Anisotropy flows in Pb–Pb collisions at LHC energies from parton scatterings with heavy quark trigger

Anisotropy flows in Pb–Pb collisions at LHC energies from parton scatterings with heavy quark trigger 1 first-author 1 corresp chenjinhui@fudan.edu.cn chenjinhui@fudan.edu.cn chenjinhui@fudan.edu.cn https://orcid.org/0000-0002-7272-7968 Key Laboratory of Nuclear Physics and Ion-beam Application (MOE), Institute of Modern Physics, Fudan University, Shanghai 200433, China Key Laboratory of Nuclear Physics and Ion-beam Application (MOE), Institute of Modern Physics, Fudan University, Shanghai 200433, China By implementing an additional heavy quark–antiquark pair production trigger in a multiphase transport (AMPT) model, we study the effect on anisotropy flows of identified particles with a focus on charged particles and quarkonium ( J /Ψ and <math id="M1"><mi>ϒ</mi></math> ). A systematic increase in the collision rate for active partons in the AMPT model with such an implementation has been observed. It leads to a slight increase of identified particles anisotropy flows as a function of transverse momentum ( p T ) and rapidity, and gives a better description of the experimental data of elliptic flow toward larger p T . Our approach provides an efficient way to study the heavy quark dynamics in the AMPT model at LHC energies. Heavy-ion collision Quark-Gluon Plasma Quarkonium Collective flow Introduction 1 In nuclear–nucleus collisions at the Relativistic Heavy Ion Collider (RHIC) and Large Hadron Collider (LHC), a system of color deconfinement, known as Quark-Gluon Plasma (QGP), is expected to be produced [ 1 1 , 2 2 ]. QGP is an almost perfect fluid in the sense that its shear viscosity to entropy density ratio is close to the minimum value [ 3 3 , 4 4 ]. Because the volume and lifetime of the QGP may be much larger and longer than those given by the confinement scale ( <math id="M2"><mrow><mo>≈</mo><mn>1</mn><mo>/</mo><msub><mi>Λ</mi><mrow><mtext>Q</mtext><mi>C</mi><mi>D</mi></mrow></msub></mrow></math> ), it is expected that the collective flow of partons should arise and have observable consequences that provide information on the dynamics in the QGP [ 5 5 ]. Studies on the anisotropic flow of particle production have contributed significantly to the characterization of the system created at RHIC and LHC [ 5 5 ]. Using a general Fourier series decomposition of the azimuthal distribution of the emitted particles, <math display="block" id="M3"><mrow><mfrac><mrow><mtext>d</mtext><mi>N</mi></mrow><mrow><mtext>d</mtext><mi>φ</mi></mrow></mfrac><mo>∝</mo><mn>1</mn><mo>+</mo><mn>2</mn><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mi>∞</mi></munderover></mstyle><msub><mi>v</mi><mi>n</mi></msub><mi>cos</mi><mo stretchy="false">[</mo><mi>n</mi><mo stretchy="false">(</mo><mi>φ</mi><mo>−</mo><msub><mi>Ψ</mi><mi>n</mi></msub><mo stretchy="false">)</mo><mo stretchy="false">]</mo><mn>,</mn></mrow></math> anisotropic flow is quantified using coefficients v n and the corresponding symmetry planes Ψ n [ 6 6 ], where φ represents the azimuthal angle of the emitted particles in the momentum space. Systematic measurements of the correlations and fluctuations of v n coefficients and Ψ n have been performed in Refs. [ 7 7 - 13 13 7-13 ]. Comprehensive comparisons with theoretical model calculations provide critical information on the event average initial density distribution in the nuclear overlap region, as well as its connection to QGP dynamics [ 14 14 - 19 19 14-19 ]. Charm and bottom quarks are important probes for the QGP. They were mainly produced in the initial state of the hard-scattering process prior to QGP formation and survived throughout the evolution stage of the QGP. Quarkonia are bound states of heavy