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Suppression and Two-Particle Correlations of Heavy Mesons in Heavy-Ion Collisions
Available online at www.sciencedirect.com
Nuclear Physics A 956 (2016) 505–508 www.elsevier.com/locate/nuclphysa
Suppression and Two-Particle Correlations of Heavy Mesons in Heavy-Ion Collisions Shanshan Caoa , Guang-You Qinb , Steffen A Bassc b Institute
a Nuclear Science Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA of Particle Physics and Key Laboratory of Quark and Lepton Physics (MOE), Central China Normal University, Wuhan, 430079, China c Department of Physics, Duke University, Durham, NC 27708, USA
Abstract We study the medium modification of heavy quarks produced in heavy-ion collisions. The evolution of heavy quarks inside the QGP is described using a modified Langevin framework that simultaneously incorporates their collisional and radiative energy loss. Within this framework, we provide good descriptions of the heavy meson suppression and predictions for the two-particle correlation functions of heavy meson pairs. Keywords: heavy flavor, nuclear modification, correlation function
1. Introduction Heavy quarks serve as excellent probes of the quark-gluon plasma (QGP) matter created in ultrarelativistic heavy-ion collisions. Experimental observations at both RHIC and LHC have revealed many interesting data on heavy flavor mesons and their decay electrons, among which the most surprising ones are their small values of RAA and large values of v2 that are comparable to those of light hadrons [1, 2, 3]. This seems inconsistent with earlier expectation of the mass hierarchy of parton energy loss and thus requires a thorough understanding of heavy flavor dynamics. We establish a comprehensive numerical framework to describe the temporal evolution of heavy flavor in heavy-ion collisions [4, 5, 6, 7], including their initial production, energy loss inside QGP and hadronization into heavy hadrons. Within this framework, we provide good descriptions of the heavy meson suppression observed at RHIC and LHC, predictions for two-particle correlations of D meson pairs are also presented [8, 9] and shown to be potential new observables that reveal more detailed information of heavy quark dynamics inside a deconfined QCD medium. 2. Heavy Meson Suppression Since heavy quarks are primarily produced in the early stage of heavy-ion collisions through hard scatterings, we use a Monte-Carlo Glauber model to initialize their positions and pQCD calculations for their momenta. The CTEQ parametrization is adopted for the parton distribution functions and the nuclear shadowing effect is taken into account by using the EPS09 parametrization. In the QGP stage, the space-time
http://dx.doi.org/10.1016/j.nuclphysa.2015.12.012 0375-9474/© 2016 Elsevier B.V. All rights reserved.
S. Cao et al. / Nuclear Physics A 956 (2016) 505–508
506
1.4
1.4 1.2
D meson 0-7.5%
1.2 1.0
0.8
ALICE D mesons 8 < pT < 16 GeV CMS non-prompt J/ψ 6.5 < pT < 30 GeV Calculation for D mesons Calculation for B mesons Calculation for non-prompt J/ψ
0.8 RAA
RAA
1.0
ALICE D0, D+, D*+ Collisional Radiative Total
0.6
0.6
0.4 0.4
0.2 0.0 0
0.2
10
20 pT (GeV)
30
40 0.0 0
Fig. 1. (Color online) The D meson RAA in 0-7.5% 2.76 TeV Pb-Pb collisions, compared between different energy loss mechanisms.
100
200
300
400
Fig. 2. (Color online) The mass hierarchy of heavy meson suppression.
