J/  azimuthal anisotropy relative to the reaction plane in Pb-Pb collisions at 158 AGeV/c Francesco Prino INFN – Sezione di Torino for the NA50 collaboration Hard Probes 2008, Illa da Toxa, June 12th 2008

Physics motivation

3 IN PLANE OUT OF PLANE Possible sources of J/  azimuthal 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)

4 Observable: v 2 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

5 J/  anisotropy : models Charmonium 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/  v 2 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

6 peripheral central J/  azimuthal anisotropy (In-In, NA60) Limited statistics (<30000 J/  events) prevents a fine binning in centrality/p T Define 2 broad centrality classes v 2 consistent with zero for central events, v 2 > 0 (2.3  ) for peripheral R. Arnaldi, QM2008

Experimental setup

8 NA50 setup – year 2000 Pb beam  E beam = 158 GeV/nucleon Beam detectors Pb 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 collisions

9 Reaction plane estimation Event plane angle  n = estimator of the reaction plane angle  RP  Exploit anisotropy of produced E T to estimate the reaction plane  n = Fourier harmonic, φ i = central azimuth of sextant i, E T i = E T in sextant i Electromagnetic calorimeter  Measures neutral (  and  0 ) E T  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

10 Event plane resolution - method 1 Monte Carlo simulation of the calorimeter response  Needed input: Measured v 2 of particles in the calorimeter acceptance Sextant-to-sextant fluctuations (via an effective MC parameter tuned on real data)  Result: NOTE: event plane resolution in flow analyses usually expressed as: RCF = called resolution correction factor  RCF = 1 in case of perfect determination of  RP

11 Event plane resolution - method 2 Sub-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-events Rapidity gap to limit non-flow correlation between the sub-events Energy of the excluded ring taken into account when extrapolating to the full calorimeter resolution

Analysis techniques

13 Analysis strategy Dimuons 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 v 2 2 different methods to calculate v 2

14 Number of J/  in azimuthal bins Method 1 = “Fitting” Build mass spectra of dimuons in bins of:  centrality (E T )  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.

15 Slightly more J/  ’s observed “in plane” Anisotropy quantified as: Elliptic anisotropy from fitting E T range (GeV) N reco (J/  ) in plane N reco (J/  ) out of plane

16 Number of J/  in azimuthal bins Method 2 = “Counting” Build E T spectra of Opposite Sign dimuons with 2.9 < M < 3.3 GeV/c 2 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/c 2  DY  from Opposite Sign dimuons in M > 4.2 GeV/c 2  Open Charm  from Opposite Sign dimuons in 2.2 < M < 2.6 GeV/c 2

17 Good agreement between the 2 analysis methods Counting analysis (not limited by low DY statistics) allows for more centrality bins Elliptic anisotropy: counting vs. fitting

18 Estimate J/  v 2 Method 1 = “Cosine spectra” Build cos[2(  dimu -  2 )] spectra of dimuons with 2.9<M<3.3 GeV/c 2 in E T (p T ) bins  Subtract combinatorial bck, DY and open charm cos[2(  dimu -  n )] spectra Calculate v ’ 2  Same formula as v 2 but with the measured event plane  2 instead of the unknown reaction plane  RP Correct for event plane resolution:  |v 2 | >= |v’ 2 |

19 J/  v 2 : from cosine spectra Positive J/  v 2  more J/  ’s exiting in plane Errors:  Error bar = statistical error from J/  v 2 ’  (Upper) band = systematic error from event plane resolution

20 Estimate J/  v n Method 2 = “Fit to N J/  in azimuthal bins” Count dimuons in 2.9<M<3.3 GeV/c 2 in bins of E T and  2 =  dimu -  2  Subtract combinatorial bck, DY and open charm Fit with:  dN/d  2 =A[ v’ 2 cos (2·  2 )] (2 free parameters) Apply resolution correction factor to go from v’ 2 to v 2 Bad quality fit

21 J/  v 2 : cosine spectra vs. fits Errors:  Error bar = statistical error from J/  v 2 ’  (Upper) band = systematic error from event plane resolution Good agreement between the two analysis methods

22 Elliptic anisotropy and v 2 vs. p T No centrality selection NOTES:  (N IN – N OUT ) / (N IN + N OUT ) = (  /4) · v 2 ’  Event plane resolution not accounted for in (N IN – N OUT ) / (N IN + N OUT ) Elliptic anisotropy seems to increase with J/  p T

23 Conclusions J/  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/  v 2 = more J/  ’s “in plane” than “out-of plane”  Observed anisotropy v 2 slightly increasing with increasing J/  p T

Backup

25 Flow from the NA50 calorimeter Original method specifically developed for the sextant geometry of the NA50 calorimeter  Fourier expansion of E T azimuthal distribution: limited to 6 terms because there are 6 sextants  a n and b n coefficients calculated with Discrete Fourier Transform:  v 2 calculated from a 2 and b 2  b 3 used to account for statistical fluctuations

26 Event plane flattening Event 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 measured by that sextant (  Poskanzer, Voloshin, PRC58 (1998) 62 )  very small correction (practically uniform calorimeter azimuthal acceptance)

27 Electromagnetic calorimeter in the backward rapidity region  v 1 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 hemisphere along the direction of spectator nucleons in the forward hemisphere  v 2 of pions in the backward region is positive (NA49, CERES)  event plane  2 directed in plane z x Proj. spect. nucleons Target spect. nucleons pions Event plane direction 11 x y 22

28 Directed anisotropy v 1 Unexpectedly large directed anisotropy  Excess of J/  observed opposite to the event plane direction (i.e. negative v 1 )  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/ 

29 Cross-checks: shifted E T bins analysis repeated by shifting the E T bins by half a bin (open circles)

30 Cross-checks: E ZDC centrality bins Similar centrality dependence as from E T analysis  Exclude a bias from centrality selection central events ( low E ZDC ) peripheral events ( high E ZDC ) From EMCALO used both for event plane and for centrality determination  E ZDC  independent centrality estimator

31 Cross-checks: event-plane flattening Different choices of flattening the event plane do not change significantly v n ’ results From

32 J/  azimuthal distribution J/  azimuthal angle from reconstructed muon momenta  azimuthal distribution not flat due to acceptance effects