Longitudinal dependence of open heavy flavor R AA in relativistic heavy-ion collisions
Caio A. G. Prado, Wen-Jing Xing, Shanshan Cao, Guang-You Qin, Xin-Nian Wang
LLongitudinal dependence of open heavy flavor R AA in relativistic heavy-ion collisions Caio A. G. Prado, Wen-Jing Xing, Shanshan Cao,
2, 3
Guang-You Qin,
1, 4 and Xin-Nian Wang
1, 4 Institute of Particle Physics and Key Laboratory of Quark and Lepton Physics ( moe ),Central China Normal University, Wuhan, Hubei, , China Department of Physics and Astronomy, Wayne State University, Detroit, MI , USA Cyclotron Institute and Department of Physics and Astronomy,Texas A&M University, College Station, TX , USA Nuclear Science Division, Lawrence Berkeley National Laboratory, Berkeley, CA , USA (Dated: November 18, 2019)Heavy flavor probes are sensitive to the properties of the quark gluon plasma ( qgp ) producedin relativistic heavy-ion collisions. A huge amount of effort has been devoted to studying differentaspects of the heavy-ion collisions using heavy flavor particles. In this work, we study the dynamicsof heavy quark transport in the qgp medium using the rapidity dependence of heavy flavor ob-servables. We calculate the nuclear modification of B and D meson spectra as well as spectra ofleptons from heavy flavor decays in the rapidity range [ − . , . R AA at finite rapidity. I. INTRODUCTION
The quark gluon plasma ( qgp ) produced in relativis-tic heavy-ion collisions is currently the most perfect fluidin nature [1–5]. Tomographic study of the qgp via jet-medium interaction and jet quenching is one of the mostimportant methods for probing such hot and dense nu-clear matter [6, 7]. Heavy quarks are particularly valu-able probes due to their large masses compared to the qcd scale [8–10]. Since they are mainly created at thevery earliest stages of the collisions, the final state observ-ables from heavy quarks contain cumulative informationof the evolution dynamics of the quark gluon plasma.One of the most common observables pertaining heavyflavor studies is the nuclear modification factor R AA ,which compares the yields in nucleus-nucleus collisionswith proton-proton collisions, giving information on howthe qgp interacts with heavy quarks. In particular, the R AA is important to understand effects that originatefrom the hot qcd matter produced in the collision and itis commonly associated with parton energy loss throughthe dense medium. It is defined as the ratio between theparticle spectrum in nuclei collisions d N AA / d p T , and thespectrum in pp collisions, d N pp / d p T [11]: R AA ( p T , y ) = 1 N d N AA / d p T d y d N pp / d p T d y , (1)in which N is the average number of binary nucleon-nucleon collisions for a given class of AA collisions.For the past several years many studies attempted touse R AA to investigate mechanisms of parton transportand energy loss [12–27]. The nuclear modification factoris often used together with other observables in order toobtain stricter constraints on phenomenological models.The anisotropic flow measurements for heavy flavor lead to the so called R AA × v puzzle [28–31], since many the-oretical model calculation underestimate v though theycan describe R AA . Further studies on the flow coeffi-cients and event-by-event fluctuations as well as eventshape engineering analysis also rely on R AA for an ini-tial constraint of parameters or validation of theoreticalmodels [32–36].Most studies so far mainly focus on the mid-rapidityregime. One may also explore the longitudinal depen-dence of heavy flavor observables which may put stricterconstraints on the currently available models and pro-vide further insight into the dynamics of heavy quarkstransport in the qgp medium. Recent studies along thisdirection focus on the rapidity dependence of the di-rect flow of D mesons [37–40], though a limited rangeof rapidity is used. We can also investigate the nuclearmodification factor which is affected mainly by the pathlength traversed by heavy quarks through the mediumand their initial production spectra. In the forward ra-pidity regime, the medium conditions differ from that atmid-rapidity, as the system is smaller and thus the pathlength is shorter. In addition, initial heavy quark pro-duction spectra in this regime also differ greatly. Thus,by exploring the behaviour of R AA with respect to rapid-ity one can obtain the