evolution of the bulk matter is simulated by a (2+1)-D viscous hydrodynamic model [10] and the in-medium evolution of heavy quarks is described using an improved Langevin equation [6, 7]: dp = −ηD (p)p + ξ + fg . dt
(1)
The first two terms on the right are taken from the classical Langevin equation describing the drag and the thermal forces heavy quarks experience while they are scattered inside a thermal medium, and are related by the fluctuation-dissipation theorem ηD (p) = κ/(2T E), in which the momentum space diffusion coefficient κ is defined as ξi (t)ξ j (t ) = κδi j δ(t − t ). The third term fg = −d pg /dt is introduced to describe the recoil force exerted on heavy quarks while they radiate gluons. We adopt the following higher-twist calculation of the medium-induced gluon distribution function to determine the rate of gluon radiation and its energymomentum distribution [11]: dNg dxdk⊥2 dt
=
4 k⊥2 qˆ t − ti 2α s (k⊥ ) P(x) 4 sin2 , π 2τ f k⊥ k⊥2 + x2 M 2
(2)
where qˆ is the gluon transport coefficient, x is the fractional energy carried by radiated gluon, and k⊥ is its transverse momentum. In our work, the spatial diffusion coefficient of heavy quarks D is related to κ and qˆ via D = 2T 2 /κ and qˆ = 2κC A /C F . After heavy quarks travel outside the QGP regime, their conversion into the hadron states are calculated based on our hybrid model of fragmentation plus coalescence [6, 7]. In Fig. 1 we show our calculations of the D meson RAA in central Pb-Pb collisions at the LHC energy. The diffusion coefficient of heavy quarks is set as D = 5/(2πT ) as tuned in [7]. We observe that collisional energy loss dominates the D meson spectrum at low pT , however, radiative energy loss is important at high pT . In Fig. 2, we present the participant number dependence of RAA for D meson, B meson and non-prompt J/ψ decayed from B meson. Due to the larger mass of b quarks than c quarks, the former lose less energy inside the QGP and therefore a larger RAA is observed for non-prompt J/ψ’s than D mesons. Calculations for heavy meson flow coefficient and for the RHIC experiment as well can be found in our earlier work [7]. 3. Transverse Momentum Imbalance and Angular Correlation Functions of D Meson Pairs In addition to the single heavy meson spectrum, the two-particle correlation functions of heavy meson pairs have also been discussed in [12, 13, 14, 8, 9] and shown able to reveal additional information on heavy flavor dynamics. In Fig. 3 we study the transverse momentum imbalance of D meson pairs in heavyion collisions. For each event, we select the D or D meson possessing the highest transverse momentum
S. Cao et al. / Nuclear Physics A 956 (2016) 505–508
507
2.0 1.5 IAA 1.0 0.3 0.5 0.0 0.2 0.4 0.6 xT
initial (pp) 60-70% 30-40% 0-10% 0.8
1
0.2
pT, trig > 4 GeV pT, asso > 2 GeV
0.1
0.165 0.160
0.2
0.4
0.6
xT
0.8
0.92 0.91 0.90 0.89 0.88 0.87 0.86 0.72
0.150
1
pT, trig > 2 GeV -π/2
π/2 Δφ
0
3π/2
col.+rad. D(2πT)=5.0 col. only D(2πT)=1.5 rad. only D(2πT)=3.0
0.80
xT < 0.4
0.76 0.72
pT, trig > 2 GeV
0.70 0.68 0.66
(a) π
Fig. 4. (Color online) The angular correlation function of DD pairs, compared between different energy loss mechanisms.
σ (Δφ) (away side)
σ (Δφ) (away side)
D-Dbar correlation PYTHIA initialization
Au-Au @ 200 GeV 0-10%
Fig. 3. (Color online) The xT distribution of DD pairs for different centralities.
0.64 0.54 0.52 0.50 0.48 0.46 0.44
0.170
0.155
(a) 0.0 0
col.+rad. D(2πT)=5.0 col. only D(2πT)=1.5 rad. only D(2πT)=3.0 col. only without flow
0.175 (1/Npair) (dNpair/dΔφ)
(1/Ntrig) (dNpair/dxT)
0.4
pT, trig > 4 GeV & pT, asso > 2 GeV pT, trig > 8 GeV & pT, asso > 4 GeV
0.68 0.76 0.74
0.4 < xT < 0.7
0.72 0.70 0.68
0.66
xT > 0.7
0.64 0.62 0.60
0
50
100
150
200
Npart
250
300
350
Fig. 5. (Color online) The away side variance of DD angular correlation functions for different pT cuts.
