D meson elliptic flow in noncentral Pb-Pb collisions at root(S)(NN)=2.76 TeV

D Meson Elliptic Flow in Noncentral Pb-Pb Collisions at p ffiffiffiffiffiffiffiffiffi s

¼ 2:76 TeV

B. Abelevet al.* (ALICE Collaboration)

(Received 14 May 2013; published 5 September 2013)

Azimuthally anisotropic distributions ofD⁰,D^þ, andD^þmesons were studied in the central rapidity region (jyj<0:8) in Pb-Pb collisions at a center-of-mass energy ffiffiffiffiffiffiffiffi

sNN

p ¼2:76 TeVper nucleon-nucleon collision, with the ALICE detector at the LHC. The second Fourier coefficientv2 (commonly denoted elliptic flow) was measured in the centrality class 30%–50% as a function of theDmeson transverse momentumpT, in the range2–16 GeV=c. The measuredv2ofDmesons is comparable in magnitude to that of light-flavor hadrons. It is positive in the range2< pT<6 GeV=cwith5:7significance, based on the combination of statistical and systematic uncertainties.

DOI:10.1103/PhysRevLett.111.102301 PACS numbers: 25.75.q, 24.10.Nz, 25.75.Ag, 25.75.Dw

Heavy-ion collisions at ultrarelativistic energies are aimed at exploring the structure of nuclear matter at extremely high temperatures and energy densities. Under these conditions, according to quantum chromodynamics (QCD) calculations on the lattice, the confinement of quarks and gluons inside hadrons is no longer effective and a phase transition to a quark-gluon plasma (QGP) occurs [1].

The measurement of anisotropy in the azimuthal distri- bution of particle momenta provides insight into the prop- erties of the QGP medium. Anisotropy in particle momenta originates from the initial anisotropy in the spatial distri- bution of the nucleons participating in the collision. The anisotropy of produced particles is characterized by the Fourier coefficients v_n¼ hcos½nð’_nÞi, where ’ is the azimuthal angle of the particle, and_nis the azimuthal angle of the initial state symmetry plane for thenth har- monic. For noncentral collisions the overlap region of the colliding nuclei has a lenticular shape and the anisotropy is dominated by the second coefficient v2, commonly denoted elliptic flow [2,3].

The v2 values measured at RHIC and LHC can be described by the combination of two mechanisms [2,4–12]. The first one, dominant at low (pT <3 GeV=c) and intermediate (3–6 GeV=c) transverse momentum, is the buildup of a collective expansion through interactions among the medium constituents. Elliptic flow develops mainly in the early stages of this collective expansion, when the spatial anisotropy is large [13–15]. The second mechanism is the path-length dependence of in-medium parton energy loss, due to medium-induced gluon radiation and elastic collisions. This is predicted to give rise to a positivev₂ for hadrons up to largep_T [16,17].

The measurement of the elliptic flow of charmed had- rons provides further insight into the transport properties of the medium. In contrast to light quarks and gluons that can be produced or annihilated during the entire evolution of the medium, heavy quarks are produced predominantly in initial hard scattering processes and their annihilation rate is expected to be small [18]. Hence, the final state heavy- flavor hadrons at all transverse momenta originate from heavy quarks that experienced all stages of the system evolution. At lowpT, charmed hadronv2 offers a unique opportunity to test whether also quarks with large mass (mc1:5 GeV=c²) participate in the collective expansion dynamics and possibly thermalize in the medium [19,20].

