J/J/ azimuthal anisotropy azimuthal anisotropy relative to the reaction relative to the reaction

plane in Pb-Pb collisions plane in Pb-Pb collisions at 158 AGeV/cat 158 AGeV/c

Francesco PrinoINFN – Sezione di Torino

for the NA50 collaboration

Hard Probes 2008, Illa da Toxa, June 12th 2008

Physics motivationPhysics motivation

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IN PLANE

OUT OF PLANE

Possible sources of J/Possible sources of J/ azimuthal anisotropyazimuthal anisotropy

Flow (= collective motion superimposed on top of the thermal motion) of c quarks Conditions:

c quarks are early-thermalized J/ formed by c-c recombination at freeze-out

Not likely to occur at SPS energies

Anisotropic (= dependent) J/ absorption cc break-up by QGP hard gluons

Wang, Yuan, PLB540 (2002) 62 Zhu, Zhuang, Xu, PLB607 (2005) 207

cc break-up by co-moving particles Heiselberg, Mattiello, PRC60 (1999) 44902

-

-

-

4

Observable: vObservable: v22

....2cos2)cos(212 21

0 RPRP vvN

d

dN

RPv 2cos2

Anisotropy in the observed particle azimuthal distribution due to correlations between the azimuthal angle of the outgoing particles and the direction of the impact parameter

Elliptic flow coefficient 2cos21 2v

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J/J/ anisotropy : models anisotropy : modelsCharmonium break-up on hard gluons present in the deconfined medium Gluon density azimuthally asymmetric in non central collisions

due to the almond shaped overlap region Sets in when the critical conditions for deconfinement are

attained

Measuring J/ v2 may help to constrain models aimed at explaining the anomalous suppression observed in Pb-Pb Zhu, Zhuang, Xu, Phys. Lett. B607 (2005) 207 Wang Yuan, Phys. Lett. B540 (2002) 62

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peripheral central

J/ azimuthal anisotropy (In-In, NA60)

• Limited statistics (<30000 J/ events) prevents a fine binning in centrality/pT

• Define 2 broad centrality classes

v2 consistent with zero for central events, v2 > 0 (2.3) for peripheral

R. Arnaldi, QM2008

Experimental setupExperimental setup

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NA50 setup – year 2000NA50 setup – year 2000

Pb beam Ebeam = 158 GeV/nucleon

Beam detectorsPb target in vacuum thickness = 4 mm

Centrality detectors EM calorimeter (1.1<lab<2.3)

Multiplicity Detector (1.1<lab<4.2)

Zero Degree Calorimeter (lab>6.3)

Muon spectrometer (2.7<lab<3.9) toroidal magnet+MWPC+hodoscopes

Study of muon pair production in Pb-Pb collisionsStudy of muon pair production in Pb-Pb collisions

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Reaction plane estimationReaction plane estimation

Event plane angle n= estimator of the reaction plane angle RP

Exploit anisotropy of produced ET to estimate the reaction plane

n = Fourier harmonic, φi = central azimuth of sextant i, ETi = ET in sextant i

6

1

6

11

cos

sintan

1

ii

iT

ii

iT

n

nE

nE

n

Electromagnetic calorimeter Measures neutral ( and 0 ) ET

Made of Pb and scintillating fibers Distance from target: 20 cm Pseudorapidity coverage: 1.1 < lab < 2.3

Azimuthal segmentation: 6 (60° wide) sextants Radial segmentation: 4 rings

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Event plane resolution - method 1Event plane resolution - method 1Monte Carlo simulation of the calorimeter response Needed input:

Measured v2 of particles in the

calorimeter acceptanceSextant-to-sextant fluctuations

(via an effective MC parameter

tuned on real data)

Result:

NOTE: event plane resolution in flow analyses usually expressed as:

RCF = <cos[2(2-RP)]>

called resolution correction factor RCF = 1 in case of perfect

determination of RP

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Event plane resolution - method 2Event plane resolution - method 2Sub-event method Based on the correlation between the event planes calculated

from two halves of the detector ( Poskanzer, Voloshin, PRC58 (1998) 62) Sub-events defined exploiting the radial segmentation of the

calorimeter (rings)Same energy collected in the 2 sub-eventsRapidity gap to limit non-flow correlation between the sub-eventsEnergy of the excluded ring taken into account when extrapolating to the full

calorimeter resolution

Analysis techniquesAnalysis techniques

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Analysis strategyAnalysis strategyDimuons under the J/ mass peak should be properly accounted Other dimuon sources in J/ mass range ≈ 5-15% (depending on

centrality)

Two kinds of analysis Azimuthal anisotropy from number of J/ in bins of azimuthal angle

2 different methods for subtraction of dimuons under the J/ peak

Azimuthal anisotropy from Fourier coefficient v2

2 different methods to calculate v2

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Number of J/Number of J/ in azimuthal bins in azimuthal bins Method 1 = “Fitting”Method 1 = “Fitting”

Build mass spectra of dimuons in bins of: centrality (ET)

azimuthal angle relative to the event plane (2=dimu-)

Fit to dimuon mass spectra 5 components

J/, ’, DY, open charm, combinatorial background

functional forms from Monte Carlo simulations with detailed description of the NA50 setup

6 free parameters 4 normalizations + J/ mass and

width

Limited by DY statistics.

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Slightly more J/’s observed “in plane”

Anisotropy quantified as:

Elliptic anisotropy from fittingElliptic anisotropy from fittingET

range(GeV)

Nreco(J/) in plane

Nreco(J/) out of plane

10-30 9100 8900

30-50 10700 10500

50-70 10700 10800

70-90 10300 9700

90-120 10900 10700

dNdNN

dNdNN

JJOUT

JJIN

)()(

)()(

4/7

4/5/

4/3

4//

4/5

4/3/

4/

4//

2

2

2

2

2

2

2

2

resolution2Ψperfectofcasein4 2vNN

NN

OUTIN

OUTIN

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Number of J/Number of J/ in azimuthal bins in azimuthal bins Method 2 = “Counting”Method 2 = “Counting”

Build ET spectra of Opposite Sign dimuons with 2.9 < M < 3.3 GeV/c2 in bins of azimuthal angle relative to the event plane and subtract: Combinatorial bck from Like Sign dimuons in 2.9 < M < 3.3 GeV/c2

DY from Opposite Sign dimuons in M > 4.2 GeV/c2

Open Charm from Opposite Sign dimuons in 2.2 < M < 2.6 GeV/c2

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Good agreement between the 2 analysis methodsCounting analysis (not limited by low DY statistics) allows for more centrality bins

Elliptic anisotropy: counting vs. Elliptic anisotropy: counting vs. fittingfitting

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Estimate J/Estimate J/ v v22 Method 1 = “Cosine spectra”Method 1 = “Cosine spectra”

Build cos[2(dimu-2)] spectra of dimuons with 2.9<M<3.3 GeV/c2 in ET (pT) bins

Subtract combinatorial bck, DY and open charm cos[2(dimu-n)] spectra

Calculate v ’2

Same formula as v2 but with the measured event plane 2 instead of the unknown reaction plane RP

Correct for event plane resolution:

|v2| >= |v’2|

)](2cos[

'

2

22

RP

vv

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J/J/ v v22 : from cosine spectra : from cosine spectra

Positive J/ v2 more J/’s exiting in planeErrors: Error bar = statistical error from J/ v2’ (Upper) band = systematic error from event plane resolution

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Estimate J/Estimate J/ v vnn Method 2 = “Fit to NMethod 2 = “Fit to NJ/J/ in azimuthal bins” in azimuthal bins”

Count dimuons in 2.9<M<3.3 GeV/c2 in bins of ET and 2=dimu-2

Subtract combinatorial bck, DY and open charm

Fit with: dN/d2 =A[ 1 + 2 v’2 cos (2·2)] (2 free parameters)

