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System-size dependence of the $D^{0} − D_{s}^{+}$ flow splitting from early $D_{s}^{+}$ formation at $\sqrt{s_{N N}} = 5.36$ TeV

Hui Du , Xiao-Wei Hao, and Wei Dai ^*

Jiaxing Zhao

Ben-Wei Zhang

Enke Wang

School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, China

Helmholtz Research Academy Hesse for FAIR (HFHF), GSI Helmholtz Center for Heavy Ion Physics, Campus Frankfurt, 60438 Frankfurt, Germany and Institut für Theoretische Physik, Johann Wolfgang Goethe-Universität, Max-von-Laue-Straße 1, D-60438 Frankfurt am Main, Germany

Key Laboratory of Quark & Lepton Physics (MOE) and Institute of Particle Physics, Central China Normal University, Wuhan 430079, China

State Key Laboratory of Nuclear Physics and Technology, Institute of Quantum Matter, South China Normal University, Guangzhou 510006, China and Guangdong Basic Research Center of Excellence for Structure and Fundamental Interactions of Matter, Guangdong Provincial Key Laboratory of Nuclear Science, Guangzhou 510006, China

^*Contact author: weidai@cug.edu.cn

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Phys. Rev. C 114, 024907 – Published 17 August, 2026

DOI: https://doi.org/10.1103/94d3-nfy8

Abstract

We investigate the elliptic-flow splitting between prompt $D^{0}$ and $D_{s}^{+}$ mesons within a heavy-quark transport framework with sequential hadronization, in which $D_{s}^{+}$ forms at $1.2 T_{c}$ and $D^{0}$ at $T_{c}$ . We present model calculations for the $p_{T}$ -differential $v_{2}$ and predictions for the $D_{s}^{+} / D^{0}$ yield ratio in O-O $0 - 20 %$ collisions at $\sqrt{s_{N N}} = 5.36$ TeV, where preliminary ALICE data are available. The sequential scenario reproduces the observed $v_{2} (D^{0}) > v_{2} (D_{s}^{+})$ ordering and predicts an enhanced $D_{s}^{+} / D^{0}$ ratio at low $p_{T}$ , whereas a simultaneous baseline yields the opposite ordering. Decomposing the hadronic splitting into its partonic components, we show that the $v_{2}$ ordering is driven by the late-stage flow accumulated by $D^{0}$ -parent charm quarks during the $1.2 T_{c} \to T_{c}$ interval, with hadronic rescattering essential to preserve the signal in small systems. A systematic scan across nine collision configurations spanning O-O and Pb-Pb centralities reveals a universal linear scaling between the hadronic splitting and the partonic flow increment accumulated during this window. This establishes the $D^{0} - D_{s}^{+}$ flow splitting as a hadronization chronometer of the QGP at $\sqrt{s_{N N}} = 5.36$ TeV.

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References (64)