flavor quark–antiquark pairs, which are believed to be suppressed because of the color screening effect in the deconfined interior of the interaction region [ 20 20 ]. They offer a complementary way to study the interaction of the heavy flavor with the medium and, thus, independently shed light on the properties of QGP [ 21 21 - 23 23 21-23 ]. Dozens of measurements in this direction have been carried out, and rich physical information has been delivered [ 24 24 - 31 31 24-31 ], with a clear future direction [ 21 21 ]. To study the characteristics of the QGP and its evolution toward chemical and thermal equilibrium, it is necessary to derive transport equations for quarks and gluons when they are in equilibrium and pre-equilibrium [ 32 32 ]. There have been several studies on deriving relativistic abelian and non-abelian transport and constraint equations for the relativistic gauge covariant Wigner operator for color particles interacting via SU( N ) gauge fields. This indicates that viscous hydrodynamic models can describe the transverse momentum spectra of light-flavor hadrons and distribution in the azimuthal angle for low p T [ 33 33 , 16 16 ]. On the other hand, transport models have been applied to study the evolution of QGP medium [ 34 34 ]. Owing to its relatively small cross section, a large event sample is required to study charm or even bottom quark transport in the QGP within hydrodynamics calculations or transport model simulations. In this study, we implement an additional heavy quark–antiquark pair production trigger in a multiphase transport (AMPT) model to study the dynamics of charm and bottom quarks in a dense light quark soup. This significantly improves the charm or bottom quark simulation efficiency, and it will be closer to the data at LHC energies because of a large charm quark production cross section [ 21 21 ]. Transport Models of Heavy Flavor 1 We employed the AMPT model with the string melting version (v2.265) to simulate the collective motion of heavy quarkonium in Pb–Pb collisions at LHC energies. The AMPT model is a hybrid model consisting of fluctuating initial conditions, parton elastic scattering, quark hadronization, and hadronic interaction [ 34 34 ]. It has been used extensively to describe the dynamics of heavy-ion collisions at RHIC and LHC energies in some recent publications [ 35 35 - 42 42 35-42 ]. For a detailed description of the AMPT model, please refer to Ref. [ 34 34 ] and Ref. [ 43 43 ] for a summary of recent developments. In the AMPT model, the initial production of heavy quarks is handled using the HIJING two-component model [ 44 44 ]. It includes pair productions ( <math id="M4"><mrow><mi>q</mi><mo>+</mo><mover accent="true"><mi>q</mi><mo>¯</mo></mover><mo>→</mo><mi>Q</mi><mo>+</mo><mover accent="true"><mi>Q</mi><mo>¯</mo></mover></mrow></math> , <math id="M5"><mrow><mi>g</mi><mo>+</mo><mi>g</mi><mo>→</mo><mi>Q</mi><mo>+</mo><mover accent="true"><mi>Q</mi><mo>¯</mo></mover></mrow></math> ) and gluon splitting ( <math id="M6"><mrow><mi>g</mi><mo>→</mo><mi>Q</mi><mo>+</mo><mover accent="true"><mi>Q</mi><mo>¯</mo></mover></mrow></math> ) with a cross section in perturbative quantum chromodynamics (QCD) at leading order: <math display="block" id="M7"><mrow><mfrac><mrow><mtext>d</mtext><msup><mi>σ</mi><mrow><mi>Q</mi><mover accent="true"><mi>Q</mi><mo>¯</mo></mover></mrow></msup></mrow><mrow><mtext>d</mtext><msubsup><mi>p</mi><mi>T</mi><mn>2</mn></msubsup><mtext>d</mtext><msub><mi>y</mi><mn>1</mn></msub><mtext>d</mtext><msub><mi>y</mi><mn>2</mn></msub></mrow></mfrac><mtext>​</mtext><mo>=</mo><mtext>​</mtext><mi>K</mi><mtext>​</mtext><mstyle