0.58
pT, trig > 4 GeV & pT, asso > 2 GeV 0
50
100
150
200
Npart
250
300
350
Fig. 6. (Color online) The away side variance of DD angular correlation functions at medium pT for different xT regions.
as the leading (trigger) meson. On the back side within |φ − φtrig | ≥ 2π/3, we select its partner with the highest transverse momentum as the subleading (associated) meson. The transverse momentum imbalance is defined as xT = pT,asso/pT,trig . In Fig. 3, we observe that as one moves from proton-proton collisions to more and more central Au-Au collisions, (a) there exist a smaller number of DD pairs per triggered event, and (b) the distribution shifts to smaller xT (i.e., larger momentum imbalance). These both result from stronger energy loss of heavy quarks inside the QGP. In the subfigure, we also present the ratios between nucleus-nucleus collisions and proton-proton collisions, i.e., IAA . The momentum imbalance not only helps quantify the energy loss of heavy quarks, but also provides us the possibility to probe specific regions of the QGP fireballs. In Ref. [9] we show that smaller xT corresponds to events initially produced at the edge of the QGP fireballs in which one heavy quark travels outside the medium without much interaction while its partner traverse the whole QGP fireball and loses significant amount of energy. On the other hand, larger xT corresponds to the initial cc pairs that are spread out smoothly over the QGP. While the transverse momentum imbalance is related to the total energy loss of heavy quarks, we find the angular correlation function of DD pairs is sensitive to the detailed energy loss mechanisms. As shown in Ref. [9], although the combination of collisional and radiative energy loss provides the best pT dependence
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S. Cao et al. / Nuclear Physics A 956 (2016) 505–508
of the D meson RAA , collisional or radiative energy loss alone may also provide a reasonable description of the experimental data, as long as the transport coefficient is properly adjusted (as given in Fig. 4) . However, with the similar amount of suppression, different energy loss mechanisms lead to very different correlation functions of DD pairs. Pure radiative energy loss does not change the peak around π compared to their initial configuration generated from Pythia. On the other hand, pure collisional energy loss is more effective in smearing out the angular distribution and leads to a peak around 0, indicating that most low momentum DD pairs tend to move collinearly in the final state because of the QGP radial flow. This near side peak disappears if the heavy quark motion is decoupled from the local fluid velocity in our calculation. In Fig. 5 we calculate the away side variances for different pT cuts, in which a non-monotonic behavior with respect to Npart is observed. This results from the competition between the transverse momentum broadening and the energy loss of heavy quarks inside the QGP. The former increases the variance towards the uniform distribution limit and is more efficient for relatively low pT , while the latter enhances the contribution from the charm quarks with higher initial pT whose variance of the away side peak is smaller. To better illustrate this competition, in Fig. 6, we divide the medium pT region of Fig. 5 into 3 different xT bins. We observe at small xT where the relative longitudinal energy loss is strong, the variance value tends to decrease monotonically. However, for higher xT , transverse momentum broadening starts to dominate in central collisions which increases the variance. And the turning point starts earlier with higher xT . 