Directed flow of charged particles at midrapidity relative to the spectator plane in Pb-Pb collisions at root s(NN)=2.76TeV

Directed Flow of Charged Particles at Midrapidity Relative to the Spectator Plane in Pb-Pb Collisions at p ffiffiffiffiffiffiffiffi s

¼ 2:76 TeV

B. Abelevet al.* (ALICE Collaboration)

(Received 18 June 2013; published 6 December 2013)

The directed flow of charged particles at midrapidity is measured in Pb-Pb collisions at ffiffiffiffiffiffiffiffi sNN

p ¼

2:76 TeVrelative to the collision symmetry plane defined by the spectator nucleons. A negative slope of the rapidity-odd directed flow component with approximately 3 times smaller magnitude than found at the highest RHIC energy is observed. This suggests a smaller longitudinal tilt of the initial system and disfavors the strong fireball rotation predicted for the LHC energies. The rapidity-even directed flow component is measured for the first time with spectators and found to be independent of pseudorapidity with a sign change at transverse momentapTbetween 1.2 and1:7 GeV=c. Combined with the observation of a vanishing rapidity-evenpT shift along the spectator deflection this is strong evidence for dipolelike initial density fluctuations in the overlap zone of the nuclei. Similar trends in the rapidity-even directed flow and the estimate from two-particle correlations at midrapidity, which is larger by about a factor of 40, indicate a weak correlation between fluctuating participant and spectator symmetry planes. These observations open new possibilities for investigation of the initial conditions in heavy-ion collisions with spectator nucleons.

DOI:10.1103/PhysRevLett.111.232302 PACS numbers: 25.75.q, 25.75.Ld

The goal of the heavy-ion program at the Large Hadron Collider (LHC) is to explore the properties of deconfined quark-gluon matter. Anisotropic transverse flow is sensi- tive to the early times of the collision, when the deconfined state of quarks and gluons is expected to dominate the collision dynamics (see reviews [1–3] and references therein), with a positive (in-plane) elliptic flow as first observed at the Alternating Gradient Synchrotron (AGS) [4,5]. A much stronger flow was subsequently measured at the Super Proton Synchrotron (SPS) [6], Relativistic Heavy Ion Collider (RHIC) [7–9], and recently at the LHC [10–12]. Elliptic flow at RHIC and the LHC is reproduced by hydrodynamic model calculations with a small value of the ratio of shear viscosity to entropy density [13–16].

Despite the success of hydrodynamics in describing the equilibrium phase of matter produced in a relativistic heavy-ion collision, there are still large theoretical uncer- tainties in determination of the initial conditions.

Significant triangular flow measured recently at RHIC [17,18] and LHC [12,19,20] energies has demonstrated [21,22] that initial energy fluctuations play an important role in the development of the final momentum-space anisotropy of the distribution of produced particles.

The collision geometry is illustrated in Fig. 1, which depicts the participant overlap region and spectators as

viewed in (a) the reaction plane and (b) the plane perpen- dicular to the beam. Figure1(a) shows the projectile and target spectators repelled in the reaction (xz) plane from the center of the colliding system along the impact parame- ter (x) direction. An alternative scenario where spectators

FIG. 1 (color online). Sketch of a noncentral heavy-ion colli- sion. See text for description of the figure.

*Full author list given at the 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.

are attracted towards the center of the system is discussed in [23].

The directed flow is characterized by the first harmonic coefficient v₁ in a Fourier decomposition of the particle azimuthal distribution with respect to one of the collision symmetry planes, , as illustrated in Fig. 1(b) and dis- cussed below

v₁ð; p_TÞfg ¼ hcosðÞi: (1) Here ¼ ln½tanð=2Þ, pT, , and are the particle pseudorapidity, transverse momentum, polar, and azimu- thal angles, respectively. The brackets ‘‘h. . .i’’ indicate an average over measured particles in all recorded events.