displaystyle="true"><munder><mo>∑</mo><mrow><mi>a</mi><mn>,</mn><mi>b</mi></mrow></munder></mstyle><msub><mi>x</mi><mn>1</mn></msub><msub><mi>f</mi><mi>a</mi></msub><mrow><mo>(</mo><mrow><msub><mi>x</mi><mn>1</mn></msub><mn>,</mn><mtext>​</mtext><msubsup><mi>μ</mi><mtext>F</mtext><mn>2</mn></msubsup></mrow><mo>)</mo></mrow><msub><mi>x</mi><mn>2</mn></msub><msub><mi>f</mi><mi>b</mi></msub><mrow><mo>(</mo><mrow><msub><mi>x</mi><mn>2</mn></msub><mn>,</mn><mtext>​</mtext><msubsup><mi>μ</mi><mtext>F</mtext><mn>2</mn></msubsup></mrow><mo>)</mo></mrow><mo>×</mo><mfrac><mrow><mtext>d</mtext><msup><mi>σ</mi><mrow><mi>a</mi><mi>b</mi><mo>→</mo><mi>Q</mi><mover accent="true"><mi>Q</mi><mo>¯</mo></mover></mrow></msup></mrow><mrow><mtext>d</mtext><mover accent="true"><mi>t</mi><mo>^</mo></mover></mrow></mfrac><mn>.</mn></mrow></math> Here, y 1 and y 2 are the rapidities of the two produced partons, the K factor aims to account for higher-order corrections of heavy quark production, a and b refer to the types of interacting partons in the initial state, x denotes the nucleon momentum fraction taken by the interaction parton, μ F represents the factorization scale, f a is the parton distribution function of parton type a in a nucleon, and <math id="M8"><mrow><msup><mi>σ</mi><mrow><mi>a</mi><mi>b</mi><mo>→</mo><mi>Q</mi><mover accent="true"><mi>Q</mi><mo>¯</mo></mover></mrow></msup></mrow></math> is the cross section for parton types a and b to produce the heavy quark pair [ 44 44 ]. Because the cross section of heavy quark production, especially for the bottom quark, is several orders of magnitude smaller than that of light quarks in heavy-ion collisions at LHC energies, it calls for a trigger for heavy quark production to increase the simulation efficiency. The algorithm was originally developed by Wang and Gyulassy [ 44 44 ] and was extended to study the bottom quark dynamics in the QGP in this study. We refer to the details in Ref. [ 44 44 ] and Ref. [ 45 45 ] and do not repeat them here. The final state parton interactions can be described by the equations of motion for the quark and gluon Wigner operators [ 46 46 , 47 47 ], which are closely connected with the classical distribution function. For example, the relativistic gauge covariant Wigner operator for spin- <math id="M9"><mrow><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow></math> particles in coordinate and momentum space [ 46 46 ]: <math display="block" id="M10"><mrow><mover accent="true"><mi>W</mi><mo>^</mo></mover><mrow><mo>(</mo><mrow><mstyle mathvariant="bold-italic" mathsize="normal"><mi>x</mi></mstyle><mn>,</mn><mstyle mathvariant="bold-italic" mathsize="normal"><mi>p</mi></mstyle></mrow><mo>)</mo></mrow><mo>=</mo><mstyle displaystyle="true"><mrow><mo>∫</mo></mrow></mstyle><mfrac><mrow><msup><mtext>d</mtext><mn>4</mn></msup><mi>y</mi></mrow><mrow><msup><mrow><mrow><mo>(</mo><mrow><mn>2</mn><mi>π</mi></mrow><mo>)</mo></mrow></mrow><mn>4</mn></msup></mrow></mfrac><msup><mi>e</mi><mrow><mo>−</mo><mi>i</mi><mstyle mathvariant="bold-italic" mathsize="normal"><mi>p</mi></mstyle><mo>⋅</mo><mstyle mathvariant="bold-italic" mathsize="normal"><mi>y</mi></mstyle></mrow></msup><mover accent="true"><mi>ψ</mi><mo>¯</mo></mover><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><msup><mi>e</mi><mrow><mfrac><mn>1</mn><mn>2</mn></mfrac><mstyle mathvariant="bold-italic" mathsize="normal"><mi>y</mi></mstyle><mo>⋅</mo><msubsup><mstyle mathvariant="bold-italic" mathsize="normal"><mi>D</mi></mstyle><mstyle mathvariant="bold-italic" mathsize="normal"><mi>x</mi></mstyle><mo>†</mo></msubsup></mrow></msup><mo>⊗</mo><msup><mi>e</mi><mrow><mo>−</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mstyle mathvariant="bold-italic" mathsize="normal"><mi>y</mi></mstyle><mo>⋅</mo><msub><mstyle mathvariant="bold-italic" mathsize="normal"><mi>D</mi></mstyle><mstyle