A. Andronic, P. Braun-Munzinger, M. K. Köhler, A. Mazeliauskas, K. Redlich, J. Stachel, and V. Vislavicius, The multiple-charm hierarchy in the statistical hadronization model, J. High Energy Phys. 07 (2021) 035.
J. Adam et al. (ALICE Collaboration), Measurement of $d_{s}^{+}$ production and nuclear modification factor in Pb-Pb collisions at $\sqrt{s_{NN}} = 2.76$ TeV, J. High Energy Phys. 03 (2016) 082.
S. Acharya et al. (ALICE Collaboration), Measurement of $d^{0}, d^{+}, d^{* +}$ and $d_{s}^{+}$ production in Pb-Pb collisions at $\sqrt{s_{NN}} = 5.02$ TeV, J. High Energy Phys. 10 (2018) 174.
V. Minissale, S. Plumari, Y. Sun, and V. Greco, Multi-charmed and singled charmed hadrons from coalescence: Yields and ratios in different collision systems at LHC, Eur. Phys. J. C 84, 228 (2024).
Y.-F. Liu, W.-J. Xing, X.-Y. Wu, S. Cao, G.-Y. Qin, and S.-Q. Li, Charmed hadron chemistry and flow in heavy and light ion collisions at the LHC, arXiv:2402.03622.
D. Ali Hassan Abdallah et al. (ALICE Collaboration), Evidence of different $Λ_{c}$ -baryon and D-meson elliptic flow in Pb–Pb collisions at $\sqrt{s_{N} N} = 5.36$ TeV with ALICE at the LHC, arXiv:2603.18966.
R. Katz, Caio A. G. Prado, J. Noronha-Hostler, and Alexandre A. P. Suaide, System-size scan of $D$ meson $R_{A A}$ and $v_{n}$ using PbPb, XeXe, ArAr, and OO collisions at energies available at the CERN Large Hadron Collider, Phys. Rev. C 102, 041901(R) (2020).
S.-Q. Li, W.-J. Xing, X.-Y. Wu, S. Cao, and G.-Y. Qin, Scaling behaviors of heavy flavor meson suppression and flow in different nuclear collision systems at the LHC, Eur. Phys. J. C 81, 1035 (2021).
J. Zhao, J. Aichelin, P. B. Gossiaux, and K. Werner, System-size dependence of energy loss and correlations of heavy mesons at energies available at the CERN Large Hadron Collider, Phys. Rev. C 111, 014907 (2025).
R. J. Fries, B. Muller, C. Nonaka, and S. A. Bass, Hadron production in heavy ion collisions: Fragmentation and recombination from a dense parton phase, Phys. Rev. C 68, 044902 (2003).
V. Greco, C. M. Ko, and P. Levai, Parton coalescence at RHIC, Phys. Rev. C 68, 034904 (2003).
M. He and R. Rapp, Hadronization and charm-hadron ratios in heavy-ion collisions, Phys. Rev. Lett. 124, 042301 (2020).
M. He, H. van Hees, and R. Rapp, Heavy-quark diffusion in the quark–gluon plasma, Prog. Part. Nucl. Phys. 130, 104020 (2023).
V. Greco, H. van Hees, and R. Rapp, Phase-space coalescence for heavy and light quarks at RHIC, Eur. Phys. J. Spec. Top. 155, 45 (2008).
S. Cao, G.-Y. Qin, and S. A. Bass, Energy loss, hadronization and hadronic interactions of heavy flavors in relativistic heavy-ion collisions, Phys. Rev. C 92, 024907 (2015).
S. Cao, K.-J. Sun, S.-Q. Li, S. Y. F. Liu, W.-J. Xing, G.-Y. Qin, and C. M. Ko, Charmed hadron chemistry in relativistic heavy-ion collisions, Phys. Lett. B 807, 135561 (2020).
P. B. Gossiaux, R. Bierkandt, and J. Aichelin, Tomography of a quark gluon plasma at RHIC and LHC energies, Phys. Rev. C 79, 044906 (2009).
M. He, R. J. Fries, and R. Rapp, $D_{s}$ -meson as quantitative probe of diffusion and hadronization in nuclear collisions, Phys. Rev. Lett. 110, 112301 (2013).
A. Beraudo, A. De Pace, M. Monteno, M. Nardi, and F. Prino, Heavy flavors in heavy-ion collisions: Quenching, flow and correlations, Eur. Phys. J. C 75, 121 (2015).
J. Zhao, J. Aichelin, P. B. Gossiaux, V. Ozvenchuk, and K. Werner, Heavy-flavor hadron production in relativistic heavy ion collisions at energies available at BNL RHIC and at the CERN LHC in the EPOS4HQ framework, Phys. Rev. C 110, 024909 (2024).
T. Song, H. Berrehrah, D. Cabrera, J. M. Torres-Rincon, L. Tolos, W. Cassing, and E. Bratkovskaya, Tomography of the quark-gluon-plasma by charm quarks, Phys. Rev. C 92, 014910 (2015).
