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Thermodynamical string fragmentation and string density effects in jets

Róbert Vértesi

Antonio Ortiz ^*

HUN-REN Wigner Research Centre for Physics DF13841 Konkoly-Thege Miklós út 29-33, 1121 Budapest, Hungary

Instituto de Ciencias Nucleares, UNAM Circuito exterior s/n Ciudad Universitaria, 04510 Mexico City, Mexico

^*Contact author: antonio.ortiz@nucleares.unam.mx

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Phys. Rev. D 112, 036009 – Published 15 August, 2025

DOI: https://doi.org/10.1103/tysz-8rh9

Abstract

It has been proposed to search for thermal and collective properties arising from parton-fragmentation processes by examining high jet charged-constituent multiplicities ( $N_{j, ch}$ ) in proton-proton (pp) collisions. This proposal was initially tested using the pythia 8event generator with the Monash tune, which incorporates multiparton interactions (MPI) and the MPI-based color reconnection (CR) model. These studies did not reveal any conclusive evidence for the presence of radial flow. In this paper, we expand upon the proposed Monte Carlo study by eliminating selection biases associated with triggering on charged particle multiplicities. Furthermore, MPI are disabled to focus exclusively on jet fragments. We analyze pp collisions at $\sqrt{s} = 13 TeV$ simulated with pythia 8, exploring different implementations of the generator: thermodynamical string fragmentation and the standard Lund fragmentation model. The impact of color-string junctions was also explored. Surprisingly, the thermodynamical string fragmentation together with the close-packing of strings mechanism predicts a hint of baryon enhancement in jets. Additionally, the light-flavor baryon-to-meson ratios as a function of $j_{T}$ exhibit similarities across all pythia 8 implementations, and hint at radial flow-like effects. In contrast, the ratio of heavy-flavor hadrons ( $Λ_{c}^{+} / D^{0}$ ) at low $j_{T}$ as a function of $N_{j, ch}$ shows a trend similar to that observed as a function of charged-particle multiplicity in minimum-bias data, suggesting that color-string junctions may play a crucial role in heavy baryon production in jets. The same mechanism also predicts a $j_{T}$ -integrated $Λ_{c}^{+} / D^{0}$ ratio that increases with increasing $N_{j, ch}$ . Interestingly, for the lowest $N_{j, ch}$ value, such a ratio is consistent with the $e^{+} e^{-}$ limit, suggesting that jet multiplicity is a potential way to explore more dilute systems covering the multiplicity gap between $e^{+} e^{-}$ and pp collisions.

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References (37)