mathvariant="bold-italic" mathsize="normal"><mi>x</mi></mstyle></msub></mrow></msup><mi>ψ</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mn>,</mn></mrow></math> where <math id="M11"><mrow><msup><mi>D</mi><mi>μ</mi></msup><mo>≡</mo><msup><mo>∂</mo><mi>μ</mi></msup><mo>+</mo><mi>i</mi><mi>g</mi><msup><mi>A</mi><mi>μ</mi></msup></mrow></math> is the covariant derivative, and <math id="M12"><mover accent="true"><mi>W</mi><mo>^</mo></mover></math> is a matrix in spinor (4×4 components) as well as in the color space ( N × N components). By using the properties of the link operators, one can derive the quantum transport equation for the QCD Wigner operator [ 46 46 , 47 47 ]. Under semiclassical and Abelian dominance approximations, in the weak-field limit, the equations of motion become a set of equations that resemble classical transport equations [ 48 48 ]. This motivated the study of the final state interaction by solving the Boltzmann equations for quarks and gluons. If only two-body interactions are considered, the Boltzmann equations can be reduced to the following: <math display="block" id="M13"><mrow><msup><mi>p</mi><mi>μ</mi></msup><msub><mo>∂</mo><mi>μ</mi></msub><mi>f</mi><mo stretchy="false">(</mo><mstyle mathvariant="bold-italic" mathsize="normal"><mi>x</mi></mstyle><mn>,</mn><mstyle mathvariant="bold-italic" mathsize="normal"><mi>p</mi></mstyle><mn>,</mn><mi>t</mi><mo stretchy="false">)</mo><mo>∝</mo><mstyle displaystyle="true"><mrow><mo>∫</mo></mrow></mstyle><mi>σ</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mstyle mathvariant="bold-italic" mathsize="normal"><mi>x</mi></mstyle><mstyle mathvariant="bold-italic" mathsize="normal"><mn>1</mn></mstyle></msub><mn>,</mn><msub><mstyle mathvariant="bold-italic" mathsize="normal"><mi>p</mi></mstyle><mstyle mathvariant="bold-italic" mathsize="normal"><mn>1</mn></mstyle></msub><mn>,</mn><mi>t</mi><mo stretchy="false">)</mo><mi>f</mi><mo stretchy="false">(</mo><msub><mstyle mathvariant="bold-italic" mathsize="normal"><mi>x</mi></mstyle><mstyle mathvariant="bold-italic" mathsize="normal"><mn>2</mn></mstyle></msub><mn>,</mn><msub><mstyle mathvariant="bold-italic" mathsize="normal"><mi>p</mi></mstyle><mstyle mathvariant="bold-italic" mathsize="normal"><mn>2</mn></mstyle></msub><mn>,</mn><mi>t</mi><mo stretchy="false">)</mo><mn>,</mn></mrow></math> where f ( x,p,t ) represents the distribution function of the parton at time t in the phase space, and <math id="M14"><mi>σ</mi></math> is the cross section for the two-body scattering of partons. Zhang's parton cascade (ZPC) model was developed to study the final-state parton interactions, which solved the Boltzmann equations for partons using the cascade method [ 48 48 ]. In this model, two partons scatter when their closest distance is less than <math id="M15"><mrow><msqrt><mrow><mi>σ</mi><mo>/</mo><mi>π</mi></mrow></msqrt></mrow></math> . The scattering angle is determined by the differential parton–parton scattering cross section. Because the cascade prescription for solving the semiclassical transport equation does not assume any particular form of the phase space distribution, it can be used to study systems far from local thermal equilibrium, and it automatically takes into account the finite mean free path effect [ 49 49 ]. The current study focuses on heavy quark dynamics at LHC energies, whe re the bottom quark may be far from thermalization and the charm quark may be close to thermalization [ 27 27 , 28 28 , 31 31 ]. Results and Discussion 1 To follow the parton scattering history in the AMPT model, we define N scat. as the number of two-body elastic scatterings suffered by a parton. The N scat. distribution of the active partons ( N scat. > 0) is shown in Fig. 1 Fig. 1 . The distributions from the AMPT model with an