4. Conclusions Within our modified Langevin approach, we have provide good descriptions of heavy meson suppression in heavy-ion collisions. Predictions for two-particle correlations are also presented which provide the possibility of revealing more detailed information of heavy quark dynamics. This work is funded by the U.S. Department of Energy under Contract Nos. DE-AC02-05CH11231 and DE-FG02- 05ER41367 within the framework of the JET Collaboration, and by the Natural Science Foundation of China (NSFC) under Grant No. 11375072. References √ [1] A. Adare, et al., Heavy Quark Production in p + p and Energy Loss and Flow of Heavy Quarks in Au+Au Collisions at sNN = 200 GeV, Phys. Rev. C84 (2011) 044905. arXiv:1005.1627, doi:10.1103/PhysRevC.84.044905. √ [2] L. Adamczyk, et al., Observation of D0 Meson Nuclear Modifications in Au+Au Collisions at sNN = 200GeV, Phys. Rev. Lett. 113 (14) (2014) 142301. arXiv:1404.6185, doi:10.1103/PhysRevLett.113.142301. √ [3] B. B. Abelev, et al., Azimuthal anisotropy of D meson production in Pb-Pb collisions at sNN = 2.76 TeV, Phys. Rev. C90 (3) (2014) 034904. arXiv:1405.2001, doi:10.1103/PhysRevC.90.034904. [4] S. Cao, S. A. Bass, Thermalization of charm quarks in infinite and finite QGP matter, Phys. Rev. C84 (2011) 064902. arXiv:1108.5101, doi:10.1103/PhysRevC.84.064902. [5] S. Cao, G.-Y. Qin, S. A. Bass, Model and parameter dependence of heavy quark energy loss in a hot and dense medium, J. Phys. G40 (2013) 085103. arXiv:1205.2396, doi:10.1088/0954-3899/40/8/085103. [6] S. Cao, G.-Y. Qin, S. A. Bass, Heavy quark dynamics and hadronization in ultra-relativistic heavy-ion collisions: collisional versus radiative energy loss, Phys. Rev. C88 (2013) 044907. arXiv:1308.0617, doi:10.1103/PhysRevC.88.044907. [7] S. Cao, G.-Y. Qin, S. A. Bass, Energy loss, hadronization and hadronic interactions of heavy flavors in relativistic heavy-ion collisions, Phys. Rev. C92 (2015) 024907. arXiv:1505.01413, doi:10.1103/PhysRevC.92.024907. [8] S. Cao, G.-Y. Qin, S. A. Bass, Dynamical Evolution, Hadronization and Angular De-correlation of Heavy Flavor in a Hot and Dense QCD Medium, Nucl.Phys. A932 (2014) 38. arXiv:1404.1081, doi:10.1016/j.nuclphysa.2014.08.047. [9] S. Cao, G.-Y. Qin, S. A. Bass, Modeling of heavy-flavor pair correlations in Au-Au collisions at 200A GeV at the BNL Relativistic Heavy Ion Collider, Phys. Rev. C92 (5) (2015) 054909. arXiv:1505.01869, doi:10.1103/PhysRevC.92.054909. [10] Z. Qiu, C. Shen, U. Heinz, Hydrodynamic elliptic and triangular flow in Pb-Pb collisions at sqrt(s)=2.76ATeV, Phys. Lett. B707 (2012) 151–155. arXiv:1110.3033, doi:10.1016/j.physletb.2011.12.041. [11] B.-W. Zhang, E. Wang, X.-N. Wang, Heavy quark energy loss in nuclear medium, Phys. Rev. Lett. 93 (2004) 072301. arXiv:nuclth/0309040, doi:10.1103/PhysRevLett.93.072301. [12] X. Zhu, N. Xu, P. Zhuang, The Effect of partonic wind on charm quark correlations in high-energy nuclear collisions, Phys. Rev. Lett. 100 (2008) 152301. arXiv:0709.0157, doi:10.1103/PhysRevLett.100.152301. [13] M. √ Nahrgang, J. Aichelin, P. B. Gossiaux, K. Werner, Azimuthal correlations of heavy quarks in Pb + Pb collisions at s = 2.76 TeV at the CERN Large Hadron Collider, Phys. Rev. C90 (2) (2014) 024907. arXiv:1305.3823, doi:10.1103/PhysRevC.90.024907. [14] J. Uphoff, F. Senzel, Z. Xu, C. Greiner, Momentum imbalance of D mesons in ultra-relativistic heavy-ion collisions at LHC, Phys. Rev. C89 (6) (2014) 064906. arXiv:1310.1340, doi:10.1103/PhysRevC.89.064906.
