1. Perspective for the measurement of D + v 2 in the ALICE central barrel Elena Bruna, Massimo Masera, Francesco Prino INFN – Sezione di Torino ECT*, Heavy Flavour workshop, Trento, September 8th 2006

2. 2 Physics motivation

3. 3 Experimental 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

4. 4 Sources of charmed meson v 2 Elliptic flow  Collective motion superimposed on top of the thermal motion Driven by anisotropic pressure gradients originating from the almond-shaped overlap zone of the colliding nuclei in non-central collisions  Requires strong interaction among constituents to convert the initial spatial anisotropy into an observable momentum anisotropy  Probes charm thermalization IN PLANE OUT OF PLANE

5. 5 Charm flow - 1st idea Batsouli at al., Phys. Lett. B 557 (2003) 26  Both pQCD charm production without final state effects (infinite mean free path) and hydro with complete thermal equilibrium for charm (zero mean free path) are consistent with single-electron spectra from PHENIX  Charm v 2 as a “smoking gun” for hydrodynamic flow of charm D from PYTHIA D from Hydro B from PYTHIA B from Hydro e from PYTHIA e from Hydro 130 GeV Au+Au (0-10%)

6. 6 Charm flow and coalescence Hadronization via coalescence of constituent quarks successfully explains observed v 2 of light mesons and baryons at intermediate p T  hint for partonic degrees of freedom Applying to D mesons:  Coalescence of quarks with similar velocities Charm quark carry most of the D momentum v 2 (p T ) rises slower for asymmetric hadrons ( D, D s )  Non-zero v 2 for D mesons even for zero charm v 2 (no charm thermalization)  Lin, Molnar, Phys. Rev. C68 (2003) 044901

7. 7 IN PLANE OUT OF PLANE Sources of charmed meson v 2 Elliptic flow  Collective motion superimposed on top of the thermal motion Driven by anisotropic pressure gradients originating from the almond-shaped overlap zone of the colliding nuclei in non-central collisions  Requires strong interaction among constituents to convert the initial spatial anisotropy into an observable momentum anisotropy  Probes charm thermalization  BUT contribution to D meson v 2 from the light quark Parton energy loss  Smaller in-medium length L in-plane (parallel to reaction plane) than out- of-plane (perpendicular to the reaction plane)  Drees, Feng, Jia, Phys. Rev. C71, 034909  Dainese, Loizides, Paic, EPJ C38, 461

8. 8 What to learn from v 2 of D mesons? Low/iterm. p T (< 2-5 GeV/c)  Flow is the dominant effect Test recombination scenario Degree of thermalization of charm in the medium  Armesto, Cacciari, Dainese, Salgado, Wiedemann, hep-ph/0511257 Large p T (> 5-10 GeV/c):  Energy loss is the dominant effect Test path-length dependence of in- medium energy loss in an almond- shaped partonic system  Greco, Ko, Rapp PLB 595 (2004) 202 other effects dominant

9. 9 Simulation strategy for D + v 2 in ALICE

10. 10 Measurement of v 2 Calculate the 2nd order coefficient of Fourier expansion of particle azimuthal distribution relative to the reaction plane  The reaction plane is unknown. Estimate the reaction plane from particle azimuthal anisotropy:   n = Event plane (n th harmonic) = estimator of the unknown reaction plane Calculate particle distribution relative to the event plane Correct for event plane resolution  Resolution contains the unknown  RP  Can be extracted from sub-events Unknown reaction plane Event plane resolution

11. 11 Motivation and method GOAL: Evaluate the statistical error bars for measurements of v 2 for D ± mesons reconstructed from their K  decay  v 2 vs. centrality (p T integrated)  v 2 vs. p T in different centrality bins TOOL: fast simulation (ROOT + 3 classes + 1 macro)  Assume to have only signal  Generate N D± (  b,  p T ) events with 1 D ± per event  For each event 1.Generate a random reaction plane (fixed  RP =0) 2.Get an event plane (according to a given event plane resolution) 3.Generate the D + azimuthal angle (φ D ) according to the probability distribution p(φ)  1 + 2v 2 cos [2(φ-  RP )] 4.Smear φ D with the experimental resolution on D ± azimuthal angle 5.Calculate v′ 2 (D + ), event plane resolution and v 2 (D + )