enhanced heavy quark trigger are flatter than those in the normal AMPT calculation, which suggests a larger scattering possibility for partons with enhanced heavy quark triggers in the event. The effect is rather small for the charm quark scenario and more significant for the bottom quark scenario. Figure 1 Figure 1 also shows the approximate average transverse radial velocity <math id="M17"><mrow><mo>〈</mo><msub><mi>β</mi><mo>⊥</mo></msub><mo>〉</mo><mo>≡</mo><mo>〈</mo><msub><mstyle mathvariant="bold-italic" mathsize="normal"><mover accent="true"><mi>r</mi><mo>^</mo></mover></mstyle><mo>⊥</mo></msub><mo>⋅</mo><msub><mstyle mathvariant="bold-italic" mathsize="normal"><mover accent="true"><mi>p</mi><mo>^</mo></mover></mstyle><mo>⊥</mo></msub><mo>〉</mo></mrow></math> of freeze-out partons with different flavor in the AMPT model as a function of N scat. , where <math id="M18"><mrow><msub><mstyle mathvariant="bold-italic" mathsize="normal"><mover accent="true"><mi>r</mi><mo>^</mo></mover></mstyle><mo>⊥</mo></msub></mrow></math> and <math id="M19"><mrow><msub><mstyle mathvariant="bold-italic" mathsize="normal"><mover accent="true"><mi>p</mi><mo>^</mo></mover></mstyle><mo>⊥</mo></msub></mrow></math> are the transverse radial position and momentum unit vectors. The <math id="M20"><mrow><msub><mi>β</mi><mo>⊥</mo></msub></mrow></math> is not exactly zero at N scat. =0 because partons can form only after a finite formation time over which the displacement of a parton depends on its momentum [ 34 34 ]. One sees that <math id="M21"><mrow><msub><mi>β</mi><mo>⊥</mo></msub></mrow></math> of heavy quarks are larger in magnitude and almost independent of N scat. , whereas it is smaller in magnitude and drops for light quarks as N scat. increases. This is understood because heavy quarks are formed earlier, and they are more likely to inherit the direction of mother partons, which will give them larger <math id="M22"><mrow><mo>〈</mo><msub><mi>β</mi><mo>⊥</mo></msub><mo>〉</mo></mrow></math> . Compared with light quarks, it is harder to push the heavy quarks away from their original trajectory, their <math id="M23"><mrow><mo>〈</mo><msub><mi>β</mi><mo>⊥</mo></msub><mo>〉</mo></mrow></math> are independent of N scat. . As the mid-rapidity hadron density of a Pb–Pb collision at <math id="M24"><mrow><msqrt><mrow><msub><mi>s</mi><mrow><mtext>NN</mtext></mrow></msub></mrow></msqrt><mo>=</mo><mn>5.02</mn></mrow></math> TeV reaches as high as a few thousand, depending on the collision centrality [ 50 50 ], triggering on an additional heavy quark–antiquark pair production has a negligible effect on the hadron density, but may affect the evolution dynamics significantly. We use these trigger events to study the properties of QGP matter created in Pb–Pb collisions at LHC energies. Figure 2 Figure 2 presents v 2 , v 3 of a charged hadron in mid-central Pb–Pb collisions at <math id="M26"><mrow><msqrt><mrow><msub><mi>s</mi><mrow><mtext>NN</mtext></mrow></msub></mrow></msqrt><mo>=</mo><mn>5.02</mn></mrow></math> TeV from AMPT model. To do a fair comparison with experimental data [ 51 51 ], the results are calculated using the two-particle correlation method [ 52 52 ]. The result from the reaction plane method, as described in Eq. (1), has been checked and is found to be consistent with Fig. 2 Fig. 2 . Overall, the AMPT calculations with the normal, enhanced heavy quark trigger scenario reproduce the experimental data reasonably well. Larger elliptic flow is seen in the enhanced heavy quark trigger scenario. The enhancement is approximately 5% and p T independent in AMPT with bottom quark trigger (cf. the bottom panel of Fig. 2 Fig. 2 ). Including the discussion in Fig. 1 Fig. 1 where the AMPT model with enhanced bottom quark–antiquark pair