For a nonfluctuating nuclear matter distribution, the directed flow in the participant zone develops along the impact parameter direction. The collision symmetry requires that the directed flow be an antisymmetric func- tion of pseudorapidity,v^odd₁ ðÞ ¼ v^odd₁ ðÞ. Because of event-by-event fluctuations in the initial energy density of the collision, the participant plane angle (^ð1Þ_PP) defined by the dipole asymmetry of the initial energy density [24,25]

and that of projectile (^p_SP) and target (^t_SP) spectators are different from the geometrical reaction plane angle _RP [xaxis in Fig.1(b)]. As a consequence, the directed flow can develop [24–27] a rapidity-symmetric compo- nent, v^even₁ ðÞ ¼v^even₁ ðÞ, which does not vanish at midrapidity.

The slope ofv^odd₁ as a function of rapidity at AGS [5,28]

and SPS [29,30] energies is driven by the difference between baryon and meson production and shadowing by the nuclear remnants. At higher (RHIC) energies a multiple zero crossing of v^odd₁ with rapidity outside the nuclear fragmentation regions was predicted as a signature of the deconfined phase transition [31,32]. However, the RHIC measurements [33–36] did not reveal such a structure. The magnitude of the directed flow depends on the amount of baryon stopping in the nuclear overlap zone [37]. The two can be related via realistic model calculations, makingv^odd₁ an important experimental probe of the initial conditions in a heavy-ion collision. The initial conditions assumed in model calculations ofv^odd₁ range from incomplete baryon stopping [37], with a positive space-momentum correla- tion, to full nucleon stopping with a tilted [32,38] or rotating [39] source of matter produced in the overlap zone of the nuclei. Model calculations generally agree on the negative sign of thev^odd₁ slope as a function of pseu- dorapidity at RHIC [33–36]. The model predictions for v^odd₁ at the LHC vary from having the same slope as at RHIC but with smaller magnitude [38] to an opposite (positive) slope with significantly larger magnitude [39,40].

The v^even₁ estimated from the two-particle azimuthal correlations at midrapidity for RHIC [41] (see also [25]) and LHC [12,20,42] energies is in approximate agreement with ideal hydrodynamic model calculations [26,27] for

dipolelike [24] energy fluctuations in the overlap zone of the nuclei. Interpretation of the two-particle correlations is complicated due to a possibly large bias from correlations unrelated to the initial geometry (nonflow) and due to the model dependence of the correction procedure for effects of momentum conservation [27]. The directed flow mea- sured relative to the spectator deflection is free from such biases and provides a cleaner probe of the initial conditions in a heavy-ion collision. It also allows for a study of the main features of the dipolelike energy fluctuations such as a vanishing transverse momentum shift of the created system along the direction of the spectator deflection.

Directed flow and its fluctuations also play an important role in understanding effects due to the strong magnetic field in heavy-ion collisions [24] and interpretation of the observed charge separation relative to the reaction plane [43] in terms of the chiral magnetic effect [44].

In this Letter, we report the charged particle directed flow measured relative to the deflection of spectator neu- trons in Pb-Pb collisions at ffiffiffiffiffiffiffiffi

sNN

p ¼2:76 TeV. About13 10⁶ minimum-bias [10] collisions in the 5%–80% central- ity range were analyzed. For the most central (0%–5%) collisions, the small number of spectators does not allow for a reliable reconstruction of their deflection.

Two forward scintillator arrays (VZERO) [45] were used to determine the collision centrality. Charged particles reconstructed in the time projection chamber (TPC) [46]

withpT >0:15 GeV=candjj<0:8were selected for the analysis.

The deflection of neutron spectators was reconstructed using a pair of zero degree calorimeters (ZDC) [47] with 22 segmentation installed 114 m from the interaction point on each side, covering thejj>8:78(beam rapidity) region. A typical energy measured by both ZDCs for 30%–

40% centrality is about 100 TeV [48]. The spectator deflec- tion in the transverse plane was measured with a pair of two-dimensional vectors

Q^t;p ðQ^t;px ; Q^t;py Þ ¼X⁴

i¼1

n_iE^t;p_i X⁴

i¼1

E^t;p_i ; (2) wherep(t) denotes the ZDC on the >0( <0) side of the interaction point,Eiis the measured signal, andni¼ ðxi; yiÞ are the coordinates of the ith ZDC segment. An asymmetry of 0.1% [49] in energy calibration of the two ZDCs and an absolute energy scale uncertainty cancel in Eq. (2). To compensate for the run-dependent variation of the LHC beam crossing position, an event-by-event cor- rectionQ^t;p!Q^t;p hQ^t;pi[3] was applied as a function of collision centrality and transverse position of the colli- sion vertex relative to the center of the ALICE detector.