Because of their large mass, charm quarks are expected to have a longer relaxation time, i.e., time scale for approach- ing equilibrium with the medium, with respect to light quarks [21]. At low and intermediate p_T, the D meson elliptic flow is expected to be sensitive to the heavy-quark hadronization mechanism. In case of substantial interac- tions with the medium, a significant fraction of low- and intermediate-momentum heavy quarks could hadronize via recombination with other quarks from the bulk of thermal- ized partons [22,23], thus enhancing thev2 of Dmesons with respect to that of charm quarks [20]. In this context, the measurement of D mesonv2 is also relevant for the interpretation of the results on J=c anisotropy [24], becauseJ=c^{’s from}cc(re)combination would inherit the anisotropy of their constituent quarks [25,26]. At highpT, theDmesonv2 can constrain the path-length dependence of parton energy loss, complementing the measurement of the nuclear modification factor R_AA [27], defined as the ratio of the yield in nucleus-nucleus to that observed inpp collisions scaled by the number of binary nucleon-nucleon collisions. A large suppression of the inclusive D meson yield (R_AA0:25) is observed in central Pb-Pb collisions at ffiffiffiffiffiffiffiffi

s_NN

p ¼2:76 TeVforp_T >5 GeV=c[28].

Theoretical models of heavy-quark interactions with the medium constituents predict, for semicentral colli- sions at the LHC, a large v2 (0.1–0.2) for D mesons at

*Full author list given at end of the article.

Published by the American Physical Society under the terms of the Creative Commons Attribution 3.0 License. Further distri- bution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

p_T 2–3 GeV=cand a decrease to about 0.05 at highp_T [29–33]. The elliptic flow of electrons from heavy-flavor decays was measured to be as large as 0.13 in Au-Au collisions at ffiffiffiffiffiffiffiffi

s_NN

p ¼200 GeV[34,35].

In this Letter we present the measurement ofv₂forD⁰, D^þ, andD^þmesons and their antiparticles reconstructed from their hadronic decays at midrapidity (jyj<0:8) in noncentral Pb-Pb collisions at ffiffiffiffiffiffiffiffi

sNN

p ¼2:76 TeV.

The measurement was carried out with the ALICE de- tector at the LHC [36]. Particle reconstruction and identi- fication were based on the detectors of the central barrel, located inside a solenoid magnet, which generates a 0.5 T field parallel to the beam direction.

The detectors used for the reconstruction of the trajec- tories of candidateDmeson decay particles are the inner tracking system (ITS), composed of six cylindrical layers of silicon detectors [37], and the time projection chamber (TPC) [38]. The reconstructed particles are identified on the basis of their specific energy depositiondE=dxin the TPC gas and of their time of flight from the interaction point to the time of flight (TOF) detector. The ITS, TPC, and TOF detectors provide full azimuthal coverage in the pseudorapidity intervaljj<0:9.

The analysis was performed on a sample of Pb-Pb collisions collected in 2011 with an interaction trigger that required coincident signals in both scintillator arrays of the VZERO detector, covering the full azimuth in the regions3:7< <1:7and2:8< <5:1. Events were further selected off-line to remove background from beam- gas interactions, using the time information provided by the VZERO and the neutron zero-degree calorimeters.

Only events with a vertex reconstructed within 10 cm from the center of the detector along the beam line were considered in the analysis. Collisions were classified according to their centrality, determined from the VZERO summed amplitudes and defined in terms of per- centiles of the total hadronic Pb-Pb cross section [39].

TheDmesonv2was measured for events in the central- ity range 30%–50%, where the initial geometrical anisot- ropy and the medium density are large. In this range, the trigger and event selection are fully efficient for had- ronic interactions. The number of selected events in the 30%–50% centrality class was9:510⁶, corresponding to an integrated luminosity ofð6:20:2Þb¹.

The decays D⁰ !K^þ, D^þ!K^þþ, and D^þ!D^0þ, and their charge conjugates, were recon- structed as described in [28,40]. D⁰ and D^þ candidates were formed using pairs and triplets of tracks withjj<

0:8,p_T>0:4 GeV=c, at least 70 associated space points in the TPC, and at least two hits in the ITS, of which at least one should be in either of the two innermost layers.D^þ candidates were formed by combiningD⁰candidates with tracks withjj<0:8,p_T>0:1 GeV=c, and at least three associated hits in the ITS. The selection of tracks with jj<0:8 limits the D meson acceptance in rapidity,

which, depending on p_T, varies fromjyj<0:7for p_T ¼ 2 GeV=ctojyj<0:8forp_T>5 GeV=c.