12. 12 D ± statistics (I) ALICE baseline for charm cross-section and p T spectra:  NLO pQCD calculations (  Mangano, Nason, Ridolfi, NPB373 (1992) 295.) Theoretical uncertainty = factor 2-3  Average between cross-sections obtained with MRSTHO and CTEQ5M sets of PDF ≈ 20% difference in  cc between MRST HO and CTEQ5M  Binary scaling + shadowing (EKS98) to extrapolate to p-Pb and Pb-Pb System Pb-Pb (0-5% centr.) p-Pb (min. bias) pp  s NN 5.5 TeV8.8 TeV14 TeV  cc NN w/o shadowing6.64 mb8.80 mb11.2 mb C shadowing (EKS98)0.650.801.  cc NN with shadowing4.32 mb7.16 mb11.2 mb N cc tot 1150.780.16 D 0 +D 0 bar1410.930.19 D + +D - 450.290.06 D s + +D s - 270.180.04 c++c-c++c- 180.120.02

13. 13 D ± statistics (II) N events for 2·10 7 MB triggers N cc = number of c-cbar pairs  MNR + EKS98 shadowing  Shadowing centrality dependence from Emelyakov et al., PRC 61, 044904 D ± yield calculated from N cc  Fraction N D± /N cc ≈0.38 Geometrical acceptance and reconstruction efficiency  Extracted from 1 event with 20000 D ± in full phase space B. R. D ±  K  = 9.2 % Selection efficiency  No final analysis yet  Assume  =1.5% (same as D 0 ) b min -b max (fm)  (%) N events (10 6 ) N cc / ev.D ± yield/ev. 0-33.60.7211845.8 3-6112.28231.8 6-9183.64216.3 9-1225.45.112.54.85 12-18428.41.20.47

14. 14 Event plane simulation Simple generation of particle azimuthal angles (  ) according to a probability distribution  Faster than complete AliRoot generation and reconstruction  Results compatible with the ones in PPR chapter 6.4 PPR chap 6.4 Our simulation

15. 15 Hadron integrated v 2 input values (chosen ≈ 2  RHIC v 2 ) N track = number of , K and p in AliESDs of Hijing events with b = Event plane resolution scenario Event plane resolution depends on v 2 and multiplicity b min -b max N track v2v2 0-31.970000.02 3-64.754000.04 6-97.632000.06 9-1210.613000.08 12-1814.11000.10

16. 16 D ± azimuthal angle resolution From 63364 recontructed D+  200 events made of 9100 D + generated with PYTHIA in -2<y<2 Average  resolution = 8 mrad = 0.47 degrees

17. 17 Simulated results for D + v 2

18. 18 v 2 vs. centrality Error bars quite large  Would be larger in a scenario with worse event plane resolution  May prevent to draw conclusions in case of small anisotropy of D mesons b min -b max N(D ± ) selected  v 2 ) 0-310700.024 3-622700.015 6-919000.016 9-128000.026 12-181250.09 2·10 7 MB events

19. 19 v 2 vs. p T p T limitsN(D ± ) sel  v 2 ) 0-0.51200.06 0.5-12300.05 1-1.53300.04 1.5-23000.04 2-34500.03 3-42100.05 4-82200.05 8-15400.11 p T limitsN(D ± ) sel  v 2 ) 0-0.51400.06 0.5-12800.04 1-1.53900.04 1.5-23600.04 2-35350.03 3-42500.05 4-82650.05 8-15500.11 p T limitsN(D ± ) sel  v 2 ) 0-0.5500.10 0.5-11000.07 1-1.51400.06 1.5-21250.06 2-31900.05 3-4900.07 4-8950.07 8-15200.15 2·10 7 MB events

20. 20 Worse resolution scenario Low multiplicity and low v2 Large contribution to error bar on v 2 from event plane resolution

21. 21 First conclusions about D + v 2 Large stat. errors on v 2 of D ± → K  in 2·10 7 MB events How to increase the statistics?  Sum D 0 →K  and D ± →K  Number of events roughly  2 → error bars on v 2 roughly /√2 Sufficient for v 2 vs. centrality (p T integrated)  Semi-peripheral trigger v 2 vs. p T that would be obtained from 2·10 7 semi-peripheral events ( 6<b<9 ) p T limitsN(D ± ) sel  v 2 ) 0-0.56450.03 0.5-112900.02 1-1.518000.017 1.5-216500.018 2-324700.015 3-411600.02 4-812250.02 8-152200.05

22. 22 How to deal with the background

23. 23 Combinatorial background Huge number (≈10 10 without PID) of combinatorial K  triplets in a HIJING central event  ≈10 8 triplets in mass range 1.84<M<1.90 GeV/c 2 (D ± peak ± 3  ) Final selection cuts not yet defined  Signal almost free from background only for p T > 6 GeV/c  At lower p T need to separate signal from background in v 2 calculation 1 HIJING central event

24. 24 First ideas for background Sample candidate K  triplets in bins of azimuthal angle relative to the event plane (  φ= φ-  2 )  Build invariant mass spectra of K  triplets in  φ bins  Extract number of D ± in  φ bins from an invariant mass analysis Quantify the anisotropy from numbers of D ± in the  φ bins x y 22 D+D+ φ φφ Event plane (estimator of the unknown reaction plane) D meson momentum as reconstructed from the K  triplet produced particles (mostly pions)