W. Busza, K. Rajagopal, and W. van der Schee, Heavy ion collisions: The big picture, and the big questions, Annu. Rev. Nucl. Part. Sci. 68, 339 (2018).
R. Bala, I. Bautista, J. Bielcikova, and A. Ortiz, Heavy-ion physics at the LHC: Review of Run I results, Int. J. Mod. Phys. E 25, 1642006 (2016).
S. Acharya et al. (ALICE Collaboration), The ALICE experiment—A journey through QCD, Eur. Phys. J. C 84, 813 (2024).
S. Acharya et al. (ALICE Collaboration), Future high-energy pp programme with ALICE, ALICE-PUBLIC-2020-005, 2020.
S. Acharya et al. (ALICE Collaboration), Study of charged particle production at high $p_{T}$ using event topology in pp, p–Pb and Pb–Pb collisions at $\sqrt{s_{NN}} = 5.02 TeV$ , Phys. Lett. B 843, 137649 (2023).
S. Acharya et al. (ALICE Collaboration), Search for jet quenching effects in high-multiplicity pp collisions at $\sqrt{s} = 13 TeV$ via di-jet acoplanarity, J. High Energy Phys. 05 (2024) 229.
S. Acharya et al. (ALICE Collaboration), Emergence of long-range angular correlations in low-multiplicity proton-proton collisions, Phys. Rev. Lett. 132, 172302 (2024).
G. Aad et al. (ATLAS Collaboration), Two-particle azimuthal correlations in photonuclear ultraperipheral Pb–Pb collisions at $\sqrt{s_{NN}} = 5.02 TeV$ with ATLAS, Phys. Rev. C 104, 014903 (2021).
A. Hayrapetyan et al. (CMS Collaboration), Observation of enhanced long-range elliptic anisotropies inside high-multiplicity jets in pp collisions at $s = 13 TeV$ , Phys. Rev. Lett. 133, 142301 (2024).
C. Werthmann, V. E. Ambrus, and S. Schlichting, System size dependence of pre-equilibrium and applicability of hydrodynamics in heavy-ion collisions, Proc. Sci, HardProbes2023 (2024) 048 [arXiv:2307.08306].
D. d’Enterria, G. K. Eyyubova, V. L. Korotkikh, I. P. Lokhtin, S. V. Petrushanko, L. I. Sarycheva, and A. M. Snigirev, Estimates of hadron azimuthal anisotropy from multiparton interactions in proton-proton collisions at $\sqrt{s} = 14 TeV$ , Eur. Phys. J. C 66, 173 (2010).
C. Bierlich, G. Gustafson, L. Lönnblad, and A. Tarasov, Effects of overlapping strings in pp collisions, J. High Energy Phys. 03 (2015) 148.
C. Bierlich, G. Gustafson, L. Lönnblad, and H. Shah, The Angantyr model for heavy-ion collisions in pythia 8, J. High Energy Phys. 10 (2018) 134.
A. Ortiz, G. Bencedi, and F. Fan, Flattenicity as centrality estimator in p–Pb collisions simulated with pythia/Angantyr, J. Phys. G 51, 125003 (2024).
A. Baty, P. Gardner, and W. Li, Novel observables for exploring QCD collective evolution and quantum entanglement within individual jets, Phys. Rev. C 107, 064908 (2023).
A. Ortiz, P. Christiansen, E. Cuautle, I. Maldonado, and G. Paić, Color reconnection and flowlike patterns in pp collisions, Phys. Rev. Lett. 111, 042001 (2013).
N. Fischer and T. Sjöstrand, Thermodynamical string fragmentation, J. High Energy Phys. 01 (2017) 140.
F. Becattini, A thermodynamical model of hadron production in $e^{+}$ $e^{-}$ collisions, in Proceedings of the 25th International Symposium on Multiparticle Dynamics (World Scientific Publishing, Singapore, 1995), pp. 480–490.
T. Sjöstrand, S. Ask, J. R. Christiansen, R. Corke, N. Desai, P. Ilten, S. Mrenna, S. Prestel, C. O. Rasmussen, and P. Z. Skands, An introduction to pythia8.2, Comput. Phys. Commun. 191, 159 (2015).
B. Andersson, G. Gustafson, G. Ingelman, and T. Sjöstrand, Parton fragmentation and string dynamics, Phys. Rep. 97, 31 (1983).
P. Skands, S. Carrazza, and J. Rojo, Tuning pythia 8.1: The Monash 2013 tune, Eur. Phys. J. C 74, 3024 (2014).
J. R. Christiansen and P. Z. Skands, String formation beyond leading colour, J. High Energy Phys. 08 (2015) 003.
C. Bierlich, G. Gustafson, and L. Lönnblad, A shoving model for collectivity in hadronic collisions, arXiv:1612.05132.
S. Acharya et al. (ALICE Collaboration), Observation of a multiplicity dependence in the $p_{T}$ -differential charm baryon-to-meson ratios in proton-proton collisions at $\sqrt{s} = 13 TeV$ , Phys. Lett. B 829, 137065 (2022).
S. Acharya et al. (ALICE Collaboration), Charm production and fragmentation fractions at midrapidity in pp collisions at $\sqrt{s} = 13 TeV$ , J. High Energy Phys. 12 (2023) 086.
A. M. Sirunyan et al. (CMS Collaboration), Production of $Λ_{c}^{+}$ baryons in proton-proton and lead-lead collisions at $\sqrt{s_{NN}} = 5.02 TeV$ , Phys. Lett. B 803, 135328 (2020).
S. Acharya et al. (ALICE Collaboration), Production of light-flavor hadrons in pp collisions at $\sqrt{s} = 7$ and $\sqrt{s} = 13 TeV$ , Eur. Phys. J. C 81, 256 (2021).
S. Acharya et al. (ALICE Collaboration), Measurement of prompt $D^{0}$ , $Λ_{c}^{+}$ , and $Σ_{c}^{0, + +} (2455)$ production in proton–proton collisions at $\sqrt{s} = 13 TeV$ , Phys. Rev. Lett. 128, 012001 (2022).
M. Cacciari, G. P. Salam, and G. Soyez, The anti- $k_{T}$ jet clustering algorithm, J. High Energy Phys. 04 (2008) 063.
S. Acharya et al. (ALICE Collaboration), Multiplicity dependence of light-flavor hadron production in pp collisions at $\sqrt{s} = 7 TeV$ , Phys. Rev. C 99, 024906 (2019).
S. Acharya et al. (ALICE Collaboration), $Λ_{c}^{+}$ production in pp collisions at $\sqrt{s} = 7 TeV$ and in p–Pb collisions at $\sqrt{s_{NN}} = 5.02 TeV$ , J. High Energy Phys. 04 (2018) 108.
S. Acharya et al. (ALICE Collaboration), $Λ_{c}^{+}$ production and baryon-to-meson ratios in pp and p–Pb collisions at $\sqrt{s_{NN}} = 5.02 TeV$ at the LHC, Phys. Rev. Lett. 127, 202301 (2021).
R. Aaij et al. (LHCb Collaboration), Prompt $Λ_{c}^{+}$ production in p–Pb collisions at $\sqrt{s_{N N}} = 5.02 TeV$ , J. High Energy Phys. 02 (2019) 102.
Z. Varga and R. Vertesi, The role of the underlying event in the enhancement in high-energy pp collisions, J. Phys. G 49, 075005 (2022).
L. Gladilin, Fragmentation fractions of $c$ and $b$ quarks into charmed hadrons at LEP, Eur. Phys. J. C 75, 19 (2015).
C. Bierlich, G. Gustafson, L. Lönnblad, and H. Shah, The dynamic hadronization of charm quarks in heavy-ion collisions, Eur. Phys. J. C 84, 231 (2024).
J. Altmann and P. Skands, String junctions revisited, J. High Energy Phys. 07 (2024) 238.

Phys. Rev. D 112, 036009– Published 15 August, 2025

Vol. 112, Iss. 3 — 1 August 2025

Received 12 June 2025
Accepted 22 July 2025

DOI: https://doi.org/10.1103/tysz-8rh9

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

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Thermodynamical string fragmentation and string density effects in jets

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