Dmeson candidates were selected with the same strat- egy as used in [28], in order to increase the statistical significance of the signal with respect to the large back- ground of all possible track combinations. The selection of the decay topology was based on the displacement of the decay tracks from the interaction vertex, the separation between the secondary and primary vertices, and the point- ing of the reconstructed D meson momentum to the primary vertex. The pion and kaon identification in the TPC and TOF detectors was utilized by applying cuts in units of resolution (at 3) around the expected mean values ofdE=dxand time of flight.

The measurement ofv2was performed by correlating the candidateDmeson azimuthal angle,’D, with the anglec2

of the so-called event plane [41], which is an estimator of the direction2of the second-order initial-state symmetry plane. The event plane anglec2was determined from the second harmonic of the azimuthal distribution of the detected charged particles: c2 ¼ ð1=2Þtan¹ðQ2;y=Q2;xÞ, where Q_2;x andQ_2;y are the transverse components of the second order flow vector,Q~2, defined event by event from the azimuthal angles ’i of a sample of N tracks, Q~2 ¼ ðP_N

i¼1wicos2’i;P_N

i¼1wisin2’iÞ. The weights wi correct for nonuniformities in the acceptance and efficiency of the detector, and optimize the event-plane resolution [41]. They are defined as the product of the trackp_Tand the inverse of the probability of reconstructing a particle with azimuthal angle ’_i. The tracks used to compute Q~₂ were required to have at least 50 associated space points in the TPC, 0< <0:8, p_T>150 MeV=c, and distance of closest approach to the primary vertex smaller than 3.2 cm along the beam direction and 2.4 cm in the transverse plane. To avoid auto correlations between theDmesons and the event plane, the angle c2 was recalculated for each candidate after subtracting from theQ~₂vector the contribution from the tracks used to form that particular candidate. A corre- lation of Dmesons with the tracks used to determine the event plane could also originate from other sources, com- monly denoted nonflow, which are not related to the corre- lation with the initial geometry symmetry plane, such as higher-mass particle decays or jets. Their effect was esti- mated to be small with respect to the other uncertainties by repeating the analysis using the event plane determined in a differentregion with the VZERO detector.

D meson candidates were classified in two groups according to their azimuthal angle relative to the event plane (’¼’Dc2): in-plane ( ð=4Þ;ð=4Þ and ð3=4Þ;ð5=4Þ) and out-of-plane ( ð=4Þ;ð3=4Þ andð5=4Þ;ð7=4Þ).

The raw signal yields were extracted in each’andpT

interval by means of a fit to the candidate invariant mass distributions (mass difference MðKÞ MðKÞ for D^þ). The fitting function was the sum of a Gaussian

function to describe the signal and an exponential (forD⁰ andD^þ) or a power-law (forD^þ) function for the back- ground. An example fit is shown in Fig. 1for D⁰ candi- dates. For each meson and in eachp_T interval, the mean and the width of the Gaussian were fixed to those obtained from a fit to the invariant mass distribution integrated over

’, whose signal peak has larger statistical significance.

The raw yields in the two ’ intervals, Nin-plane and N_out-of-plane, were obtained as the integrals over the corre- sponding Gaussian signal functions.v2 was computed as

v2 ¼ 1 R₂

4

N_in-planeN_out-of-plane

N_in-planeþN_out-of-plane

: (1)

The factor=4results from the integration of the second term, 2v2cosð2’Þ, of the dN=d’ distribution in the considered’intervals and the factor1=R2 is the correc- tion for the finite resolution in the estimation of the sym- metry plane 2 via the event plane c2 [41]. R2 was determined from the correlation between the event plane angles calculated from tracks reconstructed in the two sides of the TPC, namely,0:8< <0and0< <0:8. The resulting value is R2 ¼0:80590:0001ðstatÞ 0:024ðsystÞ.