Experimental values of the correction for the 30%–40%

centrality class are hQ^p_xðyÞi2:0ð1:5Þmm andhQ^t_xðyÞi 1:1ð0:01Þmm.

The directed flow is determined with the scalar product method [3,50]

v₁f^p_SPg ¼ 1ffiffiffi p2

2

4 huxQ^pxi ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi jhQ^txQ^pxij

p þ huyQ^pyi

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi jhQ^tyQ^pyij q

3 5;

v1f^t_SPg ¼ 1ffiffiffi p2

2

4 huxQ^txi ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi jhQ^txQ^pxij

p þ hu_yQ^t_yi

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi jhQ^tyQ^pyij q

3 5;

(3)

where u_x ¼cosandu_y¼sinare defined for charged particles at midrapidity. The odd and even components of the directed flow relative to the spectator plane [¼_SP in Eq. (1)] are then calculated from the equations

v^odd₁ fSPg ¼ ½v1f^p_SPg þv1f^t_SPg=2 (4) and

v^even₁ fSPg ¼ ½v1f^p_SPg v1f^t_SPg=2: (5) Equation (4) defines the sign ofv^odd₁ using the convention used at RHIC [33,34] and implies a positive directed flow [or deflection along the positivex-axis direction in Fig.1(a)]

of the projectile spectators.

The negative correlationshQ^txQ^pxiandhQ^tyQ^pyi[51] indi- cate a deflection of the projectile and target spectators in opposite directions. These correlations are sensitive to a combination of the spectator’s directed flow relative to the reaction plane RP and an additional contribution due to flow of spectators along the fluctuating ^p_SP and ^t_SP directions [see Fig. 1(b)]. The two contributions are not separable using current experimental techniques and both should be considered in theoretical interpretations of the results derived from Eqs. (3)–(5). Given that the transverse deflection of spectators [dspec ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ðhQ^txQ^pxi þ hQ^tyQ^pyiÞ=2 q

] is tiny compared to the ZDC detector position jzZDCj ¼ 114 m along the beam direction, one can make a rough estimate of the corresponding transverse momentum car- ried by an individual spectator:p^spec_T ffiffiffiffiffiffiffiffi

sNN

p ðdspec=zZDCÞ.

The measured d_spec is about 0.67 (0.92) mm [51] for the 5%–10% (30%–40%) centrality class which yieldsp^spec_T 16ð22ÞMeV=c. Correlations hQ^txQ^pyi and hQ^tyQ^pxi in or- thogonal directions, which can be nonzero due to residual detector effects, are less than 5% [51] of those in the aligned directions. The 10%–20% [51] difference between hQ^txQ^pxiandhQ^tyQ^pyifor midcentral collisions is mainly due to a different offset of the beam spot from the center of the ZDCs in plane and perpendicular to the LHC accelerator ring. The corresponding dominant systematic uncertainty is evaluated from the spread of results for different terms in Eq. (3) and estimated to be below 20%. The results obtained with Eq. (3) are consistent with calculations using the event plane method [3]. The results with opposite polarity of the magnetic field of the ALICE detector are consistent within 5%. Variation of the results with the collision centrality estimated with the TPC, VZERO, and silicon pixel detectors [47] and with narrowing the nominal 10 cm range of the collision vertex along the beam

direction from the center of the ALICE detector to 7 cm is less than 5%. Altering the selection criteria for the tracks reconstructed with the TPC resulted in a 3%–5% variation of the results. The systematic error eval- uated for each of the sources listed above were added in quadrature to obtain the total systematic uncertainty of the measurement.

