Advances in High Energy Physics
Volume 2016 (2016), Article ID 7140231, 12 pages
http://dx.doi.org/10.1155/2016/7140231

Review Article

An Experimental Review on Heavy-Flavor in Heavy-Ion Collision

Md. Nasim, Roli Esha, and Huan Zhong Huang

Department of Physics and Astronomy, UCLA, Los Angeles, CA 90095, USA

Received 31 May 2016; Accepted 29 August 2016

Academic Editor: Ming Liu

Copyright © 2016 Md. Nasim et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP³.

Abstract.

For over a decade now, the primary purpose of relativistic heavy-ion collisions at the Relativistic Heavy-Ion Collider (RHIC) and the Large Hadron Collider (LHC) has been to study the properties of QCD matter under extreme conditions—high temperature and high density. The heavy-ion experiments at both RHIC and LHC have recorded a wealth of data in p+p, p+Pb, d+Au, Cu+Cu, Cu+Au, Au+Au, Pb+Pb, and U+U collisions at energies ranging from  GeV to 7 TeV. Heavy quarks are considered good probe to study the QCD matter created in relativistic collisions due to their very large mass and other unique properties. A precise measurement of various properties of heavy-flavor hadrons provides an insight into the fundamental properties of the hot and dense medium created in these nucleus-nucleus collisions, such as transport coefficient and thermalization and hadronization mechanisms. The main focus of this paper is to present a review on the measurements of azimuthal anisotropy of heavy-flavor hadrons and to outline the scientific opportunities in this sector due to future detector upgrade. We will mainly discuss the elliptic flow of open charmed meson (-meson), , and leptons from heavy-flavor decay at RHIC and LHC energy.

1. Introduction

In the standard model of particle physics, the strong force is described by the theory of Quantum Chromodynamics (QCD). At ordinary temperatures or densities this force just confines the quarks into hadrons. At sufficiently high temperature and/or high baryon density, Lattice QCD predicts a transition from hadronic matter to deconfined partonic matter [1–4]. Phase diagram of QCD is full of puzzles and surprises. Experimentally it is possible to create very high temperature and high dense states of nuclear matter, by colliding two heavy nuclei at ultrarelativistic speed, which would contain asymptotically free quarks and gluons. The Relativistic Heavy-Ion Collider (RHIC) and the Large Hadron Collider (LHC) were built to study the properties of Quark-Gluon Plasma (a state of matter believed to exist just after the Big Bang) produced during collision of heavy ions at ultrarelativistic speed. The life-time of Quark-Gluon Plasma (QGP) is very short (~5–10 fm/c); hence, direct detection of QGP is not possible. Therefore, one has to rely on indirect measurement using suitable probe. Heavy quarks production in relativistic heavy-ion collisions provides unique probes of QGP.

In relativistic heavy-ion collisions, heavy quarks (c, b) are produced on a short time scale (~0.08 fm/c for production) in the initial hard partonic scatterings during the early stages of nucleus-nucleus collisions [5]. The probability of thermal production of heavy-quark pairs is small in the high temperature QGP. The interactions of heavy quarks are sensitive to medium dynamics. They decouple early in the evolution of QGP due to their large masses, thereby preserving the information from the system at early stage [6–13]. While traversing the hot and dense matter produced in nucleus-nucleus collisions, hard partons (partons with high transverse momentum ) produced in the early stages of the collision lose energy dominantly due to multiple scatterings and radiative energy loss. Hence, they become quenched. Theoretical models predict that the mechanism as well as average energy loss will be different for heavy quarks compared to light quarks [14–18]. Therefore, high charmed mesons (, , , , etc.) will show different suppression with respect to light mesons (, , , etc.). In contrast, measurements of heavy-flavor decay electrons at RHIC and charm hadrons at the LHC have shown significant suppression at high transverse momentum, , similar to that of light hadrons for central collisions. Therefore, a complete understanding of the energy loss mechanisms in the QGP medium requires systematic and precise measurements of the properties of various hadrons carrying different quark flavors at RHIC and the LHC. The dependence of the partonic energy loss on the in-medium path length is expected to be different for different energy loss mechanism. It is suggested that low-momentum heavy quarks could undergo hadronization both via fragmentation in the vacuum and recombination with other quarks from the medium [19]. Azimuthal anisotropy measurements of the production of heavy-flavor hadron with respect to the reaction plane can be very useful in addressing these questions.