The measuredD meson yield has a contribution from feed-down fromBmeson decays, which amounts to about 10%–20% [28,40], depending on the selection cuts andp_T. Indeed, the Bfeed-down contribution is enhanced by the selection criteria that are more efficient for feed-downD mesons, because their decay vertices are more displaced from the primary vertex. Thus, the measured v2 is a combination of those of promptly produced and of feed- down D mesons. Considering that the elliptic flow is additive, the value for promptly produced D mesons, v^prompt₂ , can be obtained from the measuredv^all₂ as

v^prompt₂ ¼ v^all₂

f_prompt1fprompt

f_prompt v^feed-down

2 ; (2)

where f_promptis the fraction of promptly produced Dme- sons in the measured raw yield andv^feed-down

2 is the elliptic flow of D mesons fromB decays, which depends on the dynamics of beauty quarks in the medium. These two quantities have not been measured. However, as it can be seen in Eq. (2),v^all₂ coincides withv^prompt₂ , independent of f_prompt, ifv^feed-down

2 ¼v^prompt₂ . The assumptionv^feed-down

2 ¼

v^prompt₂ was used to compute the central value of the results for the prompt Dmeson elliptic flow. The systematic un- certainty related to this assumption is discussed below.

The contributions to the systematic uncertainty on the measuredv₂originate from (i) determination ofDmeson yields and their anisotropy relative to the event plane (e.g., 10%–30% in4< p_T<6 GeV=cdepending on the meson species), (ii) nonflow effects and centrality dependence in the event plane resolution (3%), and (iii) B feed-down contribution (typically^þ45₀%).

The first contribution was estimated from the maximum deviation from the centralv₂ value obtained by repeating the yield extraction in each p_T and ’ interval when varying the fit configuration: different fit functions were used for the background; the Gaussian width and mean were left as free parameters in the fit; the yield was defined by counting the histogram entries in the invariant mass region of the signal, after subtracting the background con- tribution estimated from a fit to the side bands.

The v2 result obtained with Eq. (1) was cross-checked by using an independent technique based on fits to the measuredv2 of candidates as a function of their invariant mass, M [42]. Here v2ðMÞ was obtained with methods based on two-particle correlations, namely, the scalar prod- uct [43] and theQcumulants [44].

It was checked that the results were stable against var- iations of the cuts applied for the selection of D meson candidates, and that the reconstruction and selection effi- ciencies from Monte Carlo simulations were compatible for the in-plane and out-of-planeDmesons.

The uncertainty on the correction factorR₂for the event plane resolution has two contributions. The first one is due to the centrality dependence of R2. The averageR2 in the 30%–50% centrality interval was computed assuming that theDmeson yield is uniformly distributed as a function of centrality. A systematic uncertainty of 2% was assigned by comparing this value with an alternative estimation of the average where theR2 values in narrow centrality intervals were weighted with the D meson yields measured in the same intervals. The second contribution to the R2 uncer- tainty arises from the presence of nonflow correlations between the two subevents used to compute the resolution.

The systematic uncertainty was estimated to be of 2.3%

on the basis of the difference to theR₂value obtained using three subevents with a wider pseudorapidity gap, namely, TPC tracks and the signals in the two VZERO detectors.

The systematic uncertainty related to the contribution of D mesons from B decays was assigned by varying the

2) ) (GeV/c π M(K

1.7 1.75 1.8 1.85 1.9 1.95 2

2Entries/15 MeV/c

50 100 150 200 250 300 350 400

450 D⁰→K^-π+and charge conj.

<4 GeV/c 3<pT

ALICE Pb-Pb = 2.76 TeV sNN

Centrality 30-50%

In-plane Out-of-plane

FIG. 1 (color online). Invariant mass distributions forD⁰can- didates and their charge conjugates with3< pT<4 GeV=cfor 9:510⁶Pb-Pb collisions in the 30%–50% centrality class. The distributions are shown separately for the in-plane (open sym- bols) and out-of-plane (closed symbols) intervals of azimuthal angle. The curves show the fit functions as described in the text.

assumption on the elliptic flow of feed-downDmesons in Eq. (2) in the range 0v^feed-down