Figure2(a)shows the charged particle directed flow as a function of pseudorapidity for 10%–20%, 30%–40%, and 10%–60% centrality classes. The v^even₁ ðÞ component is found to be negative and independent of . The v^odd₁ ðÞ component exhibits a negative slope as a function of pseudorapidity. This is in contrast to the positive slope expected from the model calculations [39,40] with stronger rotation of the participant zone at the LHC than at RHIC.

Thev^odd₁ ðÞat the highest RHIC energy [34] has the same sign of the slope and a factor of 3 larger magnitude. This is consistent with a smaller tilt of the participant zone in the x-z plane [see Fig. 1(a)] as predicted in [38] for LHC energies. Figure 2(c) compares v^odd₁ with the STAR data [34] for Au-Au collisions at ffiffiffiffiffiffiffiffi

sNN

p ¼200(62) GeV down- scaled by the ratio 0.37 (0.12) of the slope at the LHC to

-0.5 0 0.5 η

1v

-0.5 0 0.5

10-3

×

(a) odd even v1

10-20%

30-40%

10-60% with fit

-0.5 0 0.5 η

〉 Tp〈/〉 xp〈

-0.5 0 0.5

(b)

>0.15 GeV/c ALICE [email protected] pT

T〉

〈p

〉/ px

〈 odd even

10-60% with fit

-0.5 0 0.5 η

1v

-0.5 0 0.5

1 (c) odd v

STAR (scaled) odd v1

>0.15 GeV/c Au-Au 30-60% pT

30-60% with fit

0.37 200GeV

×

0.12 62.4GeV

×

FIG. 2 (color online). (a)v1and (b)hpxi=hpTiversus pseudor- apidity in Pb-Pb collisions at ffiffiffiffiffiffiffiffi

sNN

p ¼2:76 TeV. (c)v^odd₁ com- pared to the STAR data [34] for Au-Au collisions at ffiffiffiffiffiffiffiffi

sNN

p ¼200 (62.4) GeV downscaled by a factor 0.37 (0.12). The statistical (systematic) uncertainties are indicated by the error bars (shaded bands). Lines (to guide the eye) represent fits with a linear (constant) function forv^odd₁ (v^even₁ ).

that at RHIC energy. These ratios indicate a strong viola- tion by a factor of 1.82 (4.55) of the beam rapidity scaling discussed in [36].

Figure 2(b) shows the relative momentum shift hp_xi=hp_Ti hp_Tcosð_SPÞi=hp_Tialong the spectator plane as a function of pseudorapidity. It is obtained by introducing a pT=hpTi weight in front of ux and uy in Eq. (3). The nonzero hp_xi^odd=hp_Ti shift has a smaller magnitude thanv^odd₁ . Thehp_xi^even vanishes which is con- sistent with the dipolelike event-by-event fluctuations of the initial energy density in a system with zero net trans- verse momentum. Disappearance of hpxi at 0 indi- cates that particles produced at midrapidity are not involved in balancing the transverse momentum carried away by spectators.

Figures3(a) and 3(b)present v₁ andhp_xi=hp_Ti versus collision centrality. The odd components were calculated by taking values at negativewith an opposite sign. Both v1 components have weak centrality dependence. The hpxi^even component is zero at all centralities, while hpxi^odd=hpTi is a steeper function of centrality thanv^odd₁ . This suggests that v^odd₁ has two contributions. The first contribution has a similar origin asv^even₁ due to asymmetric dipolelike initial energy distribution. The second contribu- tion grows almost linearly from central to peripheral

collisions and represents an effect of sideward collective motion of particles at nonzero rapidity due to expansion of the initially tilted source. This hp_xiis balanced by that of the particles produced at opposite rapidity and in very forward (spectator) regions. The magnitude ofv^odd₁ at the LHC is significantly smaller than at RHIC with a similar centrality dependence [see Fig.3(c)].

Figure4(a)presents v₁ as a function ofp_T. Both com- ponents change sign around p_T between 1.2 and 1:7 GeV=c which is expected for the dipolelike energy fluctuations when the momentum of the low p_T particles is balanced by those at high pT [24–27]. The pT depen- dence of v^even₁ relative to SP is similar to that of v^even₁ relative to^ð_PP^1Þestimated from the Fourier fits of the two- particle correlations [12,20,42], while its magnitude is smaller by a factor of 40 [27,52]. This can be interpreted as a weak correlation,hcosð^ð_PP^1ÞSPÞi 1, between the orientation of the participant and spectator collision sym- metry planes. Compared to the RHIC measurements in Fig. 4(b), v^odd₁ shows a similar trend including the sign change aroundp_Tof1:5 GeV=cin central collisions and a negative value at allpT for peripheral collisions.