Elliptic flow () measured in heavy-ion collisions is believed to arise due to the pressure gradient developed when two nuclei collide at nonzero impact parameters followed by subsequent interactions among the constituents [58–63]. The elliptic flow parameter is defined as the 2nd Fourier coefficient, , of the particle distributions in emission azimuthal angle () with respect to the reaction plane angle () [59, 64–69]:

For a given rapidity window the second coefficient is given by

where and are the and components of the particle momenta. At small transverse momentum, , a large is considered to be an evidence for the collective hydrodynamical expansion of the medium. Positive , if observed at very high , is expected to be due to path-length dependent energy loss by hard partons. Unlike light quarks and gluons, which can be produced or annihilated during the entire evolution of the medium, heavy quarks are expected to be produced mainly in initial hard scattering processes and their annihilation rate is small. Therefore, for all , the final state heavy-flavor hadrons originate from heavy quarks that have experienced each stage of the system evolution. The paper is organized in the following way. Section 2 describes sensitivity of heavy-flavor hadron as probe of QCD medium. In Section 3, elliptic flows of heavy-flavor decay electron are briefly discussed. Sections 4 and 5 describe elliptic flow of open charmed meson and , respectively, measured at RHIC and LHC. Comparisons between model and data are also presented in Sections 4 and 5. Finally, we summarize in Section 6.

2. Elliptic Flow of Heavy-Flavor as a Sensitive Probe

We have recently studied the elliptic flow of open charm mesons, using quark coalescence as a mechanism of hadronization within the framework of a multiphase transport model (AMPT) [6]. This study includes effect of partonic interaction cross-section, QCD coupling constant, and specific viscosity on elliptic flow of open charm mesons within the transport model approach. The AMPT model is a hybrid transport model [70–72]. It uses the same initial conditions as in HIJING. In the AMPT model, the value of parton-parton scattering cross-section, , is calculated by

where and are the QCD coupling constant and screening mass, respectively. Using the framework of AMPT model one can study the effect of specific viscosity on elliptic flow of hadrons. For a system of massless quarks and gluons at temperature ( MeV at RHIC energy in AMPT [73]), the specific viscosity is given by [73]

Hadronization of heavy quarks is not implemented in AMPT model. It only gives phase space information heavy quarks at freeze-out. We have implemented quark coalescence mechanism to form open charm mesons using phase space information of quarks available from AMPT model. Within the framework of coalescence mechanism [74–78], the probability of producing a hadron from a soup of partons is determined by the overlap of the phase space distribution of partons at freeze-out with the parton Wigner phase space function inside the hadron. The Wigner phase space function for quarks inside a meson is obtained from its constituent quark wave function [79, 80]:

where the relative momentum between the two quarks is and the quark wave function is given by spherical harmonic oscillator described as

with being the relative coordinate and is the size parameter related to the root mean square radius as . We have taken  fm² from [79, 80].

We have used two different values of , for example, 0.08 and 0.18, by tuning input parameters of AMPT model keeping parton-parton interaction cross-section equal to 10 mb. The values of and for different value of are shown in Table 1. Figure 1 shows ratio between for and for as function of for 10–40% central Au+Au collisions at  GeV. The red solid and open blue circles represent results for charged hadrons and , respectively. We can see that decreases with increase in specific viscosity for both and charged hadrons. This is consistent with the interpretation that increased sheer viscosity reduces transverse expansion due to increased interactions and hence reduces . We can also see that the change in for charged hadrons is ~15, whereas for it lies between 30 and 40 for  GeV/c. Therefore, the elliptic flow of open charmed meson is more sensitive to viscous properties of the QGP medium compared to light hadrons. Comparison between our calculation and data has been discussed in Section 4.

Table 1: Values of for different values of and , keeping = 10 mb for Au+Au collisions at = 200 GeV.

