596.
  24. D. Spitz, K. Boguslavski, and J. Berges, Phys. Rev. D 108, 056016 (2023).
  25. D. Spitz, J. M. Urban, and J. M. Pawlowski, Phys. Rev. D 107, 034506 (2023).
  26. D. Spitz, J. M. Urban, and J. M. Pawlowski, Phys. Rev. D 111, 114519 (2025).
  27. D. Sehayek and R. G. Melko, Phys. Rev. B 106, 085111 (2022).
  28. N. Sale, B. Lucini, and J. Giansiracusa, Phys. Rev. D 107, 034501 (2023).
  29. X. Crean, J. Giansiracusa, and B. Lucini, SciPost Phys. 17, 100 (2024).
  30. H. Edelsbrunner, D. Kirkpatrick, and R. Seidel, IEEE Trans. Inf. Theory 29, 551 (1983).
  31. H. Edelsbrunner and E. P. Mücke, ACM Trans. Graph. 13, 43 (1994).
  32. U. Bauer and H. Edelsbrunner, Trans. Am. Math. Soc. 369, 3741 (2017).
  33. F. Hensel, M. Moor, and B. Rieck, Front. Artif. Intell. 4, 681108 (2021).
  34. O. Bobrowski and P. Skraba, Sci. Rep. 13, 12274 (2023).
  35. O. Bobrowski and P. Skraba, arXiv:2406.05553.
  36. C. Maria, J.-D. Boissonnat, M. Glisse, and M. Yvinec, in Mathematical Software – ICMS 2014, edited by H. Hong and C. Yap (Springer, Berlin, 2014), pp. 167–174.
  37. D. Cohen-Steiner, H. Edelsbrunner, and J. Harer, Discrete Comput. Geom. 37, 103 (2007).
  38. D. Cohen-Steiner, H. Edelsbrunner, J. Harer, and Y. Mileyko, Found. Comput. Math. 10, 127 (2010).
  39. Y. Hiraoka, T. Shirai, and K. D. Trinh, Ann. Appl. Probab. 28, 2740 (2018).
  40. D. Spitz and A. Wienhard, arXiv:2012.05751.
  41. J. S. Moreland, J. E. Bernhard, and S. A. Bass, Phys. Rev. C 92, 011901 (2015).
  42. G. Nijs and W. van der Schee, arXiv:2304.06191.
  43. J. Weil et al., Phys. Rev. C 94, 054905 (2016).
  44. D. Oliinychenko, V. Steinberg, J. Weil, M. Kretz, J. Staudenmaier, S. Ryu, A. Schäfer, J. Rothermel, J. Mohs, F. Li, H. E. (Petersen), L. Pang, D. Mitrovic, A. Goldschmidt, L. Geiger, J.-B. Rose, J. Hammelmann, and L. Prinz, Smash-transport/smash: smash-1.8, Zenodo (2020), 10.5281/zenodo.3742965.
  45. G. Giacalone, G. Nijs, and W. van der Schee, Phys. Rev. Lett. 131, 202302 (2023).
  46. G. Nijs and W. van der Schee, Phys. Rev. C 106, 044903 (2022).
  47. https://sites.google.com/view/govertnijs/trajectum.
  48. A. Hatcher, Algebraic Topology (Cambridge University Press, Cambridge, 2002).
  49. J. R. Munkres, Elements of Algebraic Topology (CRC Press, Boca Raton, 2018).
  50. H. Edelsbrunner, D. Letscher, and A. Zomorodian, in Proceedings of the 41st Annual Symposium on Foundations of Computer Science (IEEE, Piscataway, NJ, 2000), pp. 454–463.
  51. A. Zomorodian and G. Carlsson, in Proceedings of the 20th Annual Symposium on Computational Geometry, SCG '04 (Association for Computing Machinery, New York, NY 2004), pp. 347–356.
  52. J. S. Moreland, J. E. Bernhard, and S. A. Bass, Phys. Rev. C 101, 024911 (2020).
  53. J. E. Bernhard, J. S. Moreland, S. A. Bass, J. Liu, and U. Heinz, Phys. Rev. C 94, 024907 (2016).
  54. T. Sjöstrand, S. Mrenna, and P. Z. Skands, Comput. Phys. Commun. 178, 852 (2008).

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Phys. Rev. C 112, 054909– Published 25 November, 2025
  • Received 2 September 2025
  • Accepted 8 October 2025
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