Nuclear Physics A 956 (2016) 505–508 www.elsevier.com/locate/nuclphysa
Suppression and Two-Particle Correlations of Heavy Mesons in Heavy-Ion Collisions Shanshan Caoa , Guang-You Qinb , Steffen A Bassc b Institute
a Nuclear Science Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA of Particle Physics and Key Laboratory of Quark and Lepton Physics (MOE), Central China Normal University, Wuhan, 430079, China c Department of Physics, Duke University, Durham, NC 27708, USA
Abstract We study the medium modification of heavy quarks produced in heavy-ion collisions. The evolution of heavy quarks inside the QGP is described using a modified Langevin framework that simultaneously incorporates their collisional and radiative energy loss. Within this framework, we provide good descriptions of the heavy meson suppression and predictions for the two-particle correlation functions of heavy meson pairs. Keywords: heavy flavor, nuclear modification, correlation function
1. Introduction Heavy quarks serve as excellent probes of the quark-gluon plasma (QGP) matter created in ultrarelativistic heavy-ion collisions. Experimental observations at both RHIC and LHC have revealed many interesting data on heavy flavor mesons and their decay electrons, among which the most surprising ones are their small values of RAA and large values of v2 that are comparable to those of light hadrons [1, 2, 3]. This seems inconsistent with earlier expectation of the mass hierarchy of parton energy loss and thus requires a thorough understanding of heavy flavor dynamics. We establish a comprehensive numerical framework to describe the temporal evolution of heavy flavor in heavy-ion collisions [4, 5, 6, 7], including their initial production, energy loss inside QGP and hadronization into heavy hadrons. Within this framework, we provide good descriptions of the heavy meson suppression observed at RHIC and LHC, predictions for two-particle correlations of D meson pairs are also presented [8, 9] and shown to be potential new observables that reveal more detailed information of heavy quark dynamics inside a deconfined QCD medium. 2. Heavy Meson Suppression Since heavy quarks are primarily produced in the early stage of heavy-ion collisions through hard scatterings, we use a Monte-Carlo Glauber model to initialize their positions and pQCD calculations for their momenta. The CTEQ parametrization is adopted for the parton distribution functions and the nuclear shadowing effect is taken into account by using the EPS09 parametrization. In the QGP stage, the space-time
http://dx.doi.org/10.1016/j.nuclphysa.2015.12.012 0375-9474/© 2016 Elsevier B.V. All rights reserved.
S. Cao et al. / Nuclear Physics A 956 (2016) 505–508
506
1.4
1.4 1.2
D meson 0-7.5%
1.2 1.0
0.8
ALICE D mesons 8 < pT < 16 GeV CMS non-prompt J/ψ 6.5 < pT < 30 GeV Calculation for D mesons Calculation for B mesons Calculation for non-prompt J/ψ
0.8 RAA
RAA
1.0
ALICE D0, D+, D*+ Collisional Radiative Total
0.6
0.6
0.4 0.4
0.2 0.0 0
0.2
10
20 pT (GeV)
30
40 0.0 0
Fig. 1. (Color online) The D meson RAA in 0-7.5% 2.76 TeV Pb-Pb collisions, compared between different energy loss mechanisms.
100
200
300
400
Fig. 2. (Color online) The mass hierarchy of heavy meson suppression.
evolution of the bulk matter is simulated by a (2+1)-D viscous hydrodynamic model [10] and the in-medium evolution of heavy quarks is described using an improved Langevin equation [6, 7]: dp = −ηD (p)p + ξ + fg . dt
(1)