S. Plumari, V. Minissale, S. K. Das, G. Coci, and V. Greco, Charmed hadrons from coalescence plus fragmentation in relativistic nucleus-nucleus collisions at RHIC and LHC, Eur. Phys. J. C 78, 348 (2018).
S. K. Das, J. M. Torres-Rincon, L. Tolos, V. Minissale, F. Scardina, and V. Greco, Propagation of heavy baryons in heavy-ion collisions, Phys. Rev. D 94, 114039 (2016).
V. Minissale, S. Plumari, and V. Greco, Charm hadrons in pp collisions at LHC energy within a coalescence plus fragmentation approach, Phys. Lett. B 821, 136622 (2021).
S. Shi, J. Zhao, and P. Zhuang, Heavy flavor dissociation in framework of multi-body Dirac equations, Chin. Phys. C 44, 084101 (2020).
J. Zhao, S. Shi, N. Xu, and P. Zhuang, Sequential hadronization in heavy ion collisions, Nucl. Phys. A 1005, 121898 (2021).
S. Shi, X. Guo, and P. Zhuang, Flavor dependence of meson melting temperature in relativistic potential model, Phys. Rev. D 88, 014021 (2013).
Z.-X. Xu, W. Dai, B.-W. Zhang, J. Zhao, and P. Zhuang, D-meson production via sequential hadronization in high-energy nuclear collisions, Phys. Rev. Lett. 136, 232301 (2026).
S. Pucillo (ALICE Collaboration), Recent results on strangeness enhancement in small collision systems with ALICE, arXiv:2504.02527.
G. Giacalone et al., Exploiting ${}^{20}{Ne}$ isotopes for precision characterizations of collectivity in small systems, Phys. Rev. Lett. 135, 012302 (2025).
ALICE Collaboration (unpublished).
J. S. Moreland, J. E. Bernhard, and S. A. Bass, Alternative ansatz to wounded nucleon and binary collision scaling in high-energy nuclear collisions, Phys. Rev. C 92, 011901(R) (2015).
L.-G. Pang, H. Petersen, and X.-N. Wang, Pseudorapidity distribution and decorrelation of anisotropic flow within the open-computing-language implementation CLVisc hydrodynamics, Phys. Rev. C 97, 064918 (2018).
X.-Y. Wu, G.-Y. Qin, L.-G. Pang, and X.-N. Wang, (3+1)-D viscous hydrodynamics at finite net baryon density: Identified particle spectra, anisotropic flows, and flow fluctuations across energies relevant to the beam-energy scan at RHIC, Phys. Rev. C 105, 034909 (2022).
A. Bazavov et al. (HotQCD Collaboration), Equation of state in(2+1)-flavor QCD, Phys. Rev. D 90, 094503 (2014).
J. E. Bernhard, J. S. Moreland, S. A. Bass, J. Liu, and U. Heinz, Applying Bayesian parameter estimation to relativistic heavy-ion collisions: Simultaneous characterization of the initial state and quark-gluon plasma medium, Phys. Rev. C 94, 024907 (2016).
S. Ryu, J. F. Paquet, C. Shen, G. S. Denicol, B. Schenke, S. Jeon, and C. Gale, Importance of the bulk viscosity of QCD in ultrarelativistic heavy-ion collisions, Phys. Rev. Lett. 115, 132301 (2015).
S. Cao, G.-Y. Qin, and S. A. Bass, Heavy-quark dynamics and hadronization in ultrarelativistic heavy-ion collisions: Collisional versus radiative energy loss, Phys. Rev. C 88, 044907 (2013).
W. Dai, S. Wang, S.-L. Zhang, B.-W. Zhang, and E. Wang, Transverse momentum balance and angular distribution of $b \bar{b}$ dijets in Pb+Pb collisions, Chin. Phys. C 44, 104105 (2020).
M. Cacciari, S. Frixione, N. Houdeau, M. L. Mangano, P. Nason, and G. Ridolfi, Theoretical predictions for charm and bottom production at the LHC, J. High Energy Phys. 10 (2012) 137.
K. J. Eskola, P. Paakkinen, H. Paukkunen, and C. A. Salgado, EPPS21: A global QCD analysis of nuclear PDFs, Eur. Phys. J. C 82, 413 (2022).
S. Wang, W. Dai, B.-W. Zhang, and E. Wang, Diffusion of charm quarks in jets in high-energy heavy-ion collisions, Eur. Phys. J. C 79, 789 (2019).
S. Wang, W. Dai, B.-W. Zhang, and E. Wang, $Z^{0}$ boson associated b-jet production in high-energy nuclear collisions*, Chin. Phys. C 47, 054102 (2023).
S. Wang, W. Dai, B.-W. Zhang, and E. Wang, Radial profile of bottom quarks in jets in high-energy nuclear collisions, Chin. Phys. C 45, 064105 (2021).