picture of qgp medium in a widerrange of phase space.In this study, we investigate the longitudinal depen-dence of the R AA of heavy flavor mesons (B and D) aswell as electrons and muons decayed from these parti-cles. We use the three dimensional medium profiles gen-erated from clv isc viscous hydrodynamics code [41] toconstruct averaged qgp backgrounds for different colli-sion setups. On top of the hydrodynamics backgrounds,heavy quarks are sampled and allowed to propagatethrough the medium using a previously developed frame- a r X i v : . [ nu c l - t h ] N ov work implementing a relativistic Langevin equation withgluon radiation and a hybrid fragmentation plus coales-cence model for hadronization [42, 43]. Heavy mesonsare allowed to decay into electrons and muons. Usingthe analysis framework developed for dabm od [32, 35]we obtain our final results and compare with currentlyavailable experimental data. Predictions are made fordifferent rapidity bins in the range of − . < y < . II. ELEMENTS OF THE SIMULATION
In order to simulate the propagation of heavy quarksinside the qgp we use a modified relativistic Langevinequation [42, 43] which incorporates two different pro-cesses of energy loss inside the medium: quasi-elasticscattering with light partons in the plasma and gluonradiation induced by multiple scatterings. The Langevinequation can be described by: [42, 43]d p d t = − η D ( p ) p + ξ + f g , (2)in which the last term f g is added to the originalLangevin equation and corresponds to the recoil forceexerted on the heavy quarks due to the gluon emission.The other two terms of the equation are the drag forceand the thermal force. Here we assume ξ to be inde-pendent of the momentum p and satisfies the followingcorrelation function, (cid:10) ξ i ( t ) ξ j ( t (cid:48) ) (cid:11) = κδ ij δ ( t − t (cid:48) ) (3)where κ is the momentum diffusion coefficient and re-lated to the spatial diffusion coefficient as D = 2 T /κ .For all the calculations presented in this work, the spatialdiffusion coefficient is set as D (2 πT ) = 7 which providesthe best description of the experimental data that will beshown later. The gluon radiation term in Eq. (2) is cal-culated from the probability of a gluon emission duringa fixed time interval, with the gluon emission spectrumgiven by the higher twist formalism [44–46]. More de-tails on the implementation of this improved Langevinapproach can be found in [42, 43].The study of longitudinal dependence of observablesrequires a three dimensional profile of medium evolution.Therefore, we use the (3+1)-dimensional relativistic hy-drodynamics code clv isc [41]. In this work we explorethree different collision systems: Au+Au at √ s NN =200 GeV, Pb+Pb at √ s NN = 2.76 TeV, and Pb+Pb at √ s NN = 5.02 TeV. The hydro simulation is initializedwith a smooth initial condition using the trent o [47]parametrization that mimics the IP-Glasma [48–50] atinitial time τ = 0.6 fm and evolve the medium with an e o s described by lattice qcd calculation: s95 pce , inwhich the system is partially chemically equilibrated [51].During the evolution of hydrodynamics we set the shearviscosity as η/s = 0 .
15, and the system evolves until the freeze-out temperature T FO = 137 MeV is reached. Withthese setups, the hydrodynamic model is able to providegood descriptions of the soft hadron spectra emitted fromthe qgp [41].Heavy quarks are initially sampled within the mediumbefore the hydrodynamic evolution. We determine theinitial positions of the heavy quarks production at τ =0 fm on the transverse plane using the binary collisiondistribution obtained from Monte Carlo Glauber model.The initial momentum distribution of the heavy quarksis calculated using a leading order perturbative qcd cal-culation [52] including flavor excitation and pair produc-tion processes, as well as nuclear shadowing and anti-shadowing effects [43, 53, 54]. Heavy quarks are allowedto propagate freely in the three dimensional space until τ = τ when the hydrodynamical evolution begins. Theywill then transport through the medium and lose energyaccording to the Langevin equation until their hadroniza-tion occurs at the decoupling temperature T d = 165 MeV.The hadronization of heavy quarks uses a hybrid frag-mentation and coalescence model [42, 43]. Heavy mesonsare finally decayed into electrons and muons via pythia . III. NUMERICAL RESULTS