The first two terms on the right are taken from the classical Langevin equation describing the drag and the thermal forces heavy quarks experience while they are scattered inside a thermal medium, and are related by the fluctuation-dissipation theorem ηD (p) = κ/(2T E), in which the momentum space diffusion coefficient κ is defined as ξi (t)ξ j (t ) = κδi j δ(t − t ). The third term fg = −d pg /dt is introduced to describe the recoil force exerted on heavy quarks while they radiate gluons. We adopt the following higher-twist calculation of the medium-induced gluon distribution function to determine the rate of gluon radiation and its energymomentum distribution [11]: dNg dxdk⊥2 dt
=
4 k⊥2 qˆ t − ti 2α s (k⊥ ) P(x) 4 sin2 , π 2τ f k⊥ k⊥2 + x2 M 2
(2)
where qˆ is the gluon transport coefficient, x is the fractional energy carried by radiated gluon, and k⊥ is its transverse momentum. In our work, the spatial diffusion coefficient of heavy quarks D is related to κ and qˆ via D = 2T 2 /κ and qˆ = 2κC A /C F . After heavy quarks travel outside the QGP regime, their conversion into the hadron states are calculated based on our hybrid model of fragmentation plus coalescence [6, 7]. In Fig. 1 we show our calculations of the D meson RAA in central Pb-Pb collisions at the LHC energy. The diffusion coefficient of heavy quarks is set as D = 5/(2πT ) as tuned in [7]. We observe that collisional energy loss dominates the D meson spectrum at low pT , however, radiative energy loss is important at high pT . In Fig. 2, we present the participant number dependence of RAA for D meson, B meson and non-prompt J/ψ decayed from B meson. Due to the larger mass of b quarks than c quarks, the former lose less energy inside the QGP and therefore a larger RAA is observed for non-prompt J/ψ’s than D mesons. Calculations for heavy meson flow coefficient and for the RHIC experiment as well can be found in our earlier work [7]. 3. Transverse Momentum Imbalance and Angular Correlation Functions of D Meson Pairs In addition to the single heavy meson spectrum, the two-particle correlation functions of heavy meson pairs have also been discussed in [12, 13, 14, 8, 9] and shown able to reveal additional information on heavy flavor dynamics. In Fig. 3 we study the transverse momentum imbalance of D meson pairs in heavyion collisions. For each event, we select the D or D meson possessing the highest transverse momentum
S. Cao et al. / Nuclear Physics A 956 (2016) 505–508
507
2.0 1.5 IAA 1.0 0.3 0.5 0.0 0.2 0.4 0.6 xT
initial (pp) 60-70% 30-40% 0-10% 0.8
1
0.2
pT, trig > 4 GeV pT, asso > 2 GeV
0.1
0.165 0.160
0.2
0.4
0.6
xT
0.8
0.92 0.91 0.90 0.89 0.88 0.87 0.86 0.72
0.150
1
pT, trig > 2 GeV -π/2
π/2 Δφ
0
3π/2
col.+rad. D(2πT)=5.0 col. only D(2πT)=1.5 rad. only D(2πT)=3.0
0.80
xT < 0.4
0.76 0.72
pT, trig > 2 GeV
0.70 0.68 0.66
(a) π
Fig. 4. (Color online) The angular correlation function of DD pairs, compared between different energy loss mechanisms.
σ (Δφ) (away side)
σ (Δφ) (away side)
D-Dbar correlation PYTHIA initialization
Au-Au @ 200 GeV 0-10%
Fig. 3. (Color online) The xT distribution of DD pairs for different centralities.
0.64 0.54 0.52 0.50 0.48 0.46 0.44
0.170
0.155
(a) 0.0 0
col.+rad. D(2πT)=5.0 col. only D(2πT)=1.5 rad. only D(2πT)=3.0 col. only without flow
0.175 (1/Npair) (dNpair/dΔφ)
(1/Ntrig) (dNpair/dxT)
0.4
pT, trig > 4 GeV & pT, asso > 2 GeV pT, trig > 8 GeV & pT, asso > 4 GeV
0.68 0.76 0.74
0.4 < xT < 0.7
0.72 0.70 0.68
0.66
xT > 0.7
0.64 0.62 0.60
0
50
100
150
200
Npart
250
300
350
Fig. 5. (Color online) The away side variance of DD angular correlation functions for different pT cuts.
0.58
pT, trig > 4 GeV & pT, asso > 2 GeV 0
50
100
150
200
Npart
250
300
350
Fig. 6. (Color online) The away side variance of DD angular correlation functions at medium pT for different xT regions.