Specific viscosity,

QCD coupling constant,

Screening mass,
(in fm)

0.08
0.47
1.77

0.18
0.23
0.88

Figure 1: Ratio between for and for as a function of in Au+Au collisions at  GeV for charged hadrons and for 10–40% central collisions.

3. Elliptic Flow of Heavy-Flavor Decay Electron

Measurement of electrons from semileptonic decay of heavy-flavor hadrons (also called nonphotonic electrons, NPE) is widely used to study heavy-flavor production in high-energy collisions. These NPE give the direction of the mother () mesons, especially when electron  GeV/c. Thus, of NPE serves as a proxy for of heavy quarks. Systematic measurements of the nuclear modification factor ( and ) and the elliptic flow coefficient () of heavy-flavor decay electrons were performed at RHIC and LHC energies. Figure 2 shows the azimuthal anisotropy of NPE as a function of at , 62.4, and 200 GeV as measured by STAR and PHENIX experiments [20, 21]. A comparison between different methods for measurement of has been shown. The different methods show different sensitivity to nonflow and flow fluctuation. Nonzero positive has been observed for all methods. The increase of with for  GeV/c could be due an effect of jet-like correlations as the nonflow correlation, which is estimated from p+p collision, is of the similar order with measured in Au+Au collision at high . At 39 and 62.4 GeV, is consistent with zero as shown in Figure 2(b). A very high precision measurement is required at 39 and 62.4 GeV to understand NPE at these energies.

(a)

(b)

Figure 2: (a) Comparison of azimuthal anisotropy of NPE at  GeV measured by PHENIX [20] and STAR [21]. (b) NPE using two-particle cumulant method at 200 and 62.4 and 39 GeV. The error bars represent the statistical uncertainty and the brackets represent the systematic uncertainties.

The nuclear modification factors () and elliptic flow of NPE in Pb+Pb collisions at 2.76 TeV are shown in Figure 3 [22]. A finite positive of NPE is observed for  GeV/c in Pb+Pb collision at 2.76 TeV, quite similar to Au+Au collision at 200 GeV at RHIC. Large positive of NPE at low might indicate that charm quarks participate in the collective expansion of the dense and hot QGP. Also, a strong suppression of yield of NPE is observed for  GeV/c in 0–10% most central Pb+Pb collisions.

Figure 3: Measured and of NPE in Pb+Pb collision at 2.76 TeV [22–24]. Theoretical prediction for and of NPE are shown by lines [25–29].

The results from the models calculations [25–28], which include parton energy loss in the hot and dense QCD medium, are shown as lines for both and in Figure 3. The simultaneous description of the measured and is challenging for models. BAMPS [25] gives a good description of NPE but predicts a larger in-medium suppression than measured. In BAMPS approach, heavy quarks are transported through the medium while undergoing collisional and radiative energy loss. The prediction from POWLANG [28] describes the NPE but their calculation underestimates NPE . In POWLANG, heavy quarks are transported following a Langevin approach considering collisional energy loss only. The prediction from He et al. [26, 27] (TAMU) and MC@sHQ+EPOS, Coll+Rad(LPM) [29] describes the NPE and reasonably well. Model calculation by Rapp et al. includes in-medium resonance scattering and coalescence of heavy quarks in the medium. The MC@sHG+EPOS model includes radiative and collisional energy loss in an expanding medium based on the EPOS model.

4. Elliptic Flow of Open Charmed Meson

4.1. Available Experimental Data

The elliptic flow of mesons at mid-rapidity () has been measured differentially in Pb-Pb collisions by the ALICE at LHC [30]. The transverse momentum dependencies of of , , and mesons in the 30–50% collisions centrality at  TeV are shown in Figure 4. Measurements were done using three different methods, namely, event plane, scalar product, and two-particle cumulant methods. Results from event plane method is shown in Figure 4(a). Figures 4(b) and 4(c) show results obtained with the scalar product and two-particle cumulant methods, respectively. The event plane is estimated from TPC tracks within . For the other methods, TPC tracks in were used as reference particle. The elliptic flows of , , and mesons are consistent within uncertainties. At very high ( GeV/c), is consistent with zero within the large statistical uncertainties. In range between  GeV/c, the measured is found to be larger than zero with 5.7  significance. It suggests that low charm quarks possibly participate in the collective expansion of the medium. However, the possibility that the observed -meson is completely due to the contribution from light-quark in a scenario with hadronization via recombination cannot be ruled out. We need high precision data at low and more theoretical understanding about the charm quark hadronization to understand the origin of collectivity of measured -mesons .