production presents a larger scattering possibility for active quarks, which tends to generate larger elliptic flow and is seemingly closer to v 2 data as p T increases. Figure 3 Figure 3 highlights the v 2 ( p T ) of quarkonia in middle and forward rapidity of Pb–Pb collisions at <math id="M28"><mrow><msqrt><mrow><msub><mi>s</mi><mrow><mtext>NN</mtext></mrow></msub></mrow></msqrt><mo>=</mo><mn>5.02</mn></mrow></math> TeV. The uncertainties in calculations are determined by statistics in different centrality and different rapidity bins. Our results are consistent with the experimental data considering current uncertainties. Overall, AMPT simulations on v 2 of <math id="M29"><mi>ϒ</mi></math> are smaller than those of J /Ψ. One should note that in the current version of the AMPT calculation, regeneration of J /Ψ or dissociation of <math id="M30"><mi>ϒ</mi></math> are missing, only continued two-body elastic scattering is involved, which seems to generate the finite v 2 of quarkonia. The magnitude difference between <math id="M31"><mi>ϒ</mi></math> and J /Ψ may be due to the mass of different quarks associated with each calculation. We have learned that it is also one of the key parameters in hydrodynamics calculations [ 33 33 , 16 16 ]. To study this further, we examined the differential rapidity (pseudorapidity) dependence on v 2 , as shown in Fig. 4 Fig. 4 . Because v 2 ( η ) data for a charged hadron in Pb–Pb collisions at <math id="M34"><mrow><msqrt><mrow><msub><mi>s</mi><mrow><mi>N</mi><mi>N</mi></mrow></msub></mrow></msqrt><mo>=</mo><mn>5.02</mn></mrow></math> TeV has not yet been published, we chose the data [ 54 54 ] at <math id="M35"><mrow><msqrt><mrow><msub><mi>s</mi><mrow><mtext>NN</mtext></mrow></msub></mrow></msqrt><mo>=</mo><mn>2.76</mn></mrow></math> TeV for comparison. Thus, the AMPT calculation for the charged hadron is performed on <math id="M36"><mrow><msqrt><mrow><msub><mi>s</mi><mrow><mtext>NN</mtext></mrow></msub></mrow></msqrt><mo>=</mo><mn>2.76</mn></mrow></math> TeV accordingly. Our calculations with normal or enhanced heavy quark–antiquark pair production scenarios describe the data fairly well. Although the uncertainties presented in the measurement do not allow us to distinguish between different scenarios, the difference in the calculations is of a few per cent. The value of <math id="M37"><mi>ϒ</mi></math> v 2 is positive and at a maximum at mid-rapidity, and close to zero at higher rapidity. The calculation appears to agree with the data at forward rapidity [ 31 31 ]. The value of J /Ψ v 2 is larger than <math id="M38"><mi>ϒ</mi></math> and exhibits similar rapidity dependence. However, it underpredicts the data at forward rapidity. This deviation may originate from the missing dissociation and regeneration mechanisms for heavy quarkonium in the AMPT. Further studies are required to implement these effects in the AMPT model. The enhanced heavy quark–antiquark pair production event can also be applied to study the direct flow ( v 1 ) of quarkonium. This represents a new probe for studying the strong electromagnetic field effect of hot QCD matter via v 1 measurement, particularly on the difference in v 1 ( η ) between the particle and its antiparticle [ 56 56 , 57 57 , 58 58 ]. Measurements of the open charm meson v 1 ( η ) show a difference in the slopes of D 0 and <math id="M40"><mrow><msup><mover accent="true"><mi>D</mi><mo>¯</mo></mover><mn>0</mn></msup></mrow></math> , but with a different sign from RHIC to LHC [ 59 59 , 55 55 , 60 60 ]. The origin of this physics is still debated. Because the electromagnetic field effect has not been implemented in the AMPT model, we consider the v 1 ( η ) of J /Ψ and <math id="M41"><mi>ϒ</mi></math> instead of the v 1 difference between the