2 v^prompt₂ , which includes all model predictions [29–32]. The maximum variation corresponds to the case v^feed-down

2 ¼0, which givesv^prompt₂ ¼v^all₂ =fprompt. Hence, the magnitude of the systematic uncertainty due to B feed-down is inversely proportional tof_prompt. We estimatedf_promptas described in [28] using (i)FONLL[45] predictions for promptDandB mesons, (ii)B!DþXdecay kinematics from EVTGEN

[46], (iii) reconstruction and selection efficiencies for prompt and feed-down Dmesons from simulations, and (iv) a hypothesis on the nuclear modification factor of the feed-downDmesons,R^feed-down

AA . The latter factor accounts for the medium-induced modification of thep_T distribu- tion of B mesons. Its contribution was determined by varying the ratioR^feed-down

AA =R^prompt_AA in the range 1–3, moti- vated by the lower value of RAA of prompt D mesons measured by ALICE [28] with respect to preliminary results from the CMS experiment on the RAA of J=c from B decays [47]. The B feed-down uncertainty was defined by the lower limit of the resultingf_prompt range, which depends on theDmeson species andpT. A typical value for this lower limit is 0.68, corresponding to a relative uncertainty onv^prompt₂ of^þ45₀ %.

Figure2shows the measuredv2 as a function ofpTfor D⁰, D^þ, and D^þ mesons in the 30%–50% centrality class. The symbols are positioned horizontally at the aver- agep_Tof reconstructedDmesons, determined as described in [40]. The elliptic flow of the threeDmeson species is consistent within uncertainties. An averagev2, and trans- verse momentum, ofD⁰,D^þ, andD^þwas computed using the statistical uncertainties as weights. The systematic uncertainties were propagated through the averaging pro- cedure, treating the contributions from the event-plane resolution and theB feed-down correction as fully corre- lated among the threeD meson species. The resultingD mesonv2is shown in Fig.3. It is comparable in magnitude to that of charged particles, dominated by light-flavor

hadrons [11]. The average of the measured D meson v₂ values in the interval 2< p_T<6 GeV=c is 0:204 0:030ðstatÞ 0:020ðsystÞ^þ0:092₀ (B feed-down), which is larger than zero with5:7significance. This result indicates that the interactions with the medium constituents transfer to charm quarks information on the azimuthal anisotropy of the system, suggesting that low momentum charm quarks take part in the collective motion of the system. A positivev₂is also observed forp_T>6 GeV=c, which most likely originates from the path-length depen- dence of the partonic energy loss, although the large uncer- tainties do not allow for a firm conclusion.

In summary, we have presented the first measurement of the D meson elliptic flow coefficient v2 for semicentral Pb-Pb collisions at ffiffiffiffiffiffiffiffi

sNN

p ¼2:76 TeV. A positive elliptic flow, with 5:7 significance in 2< pT<6 GeV=c, is observed. This v2 measurement, together with the observed large suppression of D mesons in central

2 4 6 8 10 12 14 16 18

2v

-0.2 0 0.2 0.4 0.6

= 2.76 TeV sNN

Pb-Pb,

Centrality 30-50%

D0 0 , Prompt D

|y|<0.8 ALICE

2 4 6 8 10 12 14 16 18

Prompt D±

|y|<0.8

2 4 6 8 10 12 14 16 18

Prompt D*±

|y|<0.8

Open box: syst. from data Shaded box: syst. from B feed-down

(GeV/c)

pT p_T (GeV/c) (GeV/c)

pT

FIG. 2 (color online). v2 as a function ofpT for prompt D⁰,D^þ, andD^þ mesons for Pb-Pb collisions in the centrality range 30%–50%. The central value was obtained with the assumption v^feed-down

2 ¼v^prompt₂ . Vertical error bars represent the statistical uncertainty, empty boxes the systematic uncertainty due to theDmeson anisotropy measurement and the event-plane resolution, and shaded boxes show the uncertainty from the contribution ofDmesons fromBfeed-down.