(a)

(b)

(c)

Figure 4: Elliptic flow as a function of in the 30–50% centrality bin, for , , and mesons with the event plane, scalar product, and two-particle cumulant methods [30]. The vertical error bars represent the statistical uncertainty; the open boxes are the systematic uncertainties.

The dependencies of in the three centrality classes 0–10%, 10–30%, and 30–50% are presented in Figure 5 [30]. of charged hadrons are also shown for comparison [31]. Both the measurements are done with the event plane method. For these three centrality classes, meson is comparable in magnitude to that of inclusive charged hadrons. These results indicate that the interactions with the medium constituents transfer information of the azimuthal anisotropy of the system to the charmed particles.

Figure 5: Comparison of meson [30] and charged-particle [31] in three centrality classes as a function of . The vertical error bars represent the statistical uncertainty; the open boxes are the systematic uncertainties.

The STAR experiment at RHIC has also reported the first preliminary results of at mid-rapidity () in Au+Au collision at  GeV using newly installed Heavy-Flavor Tracker (HFT) [32, 47]. The -meson measured by STAR in minimum bias (0–80%) Au+Au collisions at  GeV is shown in Figure 6(a) [32]. Measurements are done at mid-rapidity (). The blue and black data points are measured using two-particle correlation and event plane method, respectively. Results from both the methods are consistent within statistical uncertainty. is shown by red symbol and calculated using event plane method. azimuthal anisotropy is nonzero for  GeV/c. Figure 6(b) shows the comparison of with other mesons species ( and ). It seems that for  GeV/c is systematically lower than [33] and [34], but one should be very careful while comparing different particle species for a wide centrality bin, for example, 0–80% centrality bin as the production of heavy open charmed meson is more biased towards central collisions than light hadrons like and [6].

(a)

(b)

Figure 6: (a) The elliptic flow of and meson as a function of in minimum bias (0–80) Au+Au collisions at  GeV [32]. (b) for compared to that of light mesons ( and ) [33, 34]. The vertical error bars represent the statistical uncertainty; the cap symbols are the systematic uncertainties.

4.2. Model Comparisons at LHC Energy

Various observables are compared to theoretical calculations to understand the physical mechanism behind the measurements. In this section, we will discuss the most recent theoretical baseline calculations for the elliptic flow of open charm meson. Simultaneous description of the measured and by theoretical model is a challenging job and is an open issue [26, 35–46, 81, 82]. In Figure 7   (in 30–50% central collisions) and (in 0–20% central collisions) of D mesons (average of , , and ) in Pb-Pb collisions at  TeV is shown and compared to selected model predictions.

Figure 7: -mesons and in 30–50% semicentral Pb-Pb collisions at  TeV and comparison with selected theoretical models [26, 35–46].

4.2.1. Coalescence Based Models

The model by Cao et al. is based on the Langevin approach where the space-time evolution of the medium is modeled using viscous hydrodynamic. In this model, hadronization is done using quark coalescence mechanism. This model describes in central collisions very well but tends to underestimate at low . The model [44], labeled as MC@sHQ+EPOS, Coll+Rad(LPM), is a perturbative QCD (pQCD) model that includes collisional and radiative energy loss mechanisms for heavy quarks. Hadronization is performed via quark recombination in this model. It underestimates the low- suppression but yields a substantial anisotropy (~10) which slightly underestimates observed data. It correctly describes high- suppression. In the TAMU model [26], heavy-quark transport coefficient is calculated within a nonperturbative T-matrix approach. This model includes hydrodynamic medium evolution and quark coalescence as a mechanism of hadronization. This model provides a good description of the observed suppression of D mesons over the entire range. However, it fails to reproduce observed anisotropy for  GeV/c. The Ultrarelativistic Quantum Molecular Dynamics (UrQMD) [45, 46] model is based on a microscopic transport theory where the phase space description of the reactions is important. The hybrid UrQMD model includes a realistic description of the medium evolution by combining hadronic transport and ideal hydrodynamics. Hadronization via quark recombination is implemented. The model describes the measured anisotropy and suppression in the interval  GeV/c but fails to explain the data for very low and high region.