According to hydrodynamic model calculations [24,27,53] particles with lowpT should flow in the direc- tion opposite to the largest density gradient. This, together with the negative even and oddv1 components relative to SPmeasured for particles at midrapidity with low trans- verse momentum (pT &1:2 GeV=c) allows one, in prin- ciple, to determine if spectators deflect away from or towards the center of the system. However, a detailed

centrality percentile

10 20 30 40 50 60 70 80

1v

-0.5 0

10-3

×

>0.15 GeV/c

|<0.8 pT

η ALICE [email protected] |

odd even

(a)

v1

centrality percentile

10 20 30 40 50 60 70 80

〉 Tp〈/〉 xp〈

-0.5 0

odd even

(b)

T〉

〈p

〉/ px

〈

Centrality percentile

0 10 20 30 40 50 60 70 80

1v

-0.5 0

(c)

STAR (scaled) odd v1

ALICE odd v1

0.37 Au-Au@200GeV

×

0.12 Au-Au@62GeV

×

FIG. 3 (color online). (a)v1and (b)hpxi=hpTiversus central- ity. (c)v^odd₁ comparison with STAR data [34]. See text and Fig.2 for description of the data points.

, GeV/c pT

0.5 1 1.5 2 2.5 3 3.5 4 4.5

1v

0 2

10-3

×

|<0.8 η ALICE [email protected] | odd even v1

(a)

5-80%

polynomial fits

(GeV/c) pT

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

1v

0 2

ALICE odd v1

|<1.3 (b) η Au-Au@200GeV | STAR (scaled) odd v1

5-40%

40-80%

0.37 5-40%

×

0.37 40-80%

×

FIG. 4 (color online). (a) v1 versus transverse momentum.

(b)v^odd₁ comparison with STAR data [34]. See text and Fig.2 for description of the data points. Lines (to guide the eye) represent fits with a third order polynomial.

theoretical calculation of the correlation between fluctua- tions in the spectator positions and energy density in the participant zone such as in [23] is required to provide a definitive answer to this question.

In summary, thev^odd₁ andv^even₁ components of charged particle directed flow at midrapidity, jj<0:8, are mea- sured relative to the spectator plane for Pb-Pb collisions atffiffiffiffiffiffiffiffi

sNN

p ¼2:76 TeV. The v^odd₁ has a negative slope as a function of pseudorapidity with a magnitude about 3 times smaller than at the highest RHIC energy. This suggests a smaller tilt of the medium created in the participant zone at the LHC, with insufficient rotation to alter the slope of v^odd₁ ðÞ as predicted in [39,40]. As a function of p_T,v^odd₁ andv^even₁ cross zero atpT between 1.2 and1:7 GeV=cfor semicentral collisions. Disappearance ofhpxifor particles produced close to zero rapidity suggest that they do not play a role in balancing the pT kick of spectators. The shape of v^even₁ ðp_TÞ and a vanishing hp_xi^even is consistent with dipolelike fluctuations of the initial energy density in the participant zone. A similar shape but with about 40 times larger magnitude was observed for an estimate of v^even₁ ðpTÞrelative to the participant plane from the Fourier fits of the two-particle correlation [12,20,42]. This indi- cates that fluctuating participant and spectator collision symmetry planes are weakly correlated, which is important experimental input for modeling the ill-constrained initial conditions of a heavy-ion collision. Future studies of the directed flow at midrapidity using identified particles and extension of the v1 measurements to forward rapidities should provide a stronger constraint on the effects of initial density fluctuations in the formation of directed flow.

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 accelerator teams for the outstanding performance of the LHC complex. The ALICE Collaboration acknowledges the following funding agencies 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); USA Department of Energy, USA National Science Foundation, the State of Texas, and the State of Ohio.

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