X.-F Xue, Z.-X. Xu, W. Dai, J. Zhao, and B.-W. Zhang, Bayesian inference of heavy-quark dissipation and jet transport parameters from D-meson observables in heavy-ion collisions at energies available at the CERN Large Hadron Collider, Phys. Rev. C 113, 054902 (2026).
R. Kubo, The fluctuation-dissipation theorem, Rep. Prog. Phys. 29, 255 (1966).
L. Altenkort, O. Kaczmarek, R. Larsen, S. Mukherjee, P. Petreczky, H.-T. Shu, and S. Stendebach (HotQCD Collaboration), Heavy quark diffusion from 2+1 flavor lattice QCD with 320 MeV pion mass, Phys. Rev. Lett. 130, 231902 (2023).
P. Petreczky, Quarkonium in hot medium, J. Phys. G: Nucl. Part. Phys. 37, 094009 (2010).
X. Guo and X.-N. Wang, Multiple scattering, parton energy loss and modified fragmentation functions in deeply inelastic $eA$ scattering, Phys. Rev. Lett. 85, 3591 (2000).
B.-W. Zhang, E. Wang, and X.-N. Wang, Heavy quark energy loss in nuclear medium, Phys. Rev. Lett. 93, 072301 (2004).
B.-W. Zhang, E.-k. Wang, and X.-N. Wang, Multiple parton scattering in nuclei: Heavy quark energy loss and modified fragmentation functions, Nucl. Phys. A 757, 493 (2005).
A. Majumder, Hard collinear gluon radiation and multiple scattering in a medium, Phys. Rev. D 85, 014023 (2012).
W.-T. Deng and X.-N. Wang, Multiple parton scattering in nuclei: Modified DGLAP evolution for fragmentation functions, Phys. Rev. C 81, 024902 (2010).
M. Xie, S.-Y. Wei, G.-Y. Qin, and H.-Z. Zhang, Extracting jet transport coefficient via single hadron and dihadron productions in high-energy heavy-ion collisions, Eur. Phys. J. C 79, 589 (2019).
M. He and R. Rapp, Charm-baryon production in proton-proton collisions, Phys. Lett. B 795, 117 (2019).
J. M. Torres-Rincon, G. Montaña, À. Ramos, and L. Tolos, In-medium kinetic theory of D mesons and heavy-flavor transport coefficients, Phys. Rev. C 105, 025203 (2022).
R. J. Fries, V. Greco, and P. Sorensen, Coalescence models for hadron formation from quark gluon plasma, Annu. Rev. Nucl. Part. Sci. 58, 177 (2008).
J. Zhao, S. Shi, N. Xu, and P. Zhuang, Sequential coalescence with charm conservation in high energy nuclear collisions, arXiv:1805.10858.
J. Zhao et al., Hadronization of heavy quarks, Phys. Rev. C 109, 054912 (2024).
J. Zhao, J. Aichelin, P. B. Gossiaux, and K. Werner, Correlations between heavy mesons and the creation of the charmonia, bottomonia, and $B_{c}$ mesons in high energy $pp$ collisions, Phys. Rev. D 113, 116022 (2026).
C. Peterson, D. Schlatter, I. Schmitt, and P. M. Zerwas, Scaling violations in inclusive $e^{+} e^{-}$ annihilation spectra, Phys. Rev. D 27, 105 (1983).
M. Lisovyi, A. Verbytskyi, and O. Zenaiev, Combined analysis of charm-quark fragmentation-fraction measurements, Eur. Phys. J. C 76, 397 (2016).
R. Bellwied, S. Borsanyi, Z. Fodor, S. D. Katz, and C. Ratti, Is there a flavor hierarchy in the deconfinement transition of QCD?, Phys. Rev. Lett. 111, 202302 (2013).
A. Beraudo, A. De Pace, M. Monteno, M. Nardi, and F. Prino, Development of heavy-flavour flow-harmonics in high-energy nuclear collisions, J. High Energy Phys. 02 (2018) 043.

Phys. Rev. C 114, 024907– Published 17 August, 2026

Vol. 114, Iss. 2 — August 2026

Received 25 May 2026
Accepted 20 July 2026

DOI: https://doi.org/10.1103/94d3-nfy8

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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System-size dependence of the $D^{0} − D_{s}^{+}$ flow splitting from early $D_{s}^{+}$ formation at $\sqrt{s_{N N}} = 5.36$ TeV

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System-size dependence of the D0−Ds+ flow splitting from early Ds+ formation at sNN=5.36 TeV

Abstract

Physics Subject Headings (PhySH)

Article Text

References (64)

System-size dependence of the $D^{0} − D_{s}^{+}$ flow splitting from early $D_{s}^{+}$ formation at $\sqrt{s_{N N}} = 5.36$ TeV