Hai Wang ? Jin-Hui Chen

Abstract We study the production and angular correlation of charm hadrons in hot and dense matter produced in highenergy nuclear–nuclear collisions within a multiphase transport model (AMPT). By triggering additional charm–anticharm quark pair production in the AMPT, the model describes the D0 nuclear modification factor in the low and intermediate pT regions in Au + Au collisions at200 GeV reasonably well. Further exploration of the D0 pair azimuthal angular correlation for different centralities shows clear evolution from low-multiplicity to high-multiplicity events, which is associated with the number of charm quark interactions with medium partons during AMPT transport.

Keywords Heavy-ion collision · Heavy flavor · Nuclear modification factor · Two-particle correlations

1 Introduction

In high-energy nuclear collisions, heavy-flavor quarks are produced predominantly in the initial phase because of their large mass (mc/b＞＞ΛQCD). The modification of their production in transverse momentum (pT) due to energy loss and radial flow and in azimuth due to anisotropic flows is sensitive to the heavy quark dynamics in the hot and dense strongly interacting quark–gluon plasma(QGP) [1–3]. Recent experimental measurements of highpTD-meson production at RHIC and LHC energies show strong suppression of central heavy-ion collisions [4–6],suggesting significant energy loss by charm quarks inside the QGP medium.

Analysis of multiparticle angular correlations is a powerful tool for exploring the properties of the QGP and the underlying mechanism of particle production in hot quantum chromodynamic (QCD) matter [12–20]. Unlike light quarks and gluons,heavy quarks suppress small-angle gluon radiation, which results in a small radiated energy loss [21, 22]. In hadron–hadron collisions, which are dominated by the initial production effect,a distinct feature appears in the azimuthal angular correlation of DˉD, with clear suppression on the near side and enhancement on the away side [23]. In nuclear–nuclear collisions, the angular correlation may be affected by the interactions of charm quarks in the QGP, which is argued to be a signature of a strongly coupled QGP owing to the collective partonic wind effect [23]. The evolution of the azimuthal angular correlation of charm hadron pairs in the QGP has not been carefully studied in a realistic transport calculation, and that lack motivates the current work.

2 Charm quark production in AMPT model

The AMPT model is a hybrid model [24]. It has been extensively used for studying the bulk medium using the microscopic dynamical processes of evolving systems, as reported in recent papers [25–27].In this model,the initial conditions are taken from the HIJING event generator [28, 29]. In the default AMPT model, the partonic matter consists only of minijet partons from HIJING. It is different in the string melting scenario, in which the hadrons generated by HIJING are dissociated according to their valence quark structures, and the resulting partonic matter is thus much denser. The evolution of the partonic matter is simulated using the parton cascade model ZPC [30], and the partons are converted to hadrons after they stop scattering. In the default AMPT model, the partons are first combined with their parent strings,which then fragment using the Lund string fragmentation model [31].In the string melting AMPT model, the nearest partons are converted into hadrons via the coalescence model [24]. In both versions of the AMPT model, the scattering of hadrons is described by a relativistic transport model [32].

with j ≥1. The HIJING model has two components with two key parameters, the minijet transverse momentum cutoff p0and the soft interaction cross section σsoft. σsoftcontrols the elastic, inelastic, and total cross sections. The production probability for soft interactions without hard processes is

The elastic, inelastic, and total cross sections of binary collisions are thus calculated in the model [28, 29].

3 Results and discussion

3.1 D0 meson pT distribution and RAA in AMPT model

Fig.1 (Color online) D0 meson pT spectra in central Au + Au collisions at =200 GeV. Open symbols represent results of AMPT model calculation for different configurations; solid symbols are experimental data [4]

where Ncollrepresents the number of binary collisions in the reaction.

Fig.2 (Color online)D0 meson RAA in central Au+Au collisions at=200 GeV. Dashed lines represent results of AMPT model calculation for different configurations. Data points are experimental measurements [4]

3.2 D0 meson azimuthal angular correlation

We use the two-particle azimuthal angular correlation function to study the charm quark dynamics evolution in the hot and dense medium using the AMPT model, in which multi-parton scattering may have a significant effect on the correlation function C （Δ φ）. In our study, C （ Δφ） is built as follows:

where Δη is the relative pseudorapidity, and Δφ is the relative azimuthal angle between charm hadron pairs. The signal pair distribution, S（Δη，Δφ）, represents the yield of charm hadron pairs that come from the same event:

In addition,B（Δη，Δφ）is built from the mixed event charm hadron pairs distribution:

which is flat in our calculation.

The one-dimensional correlation function along Δφ can be constructed from the C （Δη，Δφ） distribution by integrating over Δη:

Fig.3 D0 meson azimuthal angular correlations vs. centrality in Au + Au collisions at=200 GeV for default or string melting AMPT models and various ratios of the two

To eliminate the trigger effect in the initial stage and focus on the multi-parton scattering effect, we define the ratio of the correlation functions of the default and string melting AMPT models:

The results are shown as open triangles in Fig.3. They show a convex distribution versus Δφ owing to the multiparton scattering interaction in the string melting AMPT model. The result for peripheral collisions is far from the flat distribution among the three centralities, probably because charm quarks usually lose the most energy in the first collision [11].