4.2.2. Fragmentation Based Models

In WHDG model, the observed anisotropy results from path-length dependent energy loss and hadronization are performed using vacuum fragmentation function. This model describes in central collisions reasonably well but tends to underestimate at low . BAMPS model is a partonic transport model which includes multiparton scattering based on Boltzmann approach. Like WHDG model, in BAMPS, hadronization is performed using vacuum fragmentation functions. BAMPS model describes both and reasonably well. POWLANG [42, 43] is also a transport model which is based on collisional processes treated within the framework of Langevin dynamics. Hadronization, in this model, is done using vacuum fragmentation functions. This model overestimates the high- suppression and significantly underestimates observed at low .

In summary, models including hadronization of charm quarks from recombination with light quarks from the medium (e.g., TAMU) provide a better description of the data at low transverse momentum.

4.3. Model Comparisons at RHIC Energy

Figure 8 shows and of -meson for 0–80% and 0–10% centrality, respectively, in Au+Au collisions at  GeV with selected theoretical model predictions. The physics of DUKE model by Cao et al. and TAMU is already discussed before. The SUBATECH [49] model based on pQCD calculation with the diffusion coefficient parameter ~2–4. These three models can describe suppression reasonably well; however, DUKE model underestimates measured anisotropy. The TAMU and SUBATECH describe -meson data reasonably well.

Figure 8: -mesons (0–80%) [32, 47] and (0–10%) [48] in Au+Au collisions at  GeV and comparison with selected theoretical models [26, 38, 49].

Figure 9(a) shows comparison between our AMPT model calculations [6] for -meson and measured -meson at 2.76 TeV for 30–50% central collisions by the ALICE experiment. Here is taken to be 1.5 mb and 10 mb with other parameters tuned for LHC data (charged hadron and multiplicity). Previous study shows that 1.5 mb parton-parton scattering cross-section is sufficient to described charged hadron at mid-rapidity for  GeV/c. However, we find that cross-sections of both 1.5 and 10 mb underestimate LHC -meson data. It would be very interesting to see how the data and model behave at low (below 2 GeV/c). Therefore, the results from future ALICE upgrade [83] will be very useful to study both heavy-flavor and charged hadrons at low . Figure 9(b) shows the comparison between with AMPT model predictions at top RHIC energy. AMPT model calculation roughly explains data within large statistical errors.

(a)

(b)

Figure 9: (a) Elliptic flow of meson at mid-rapidity in Pb+Pb collision at  TeV for 30–50% centrality and model predictions from AMPT. Only statistical error is shown for ALICE data. (b) Elliptic flow of meson at midrapidity in 0–80% min-bias Au+Au collision at  GeV and prediction from AMPT. Only statistical error is shown for STAR preliminary data.

5. Elliptic Flow of

meson is bound state of charm () and anticharm () quark. It was discovered independently by two research groups on 11 November 1974 [84, 85]. The importance of this discovery is highlighted by the fact that the subsequent rapid changes in high-energy physics around that time came to be collectively known as the “November Revolution.” In relativistic heavy-ion collisions, can be produced mainly by recombination of charm () and anticharm and/or direct pQCD processes. By measuring anisotropic flow of , one may infer the relative contribution of particles from recombination and from direct pQCD processes. produced from quark recombination will inherit the flow of charm quarks. On the other hand, if is produced from direct pQCD processes, it should have very little . A detailed comparison between experimental measurements and models on will be helpful to understand the production mechanism of .