(GeV/c) pT

0 2 4 6 8 10 12 14 16 18

2v

-0.2 0 0.2 0.4

|>2}

η

∆ {EP,|

v2

Charged particles,

2{EP}

v average, |y|<0.8, , D*+

,D+

Prompt D0

Syst. from data Syst. from B feed-down

= 2.76 TeV sNN

Pb-Pb,

Centrality 30-50%

ALICE

FIG. 3 (color online). Average ofD⁰,D^þ, and D^þ v2 as a function ofpT, compared to charged-particlev2[11] measured with the event plane (EP) method. The symbols are positioned horizontally at the averagepT of the threeDmeson species.

collisions [28], provides a stringent constraint to theoreti- cal models describing the interaction of heavy quarks with the medium.

The ALICE Collaboration would like to thank all its engineers and technicians for their invaluable contributions to the construction of the experiment and the CERN ac- celerator teams for the outstanding performance of the LHC complex. The ALICE Collaboration would like to thank M. Cacciari for providing the pQCD predictions used for the feed-down correction. The ALICE Collaboration acknowledges the following funding agen- cies for their support in building and running the ALICE detector: State Committee of Science, World Federation of Scientists (WFS) and Swiss Fonds Kidagan, Armenia, Conselho Nacional de Desenvolvimento Cientı´fico e Tecnolo´gico (CNPq), Financiadora de Estudos e Projetos (FINEP), Fundac¸a˜o de Amparo a` Pesquisa do Estado de Sa˜o Paulo (FAPESP); National Natural Science Foundation of China (NSFC), the Chinese Ministry of Education (CMOE) and the Ministry of Science and Technology of China (MSTC); Ministry of Education and Youth of the Czech Republic; Danish Natural Science Research Council, the Carlsberg Foundation and the Danish National Research Foundation; The European Research Council under the European Community’s Seventh Framework Programme; Helsinki Institute of Physics and the Academy of Finland; French CNRS- IN2P3, the ‘‘Region Pays de Loire,’’ ‘‘Region Alsace,’’

‘‘Region Auvergne,’’ and CEA, France; German BMBF and the Helmholtz Association; General Secretariat for Research and Technology, Ministry of Development, Greece; Hungarian OTKA and National Office for Research and Technology (NKTH); Department of Atomic Energy and Department of Science and Technology of the Government of India; Istituto Nazionale di Fisica Nucleare (INFN) and Centro Fermi–

Museo Storico della Fisica e Centro Studi e Ricerche

‘‘Enrico Fermi,’’ Italy; MEXT Grant-in-Aid for Specially Promoted Research, Japan; Joint Institute for Nuclear Research, Dubna; National Research Foundation of Korea (NRF); CONACYT, DGAPA, Me´xico, ALFA-EC and the EPLANET Program (European Particle Physics Latin American Network) Stichting voor Fundamenteel Onderzoek der Materie (FOM) and the Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO), Netherlands; Research Council of Norway (NFR); Polish Ministry of Science and Higher Education; National Authority for Scientific Research—NASR (Autoritatea Nat¸ionala˘ pentru Cercetare S¸tiint¸ifica˘–ANCS); Ministry of Education and Science of Russian Federation, Russian Academy of Sciences, Russian Federal Agency of Atomic Energy, Russian Federal Agency for Science and Innovations and The Russian Foundation for Basic Research; Ministry of Education of Slovakia; Department of Science and Technology, South Africa;CIEMAT, EELA,

Ministerio de Economı´a y Competitividad (MINECO) of Spain, Xunta de Galicia (Consellerı´a de Educacio´n), CEADEN, Cubaenergı´a, Cuba, and IAEA (International Atomic Energy Agency); Swedish Research Council (VR) and Knut & Alice Wallenberg Foundation (KAW); Ukraine Ministry of Education and Science; United Kingdom Science and Technology Facilities Council (STFC); The United States Department of Energy, the United States National Science Foundation, the State of Texas, and the State of Ohio.

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