4 Summary and outlook

AcknowledgementsWe are grateful to Dr. Chen Zhong, who maintains the high-performance computer center at which the calculations for the current study were performed. We thank Dr. Song Zhang for discussions of the correlation function analysis.

Author contributionsAll authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Hai Wang and Jin-Hui Chen.The first draft of the manuscript was written by Hai Wang, and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

book=16,ebook=18

15. J.Adam, L. Adamczyk,J. Adams et al.,Azimuthal harmonics in small and large collision systems at rhic top energies.Phys.Rev.Lett. 122, 172301 (2019). https://doi.org/10.1103/PhysRevLett.122.172301

17. A. Bzdak, G.L. Ma, Elliptic and triangular flow in p-pb and peripheral pb–pb collisions from parton scatterings. Phys. Rev.Lett. 113, 252301 (2014). https://doi.org/10.1103/PhysRevLett.113.252301

18. J. Chen, D. Keane, Y.G. Ma et al., Antinuclei in heavy-ion collisions. Phys. Rep. 760, 1–39 (2018). https://doi.org/10.1016/j.physrep.2018.07.002

19. L.Y. Zhang, J.H. Chen, Z.W. Lin et al., Two-particle angular correlations in heavy ion collisions from a multiphase transport model. Phys. Rev. C 99, 054904 (2019). https://doi.org/10.1103/PhysRevC.99.054904

20. L.Y. Zhang, J.H. Chen, Z.W. Lin et al., Two-particle angular correlations in pp and p-Pb collisions at energies available at the cern large hadron collider from a multiphase transport model.Phys. Rev. C 98, 034912 (2018). https://doi.org/10.1103/Phys RevC.98.034912

21. N. Armesto, C.A. Salgado, U.A. Wiedemann, Medium induced gluon radiation off massive quarks fills the dead cone.Phys.Rev.D 69, 114003 (2004). https://doi.org/10.1103/PhysRevD.69.114003

22. M.Djordjevic,M.Gyulassy,Heavy quark radiative energy loss in QCD matter.Nucl.Phys.A 733,265–298(2004).https://doi.org/10.1016/j.nuclphysa.2003.12.020

23. X. Zhu, N. Xu, P. Zhuang, Effect of partonic wind on charm quark correlations in high-energy nuclear collisions. Phys. Rev.Lett. 100, 152301 (2008). https://doi.org/10.1103/PhysRevLett.100.152301

24. Z.W.Lin,C.M.Ko,B.A.Li et al.,Multiphase transport model for relativistic heavy ion collisions.Phys.Rev.C 72,064901(2005).https://doi.org/10.1103/PhysRevC.72.064901

25. T.Shao,J.Chen,C.M.Ko et al.,Enhanced production of strange baryons in high-energy nuclear collisions from a multiphase transport model. Phys. Rev. C 102, 014906 (2020). https://doi.org/10.1103/PhysRevC.102.014906

26. S.Zhang,Y.G.Ma,G.L.Ma et al.,Collision system size scan of collective flows in relativistic heavy-ion collisions.Phys.Letts.B 804, 135366 (2020). https://doi.org/10.1016/j.physletb.2020.135366

27. C. Zhang, L. Zheng, F. Liu et al., Update of a multiphase transport model with modern parton distribution functions and nuclear shadowing. Phys. Rev. C 99, 064906 (2019). https://doi.org/10.1103/PhysRevC.99.064906

28. X.N. Wang, M. Gyulassy, Hijing: a monte carlo model for multiple jet production in pp, pA, and AA collisions. Phys. Rev.D 44, 3501 (1991). https://doi.org/10.1103/PhysRevD.44.3501

29. M. Gyulassy, X. Wang, Hijing 1.0: a Monte Carlo program for parton and particle production in high-energy hadronic and nuclear collisions.Comput.Phys.Commun.83,307–331(1994).https://doi.org/10.1016/0010-4655(94)90057-4

30. B. Zhang, Zpc 1.0.1: a parton cascade for ultrarelativistic heavy ion collisions. Comput. Phys. Commun. 109, 193–206 (1998).https://doi.org/10.1016/S0010-4655(98)00010-1

31. T. Sjostrand, High-energy-physics event generation with pythia 5.7 and jetset 7.4. Comput. Phys. Commun. 82, 74–89 (1994).https://doi.org/10.1016/0010-4655(94)90132-5

32. B.A. Li, C.M. Ko, Formation of superdense hadronic matter in high energy heavy-ion collisions. Phys. Rev. C 52, 2037–2063(1995). https://doi.org/10.1103/PhysRevC.52.2037

33. D.W.Duke,J.F.Owens,Q2-dependent parametrizations of parton distribution functions.Phys.Rev.D 30,49–54(1984).https://doi.org/10.1103/PhysRevD.30.49

34. L. Zheng, C. Zhang, S. Shi et al., Improvement of heavy flavor productions in a multi-phase transport model updated with modern npdfs. Phys. Rev. C 101, 034905 (2020). https://doi.org/10.1103/PhysRevC.101.034905

35. T.Song,H.Berrehrah,D.Cabrera et al.,Charm production in Pb+ Pb collisions at energies available at the cern large hadron collider.Phys.Rev.C 93,034906(2016).https://doi.org/10.1103/PhysRevC.93.034906