particle and antiparticle in our current framework. In this aspect, we used the coordinate system of the model with the x -axis along the impact parameter direction ( <math id="M42"><mover accent="true"><mi>b</mi><mo>→</mo></mover></math> ) of each event in the transverse plane, with the center of the projective and target nuclei at the transverse coordinates ( b /2, 0) and (- b /2, 0). The direction of the projectile momentum specifies the z -axis; consequently, the total angular momentum of the system is along the - y direction. Figure 5 Figure 5 shows our results for J /Ψ and <math id="M43"><mi>ϒ</mi></math> together with the charged hadron in Pb–Pb collisions at <math id="M44"><mrow><msqrt><mrow><msub><mi>s</mi><mrow><mtext>NN</mtext></mrow></msub></mrow></msqrt><mo>=</mo><mn>5.02</mn></mrow></math> TeV. It can be seen that quarkonia present an order of magnitude larger v 1 ( η ) than charged hadrons, presumably because of the early formation and larger mass. In comparison with the data [ 55 55 ], the v 1 ( η ) of the charged hadron from the AMPT model is on the correct sign but an order of magnitude lower. Because the dynamics that generates v 1 is quite complicated, it may depend on the equation of state, mean-field potentials, particle scattering, shadowing from spectator nucleons, and tilt of the hot dense QCD matter in the x – z plane [ 58 58 ]. Our results rely on two-body parton elastic scattering, and naive quark hadronization can be understood. Future studies with more realistic dynamics are of interest. Summary 1 In summary, we have implemented an additional heavy flavor quark–antiquark pair production trigger in the AMPT model to study their dynamics in hot and dense media created in high-energy heavy-ion collisions. In this study, we have focused on the heavy flavor quarkonium anisotropy flows in Pb–Pb collisions at LHC energies. 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Sirunyan , et al. , Measurement of prompt D 0 and <math id="M72"><mrow><msup><mrow><mover accent="true"><mtext>D</mtext><mo stretchy="true">¯</mo></mover></mrow><mn>0</mn></msup></mrow></math> meson azimuthal anisotropy and search for strong electric fields in PbPb collisions at <math id="M73"><mrow><msqrt><mrow><msub><mi>s</mi><mrow><mtext>NN</mtext></mrow></msub></mrow></msqrt><mo>=</mo></mrow></math> 5.02 TeV . Phys. Lett. B 816 , 136253 ( 2021 ). doi: 10.1016/j.physletb.2021.136253 http://doi.org/10.1016/j.physletb.2021.136253 Measurement of prompt D0 and D¯0 meson azimuthal anisotropy and search for strong electric fields in PbPb collisions at sNN= 5.02 TeV All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Hai Wang and Jinhui Chen. The first draft of the manuscript was written by Hai Wang and Jin-Hui Chen, and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript. Discussions with Dr. Hui Li are gratefully acknowledged. 10.1007/s41365-022-00999-y This work was supported in part by the Strategic Priority Research Program of the Chinese Academy of Sciences (No. XDB34030200), the Guangdong Major Project of Basic and Applied Basic Research (No. 2020B0301030008), and the National Natural Science Foundation of China (Nos. 12025501, 11890710, 11890714, and 11775288). 2021-11-24 2021-12-21 2021-12-30 2022-02-23 2022-03-18 © China Science Publishing & Media Ltd. (Science Press), Shanghai Institute of Applied Physics, the Chinese Academy of Sciences, ChineseNuclear Society and Springer Nature Singapore Pte Ltd. 2022 This is a post-peer-review, pre-copyedit version of an article published in Nuclear Science and Techniques. The final authenticated version is available online at: http://dx.doi.org/10.1007/s41365-022-00999-y http://dx.doi.org10.1007/s41365-022-00999-y . 2022 Nuclear Science and Techniques 02 33