The results for the D meson nuclear modification fac-tor are shown in Fig. 1 for collisions of Au+Au at √ s NN = 200 GeV, Pb+Pb at √ s NN = 2.76 TeV, andPb+Pb at √ s NN = 5.02 TeV. The solid red curves in theplots correspond to the D meson spectra at mid-rapiditywhich are compared with experimental data. We ob-serve a good agreement with cms data for both Pb+Pbcollisions throughout the whole p T range. Since cms data slightly disagree with alice , our results overesti-mate R AA for √ s NN = 2.76 TeV case in comparison with alice data. For the lowest energy collision of Au+Auat √ s NN = 200 GeV our results show consistency withdata from the star experiment for p T ≥ p T regime a complex interplay of different physicalprocesses is expected to occur. One important effect isthe recombination mechanism which tends to dominatethe heavy quark hadronization at this regime.We also show in Fig. 1 predictions for forward rapidity R AA between 1 . < | y | < . . < | y | < . p T at large rapidity, as observed in the toppanel of the figure for the long-dashed green curve. Whenincreasing the rapidity, we observe a larger suppressionat the high p T regime, even though the expected mediumsize in these conditions is smaller. Since R AA not onlydepends on the path length experienced by the partoninside the medium, but also on the initial productionspectra, we expect these two effects to compete in thefinal result. Here, a stronger effect from the initial heavyquark spectra is observed to dominate in this region of p T .Using the same simulation conditions as above, we p T (GeV)0 . . . . R AA D , | y | < . | y | < . . < | y | < . . < | y | < . Au+Au @ 200 GeV
D meson0 10 20 30 40 p T (GeV)0 . . . . R AA D , | y | < . , D + , D ∗ + av., | y | < . | y | < . . < | y | < . . < | y | < . Pb+Pb @ 2.76 TeV p T (GeV)0 . . . . R AA D , | y | < . | y | < . . < | y | < . . < | y | < . Pb+Pb @ 5.02 TeV
FIG. 1. (Color online) Nuclear modification factor of Dmesons for central collisions in different ranges of rapidity.Mid-rapidity results are compared with data from star [55](top), alice [56] and cms [57] (middle), and cms [58] (bot-tom) at their respective collision energies. show in Fig. 2 the results for the B meson R AA . We ob-serve the same trend as the case for D mesons at high p T ,where a larger parton suppression is observed for largerrapidity bins. However, in the case of B mesons we see aclearer separation of the curves at low p T , together witha more evident crossing for p T < p T regimes may be-have differently than that at high p T . Our results areconsistent with previous observations on the π nuclearmodification factor [62], though the crossing points seemto be at lower p T in the case of heavy quarks.After simulation of the heavy meson decays into elec-trons and muons, we can obtain the nuclear modificationfactor for these leptons. In Fig. 3 we show heavy fla-vor electron results. The plots show an additional curvewith a smaller rapidity range of | y | < . p T (GeV)0 . . . . R AA | y | < . . < | y | < . . < | y | < . Au+Au @ 200 GeV
B meson0 10 20 30 40 p T (GeV)0 . . . . R AA | y | < . . < | y | < . . < | y | < . Pb+Pb @ 2.76 TeV p T (GeV)0 . . . . R AA | y | < . . < | y | < . . < | y | < . Pb+Pb @ 5.02 TeV
FIG. 2. (Color online) Nuclear modification factor of Bmesons for central collisions in different ranges of rapidityfor Au+Au at √ s NN = 200 GeV (top), Pb+Pb at √ s NN =2.76 TeV (middle) and Pb+Pb at √ s NN = 5.02 TeV (bottom). compared with data from alice . The top plot of the fig-ure shows good agreement with data from the phenix ,even though the rapidity ranges being compared are notexactly the same. In fact, it is expected that aroundthe mid-rapidity regime, the differences in rapidity havelittle influence on the results. We also observe a goodagreement within error bars for the Pb+Pb collisions at p T (cid:38) √ s NN = 2.76 TeV which is consistentwith the previous result for D mesons in comparison with alice in Fig. 1. However, overall agreement are observedat both mid and large rapidities.In addition to the mid-rapidity results, Fig. 3 also in-cludes forward rapidity predictions for heavy flavor elec-trons. These results reflect what has already been ob-served for D and B mesons as we see an increase of sup-pression for large p T electrons with large rapidity. We p T (GeV)0 . . . . R AA e ± ← b , c, | y | < .