as the leading (trigger) meson. On the back side within |φ − φtrig | ≥ 2π/3, we select its partner with the highest transverse momentum as the subleading (associated) meson. The transverse momentum imbalance is defined as xT = pT,asso/pT,trig . In Fig. 3, we observe that as one moves from proton-proton collisions to more and more central Au-Au collisions, (a) there exist a smaller number of DD pairs per triggered event, and (b) the distribution shifts to smaller xT (i.e., larger momentum imbalance). These both result from stronger energy loss of heavy quarks inside the QGP. In the subfigure, we also present the ratios between nucleus-nucleus collisions and proton-proton collisions, i.e., IAA . The momentum imbalance not only helps quantify the energy loss of heavy quarks, but also provides us the possibility to probe specific regions of the QGP fireballs. In Ref. [9] we show that smaller xT corresponds to events initially produced at the edge of the QGP fireballs in which one heavy quark travels outside the medium without much interaction while its partner traverse the whole QGP fireball and loses significant amount of energy. On the other hand, larger xT corresponds to the initial cc pairs that are spread out smoothly over the QGP. While the transverse momentum imbalance is related to the total energy loss of heavy quarks, we find the angular correlation function of DD pairs is sensitive to the detailed energy loss mechanisms. As shown in Ref. [9], although the combination of collisional and radiative energy loss provides the best pT dependence
508
S. Cao et al. / Nuclear Physics A 956 (2016) 505–508
of the D meson RAA , collisional or radiative energy loss alone may also provide a reasonable description of the experimental data, as long as the transport coefficient is properly adjusted (as given in Fig. 4) . However, with the similar amount of suppression, different energy loss mechanisms lead to very different correlation functions of DD pairs. Pure radiative energy loss does not change the peak around π compared to their initial configuration generated from Pythia. On the other hand, pure collisional energy loss is more effective in smearing out the angular distribution and leads to a peak around 0, indicating that most low momentum DD pairs tend to move collinearly in the final state because of the QGP radial flow. This near side peak disappears if the heavy quark motion is decoupled from the local fluid velocity in our calculation. In Fig. 5 we calculate the away side variances for different pT cuts, in which a non-monotonic behavior with respect to Npart is observed. This results from the competition between the transverse momentum broadening and the energy loss of heavy quarks inside the QGP. The former increases the variance towards the uniform distribution limit and is more efficient for relatively low pT , while the latter enhances the contribution from the charm quarks with higher initial pT whose variance of the away side peak is smaller. To better illustrate this competition, in Fig. 6, we divide the medium pT region of Fig. 5 into 3 different xT bins. We observe at small xT where the relative longitudinal energy loss is strong, the variance value tends to decrease monotonically. However, for higher xT , transverse momentum broadening starts to dominate in central collisions which increases the variance. And the turning point starts earlier with higher xT . 4. Conclusions Within our modified Langevin approach, we have provide good descriptions of heavy meson suppression in heavy-ion collisions. Predictions for two-particle correlations are also presented which provide the possibility of revealing more detailed information of heavy quark dynamics. This work is funded by the U.S. Department of Energy under Contract Nos. DE-AC02-05CH11231 and DE-FG02- 05ER41367 within the framework of the JET Collaboration, and by the Natural Science Foundation of China (NSFC) under Grant No. 11375072. References √ [1] A. Adare, et al., Heavy Quark Production in p + p and Energy Loss and Flow of Heavy Quarks in Au+Au Collisions at sNN = 200 GeV, Phys. Rev. C84 (2011) 044905. arXiv:1005.1627, doi:10.1103/PhysRevC.84.044905. √ [2] L. Adamczyk, et al., Observation of D0 Meson Nuclear Modifications in Au+Au Collisions at sNN = 200GeV, Phys. Rev. Lett. 113 (14) (2014) 142301. arXiv:1404.6185, doi:10.1103/PhysRevLett.113.142301. √ [3] B. B. Abelev, et al., Azimuthal anisotropy of D meson production in Pb-Pb collisions at sNN = 2.76 TeV, Phys. Rev. C90 (3) (2014) 034904. arXiv:1405.2001, doi:10.1103/PhysRevC.90.034904. [4] S. Cao, S. A. Bass, Thermalization of charm quarks in infinite and finite QGP matter, Phys. Rev. C84 (2011) 064902. arXiv:1108.5101, doi:10.1103/PhysRevC.84.064902. [5] S. Cao, G.-Y. Qin, S. A. Bass, Model and parameter dependence of heavy quark energy loss in a hot and dense medium, J. Phys. G40 (2013) 085103. arXiv:1205.2396, doi:10.1088/0954-3899/40/8/085103. [6] S. Cao, G.-Y. Qin, S. A. Bass, Heavy quark dynamics and hadronization in ultra-relativistic heavy-ion collisions: collisional versus radiative energy loss, Phys. Rev. C88 (2013) 044907. arXiv:1308.0617, doi:10.1103/PhysRevC.88.044907. [7] S. Cao, G.-Y. Qin, S. A. Bass, Energy loss, hadronization and hadronic interactions of heavy flavors in relativistic heavy-ion collisions, Phys. Rev. C92 (2015) 024907. arXiv:1505.01413, doi:10.1103/PhysRevC.92.024907. [8] S. Cao, G.-Y. Qin, S. A. 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