Apply resolution correction factor to go from v’2 to v2

Bad quality fit

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J/J/ v v22 : cosine spectra vs. fits : cosine spectra vs. fits

Errors: Error bar = statistical error from J/ v2’ (Upper) band = systematic error from event plane resolution

Good agreement between the two analysis methods

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Elliptic anisotropy and vElliptic anisotropy and v22 vs. p vs. pTT

No centrality selectionNOTES: (NIN – NOUT) / (NIN + NOUT) = (/4) · v2’ Event plane resolution not accounted for in (NIN – NOUT) / (NIN + NOUT)

Elliptic anisotropy seems to increase with J/ pT

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ConclusionsConclusionsJ/ anisotropy relative to the reaction plane measured in Pb-Pb collisions at 158 A GeV/c from NA50 experiment Event plane from azimuthal distribution of neutral transverse

energy Event plane resolution extracted in 2 independent ways:

from Monte Carlo simulations by adapting the sub-event method to the geometrical segmentation of the NA50

electromagnetic calorimeter

J/ reconstructed from +- decay in the dimuon spectrometer

Elliptic anisotropy results:

Observed a positive (in-plane) J/ v2 = more J/’s “in plane” than “out-of plane”

Observed anisotropy v2 slightly increasing with increasing J/ pT

BackupBackup

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Flow from the NA50 calorimeterFlow from the NA50 calorimeterOriginal method specifically developed for the sextant geometry of the NA50 calorimeter Fourier expansion of ET azimuthal distribution:

limited to 6 terms because there are 6 sextants

an and bn coefficients calculated with Discrete Fourier Transform:

v2 calculated from a2 and b2

b3 used to account for statistical fluctuations

)3sin()2sin()2cos(sincos 322110

bbabaad

dET

6sin

6

6)12(cos

6

1

n

n

Ekn

aTk

kn

6sin

6

6)12(sin

6

1

n

n

Ekn

bTk

kn

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Event plane flatteningEvent plane flatteningEvent plane azimuthal distribution should be flat (isotropic) no preferential direction for the impact parameter

Acceptance correction Flattening by weighting each sextant with the inverse of <ET> measured by

that sextant ( Poskanzer, Voloshin, PRC58 (1998) 62) very small correction (practically uniform calorimeter azimuthal acceptance)

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Electromagnetic calorimeter in the backward rapidity region v1 of pions in the backward region is positive (NA49, WA98)

pions flow in the opposite direction with respect to spectator nucleons

Event plane 1 directed: opposite to the direction of spectator nucleons in the backward hemispherealong the direction of spectator nucleons in the forward hemisphere

v2 of pions in the backward region is positive (NA49, CERES)

event plane 2 directed in plane

z

xProj. spect. nucleons

Target spect. nucleons

pions

pions

Event plane directionEvent plane direction

1

x

y

2

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Directed anisotropy vDirected anisotropy v11

Unexpectedly large directed anisotropy Excess of J/ observed opposite to the event plane direction (i.e.

negative v1) Very large systematic error bar coming from the estimation of the

resolution of the first order event plane

(Part of) this anti-correlation between J/ and 1 directions may be due to momentum conservation effect Event plane 1 not corrected for the momentum taken by the J/

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Cross-checks: shifted ECross-checks: shifted ETT bins bins

< cos[2(dimu-2)] > analysis repeated by shifting the ET bins by half a bin (open circles)

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Cross-checks: ECross-checks: EZDCZDC centrality bins centrality bins

Similar centrality dependence as from ET analysis Exclude a bias from centrality selection

central events ( low EZDC ) peripheral events ( high EZDC )

From <cos>

EMCALO used both for event plane and for centrality determination EZDC independent centrality estimator

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Cross-checks: event-plane flatteningCross-checks: event-plane flattening

Different choices of flattening the event plane do not change significantly vn’ results

From <cos> From <cos>

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J/J/ azimuthal distribution azimuthal distributionJ/ azimuthal angle from reconstructed muon momenta

azimuthal distribution not flat due to acceptance effects

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211

dimu tan

xx

yy

pp

pp