35 (PHENIX) | y | < . | y | < . . < | y | < . . < | y | < . Au+Au @ 200 GeV
Heavy flavor electron0 5 10 15 20 p T (GeV)0 . . . . R AA e ± ← b , c, | y | < . | y | < . | y | < . . < | y | < . . < | y | < . Pb+Pb @ 2.76 TeV p T (GeV)0 . . . . R AA e ± ← b , c, | y | < . | y | < . | y | < . . < | y | < . . < | y | < . Pb+Pb @ 5.02 TeV
FIG. 3. (Color online) Nuclear modification factor of heavyflavor electrons for central collisions in different ranges of ra-pidity. Mid-rapidity results are compared with data from phenix [59] (top), alice [60] (middle), and alice [61] (bot-tom) at their respective collision energies. also note the crossing between spectra with different ra-pidities at low p T for Pb+Pb collisions.By simulating the heavy flavor mesons to decay intomuons, we obtain the results shown in Fig. 4. We com-pare our forward rapidity results, showing in long-dashedgreen curves, with the experimental data for Pb+Pb col-lisions at both √ s NN = 2.76 TeV and √ s NN = 5.02 TeV.The comparison shows good agreement with data for thelarger beam energy at high p T . In particular, by compar-ing Figs. 4 and 3, we can see that for the high p T regimethere should be enough resolution to study the rapiditydependence of heavy flavor R AA by comparing theory cal-culations to data, though the current data error bars arestill large. In addition, heavy flavor muon R AA obtainedfrom the simulation falls slightly bellow the experimentaldata for low p T as is the case with heavy flavor electrons. p T (GeV)0 . . . . R AA | y | < . . < | y | < . . < | y | < . Au+Au @ 200 GeV
Heavy flavor muon0 4 8 12 16 20 p T (GeV)0 . . . . R AA µ ± ← b , c, 2 . < | y | < . | y | < . . < | y | < . . < | y | < . Pb+Pb @ 2.76 TeV p T (GeV)0 . . . . R AA µ ± ← b , c, 2 . < | y | < . | y | < . . < | y | < . . < | y | < . Pb+Pb @ 5.02 TeV
FIG. 4. (Color online) Nuclear modification factor of heavyflavor muons for central collisions in different ranges of ra-pidity for Au+Au at √ s NN = 200 GeV (top), Pb+Pb at √ s NN = 2.76 TeV (middle) and Pb+Pb at √ s NN = 5.02 TeV(bottom). Results are compared with experimental data from alice [63, 64] at forward rapidity. Despite that, for √ s NN = 2.76 TeV collision, our resultsare consistent with experimental data within error bars,though at this p T interval, different rapidity bins are alsoindistinguishable. Finally, the nuclear modification fac-tor for Au+Au collisions are predicted in the top panel.Fig. 5 shows the rapidity dependence of the nuclearmodification factor for different p T ranges for all the col-lision systems considered so far. In these plots, compar-ing different collision energies shows a widening of the R AA curves with increasing energy. In other words, thegreater the collision energy, the farther from the mid-rapidity regime we observe a deviation on the R AA be-haviour. Another interesting observation is that for twohigher energy Pb+Pb collisions the nuclear modificationfactor is larger at higher p T , while for Au+Au collisions . . Au+Au @ 200 GeV
D meson < p T [ GeV ] < < p T [ GeV ] < < p T [ GeV ] < < p T [ GeV ] < HF electron0 . . R AA Pb+Pb @ 2.76 TeV − − . . . Pb+Pb @ 5.02 TeV − y − FIG. 5. (Color online) Nuclear modification factor for selected p T ranges differential in rapidity for B mesons (left), Dmesons (middle), and heavy flavor electrons (right) in central collision systems of Au+Au √ s NN = 200 GeV (top), Pb+Pb √ s NN = 2.76 TeV (middle), and Pb+Pb √ s NN = 5.02 TeV (bottom). R AA is smaller for larger p T . Again this is due to the ini-tial production spectra of heavy quarks: at the same p T the spectrum is steeper in lower energy nuclear collisions.The above results suggest that measurements of high- p T particles at finite rapidity may put more constraintson the R AA for better understanding of heavy flavortransport inside the qgp . On the other hand, heavy fla-vor production in low p T region can be further tested inthe forward rapidity regime and lower collision energiesdue to its physical complexity. IV. CONCLUSIONS
In this work we couple the (3+1)-dimensional viscoushydrodynamic medium background modeled by clv iscwith a relativistic Langevin equation based transportmodel incorporating both collisional and radiative energyloss of heavy quarks in order to investigate the longi-tudinal dependence of heavy flavor nuclear modificationfactor. We verified the consistency between our imple-mentation in a 3-dimensional setup and the currentlyavailable experimental data at the mid-rapidity regimefor different collision energies. Muon data at finite rapid-ity were also used to further validate our model. Withour simulation, we provided predictions for forward ra-pidity R AA of heavy flavor mesons and leptons for threedifferent collision energies. We find that the smaller sizeof the medium at larger rapidity and the steeper initial spectra of heavy quarks at larger rapidity compete witheach other. In the end, heavy quarks display small R AA at large rapidity for large p T regime. The nuclear modi-fication behavior at low p T regime is more complex dueto the interplay of the recombination and other physicseffects.Further studies on the longitudinal dependence ofheavy flavor observables are still necessary, in particu-lar, the dependence of flow coefficients coupled with R AA may provide more sensitive constraints on phenomeno-logical models for better understanding of the quarkgluon plasma. We hope that the predictions presentedin this paper encourage the measurement of finite rapid-ity observables of heavy flavor final state particles withhigher precision. ACKNOWLEDGMENTS
This work is supported in part by the Natural Sci-ence Foundation of China ( nsfc ) under Grant Nos. , , and , bythe China Scholarship Council ( csc ) under GrantNo. , by the U.S. Department of En-ergy ( doe ) under grant Nos. DE-AC02-05CH11231 and
DE-SC0013460 , and by the U.S. Natural Science Foun-dation ( nsf ) under grant No.
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