Figure 10 shows elliptic flow of at mid-rapidity in 0–80% min-bias Au+Au events at  GeV [50] compared with charged hadrons [51] and meson [52] in (a) and with theoretical calculations in (b). is found to be very small in comparison to that of charged hadrons and -meson. Model which include production from coalescence of thermalized [54] give the maximum of to be almost the same in magnitude as light hadrons. of produced from initial pQCD processes [53] is predicted to be very small compared to light hadrons. Models that include production from both initial pQCD process and coalescence mechanism [55, 56] also give much smaller in comparison to light hadrons.

(a)

(b)

Figure 10: Elliptic flow of for particles at mid-rapidity in 0–80% min-bias Au+Au events at  GeV [50] compared with charged hadrons [51] and the meson [52] (a) and theoretical calculations [53–56] (b).

In summary, models that include production from both initial pQCD process and coalescence production or entirely from initial pQCD process describe the data better at top RHIC energy. At this point, it is still unclear and we would need very high precision measurements to estimate the fraction of the total yield that comes from pQCD and coalescence processes.

ALICE collaboration also reported the measurement of the elliptic flow of in Pb-Pb collisions at  TeV within the rapidity range [57]. for noncentral (20–60%) Pb-Pb collisions at  TeV is shown in Figure 11. Unlike RHIC, an indication of nonzero is observed with a maximum value of (stat) (syst) for noncentral (20–60%) Pb-Pb collisions. Calculations from two transport models [56, 86] are also shown for comparison. Transport model calculations that include a regeneration component (30) from deconfined charm quarks in the medium describe data very well.

Figure 11: at forward rapidity () for noncentral (20–60%) Pb-Pb collisions at  TeV [57].

6. Summary and Discussion

In summary, the measurement of elliptic flow of heavy flavor can provide valuable information about the QGP medium. This article reviewed several important results from RHIC and LHC experiments and discussed their implications. In this review article, we have focused on measurements of heavy-flavor as a function of , collision centrality, and energy carried out in RHIC and LHC experiments. We also discussed the comparison of these experimental measurements with available theoretical model predictions.

Measurement of azimuthal anisotropy of nonphotonic electron is discussed at , 62.4, 200 GeV, and 2.76 TeV. NPE is consistent with zero at and 62.4 GeV while it is nonzero at  GeV and 2.76 TeV. Large positive of NPE at low might indicate that charm quarks participate in the collective expansion of the dense and hot QGP. Elliptic flows of open charm -meson measured by STAR and ALICE experiments are presented. A nonzero positive flow has been observed at  GeV and 2.76 TeV. Models that include recombination as mechanism of hadronization explain nonzero positive at low ; however, a simultaneous description of and is still an open issue. We also discussed the elliptic flow of measured at  GeV and 2.76 TeV by STAR (at mid-rapidity) and ALICE (at forward rapidity). flow is consistent with zero at RHIC; however, the measurement is statistically limited. A positive has been observed  TeV. Transport model calculations that include a regeneration component from deconfined charm quarks in the medium describe data very well within current statistical uncertainties.

A precise measurement of heavy-flavor hadrons will provide information on fundamental properties of the medium, such as the transport coefficient and hadronization mechanisms. As we discussed, current heavy-flavor measurements are limited by statistics. In order to circumvent this, recent upgrades have been made in STAR with the introduction of the Heavy-Flavor Tracker (HFT) and Muon Telescope Detector (MTD) and dedicated high statistics run in 2016. We hope to see the results from these soon. The ALICE experiment is also upgrading its detectors to pursue high precision measurements in the heavy-flavor sector [83]. ALICE is upgrading Inner Tracking System (ITS) for better position and momentum resolution with a faster readout using frontier technologies. The upgraded readout data collection rate of ALICE is expected to increase by a factor of 100. With the current set-up of ALICE, the flow analysis of , , and is not accessible in Pb-Pb due to the limited statistics. Among all open charmed mesons, has been considered as quantitative probe for charm quark hadronization. A comparison of and and could be interesting to shed light on heavy-quark dynamics. The new ITS is expected to allow for a precise measurement of the all -mesons down to very low momentum [83].

Competing Interests

The authors declare that there is no conflict of interests regarding the publication of this paper.

Acknowledgments

This work is supported by DOE Grant (Project no. 444025-HU- 206 22446) of Department of Physics and Astronomy, UCLA, USA.

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