25. 25 Analysis in 2 bins of  φ Non-zero v 2  difference between numbers of D ± in-plane and out-of-plane Extract number of D ± in 90º “cones”:  in-plane (-45<  φ<45 U 135<  φ<225)  out-of-plane (45<  φ<135 U 225<  φ<315)

26. 26 Analysis in more bins of  φ 16 Δ φ bins Fit number of D ± vs.  φ with K[1 + 2v 2 cos(2  φ) ] 0<b<33<b<66<b<9 v 2 values and error bars compatible with the ones obtained from

27. 27 Other ideas for background Different analysis methods to provide: 1. Cross checks 2. Evaluation of systematics Apply the analysis method devised for  s by Borghini and Ollitrault [ PRC 70 (2004) 064905 ]  Used by STAR for  s  To be extended from pairs (2 decay products) to triplets (3 decay products) Extract the cos[2(φ-  RP )] distribution of combinatorial K  triplets from:  Invariant mass side-bands  Different sign combinations (e.g. K +  +  + and K -  -  - )

28. 28 Backup

29. 29 Flow = collective motion of particles (due to high pressure arising from compression and heating of nuclear matter) superimposed on top of the thermal motion  Flow is natural in hydrodynamic language, but flow as intended in heavy ion collisions does not necessarily imply (ideal) hydrodynamic behaviour Isotropic expansion of the fireball:  Radial transverse flow Only type of flow for b=0 Relevant observables: p T (m T ) spectra Anisotropic patterns:  Directed flow Generated very early when the nuclei penetrate each other –Expected weaker with increasing collision energy Dominated by early non-equilibrium processes  Elliptic flow (and hexadecupole…) Caused by initial geometrical anisotropy for b ≠ 0 –Larger pressure gradient along X than along Y Develops early in the collision ( first 5 fm/c ) Flow in the transverse plane x y x y z x

30. 30 D s probe of hadronization:  String fragmentation: D s + (cs) / D + (cd) ~ 1/3  Recombination: D s + (cs) / D + (cd) ~ N(s)/N(d) (~ 1 at LHC?) Chemical non-equilibrium may cause a shift in relative yields of charmed hadrons:  Strangeness oversaturation (  s >1) is a signature of deconfinement D s v 2 important test for coalescence models  Molnar, J. Phys. G31 (2005) S421. D s +  K + K -  + : motivation I. Kuznetsova and J. Rafelski

31. 31 Glauber calculations (I) N-N c.s.:   cc from HVQMNR  + shadowing Pb Woods-Saxon

32. 32 Glauber calculations (II) N-N c.s.:   cc from HVQMNR  + shadowing Pb Woods-Saxon

33. 33 Shadowing parametrization  Eskola et al., Eur. Phys. J C 9 (1999) 61.  Emel’yanov et al., Phys. Rev. C 61 (2000) 044904. R g (x~10 -4,Q 2 =5 GeV 2 ) = 65% from EKS98

34. 34 Why elliptic flow ? At t=0: geometrical anisotropy (almond shape), momentum distribution isotropic Interaction among consituents generate a pressure gradient which transform the initial spatial anisotropy into a momentum anisotropy  Multiple interactions lead to thermalization  limiting behaviour = ideal hydrodynamic flow The mechanism is self quenching  The driving force dominate at early times  Probe Equation Of State at early times

35. 35 In-plane vs. out-of-plane Elliptic flow coefficient: v 2 >0 In plane elliptic flow v 2 <0 Out of plane elliptic flow Isotropic V 2 =10% V 2 = - 10%

36. 36 More details on v 2 error bars b min -b max N(D ± ) selected  v 2 ’) RCF  RCF)  v 2 ) (from v2’ + from RCF) 0-310700.02130.8960.0060.024 (= √ (0.024 2 + 0.0002 2 ) 3-622700.01480.97080.00090.015 (= √ (0.015 2 + 0.00001 2 ) 6-919000.01590.97710.00070.016 (= √ (0.016 2 + 0.00003 2 ) 9-128000.0250.9710.0010.026 (= √ (0.026 2 + 0.00006 2 ) 12-181250.0610.650.060.09 (= √ (0.09 2 + 0.002 2 ) b min -b max N(D ± ) selected  v 2 ’) RCF  RCF)  v 2 ) (from v2’ + from RCF) 0-310700.0220.760.0140.029 (= √ (0.029 2 + 0.0002 2 ) 3-622700.0150.9340.0020.016 (= √ (0.016 2 + 0.00007 2 ) 6-919000.0160.9530.0020.017 (= √ (0.017 2 + 0.00006 2 ) 9-128000.0250.9340.0040.027 (= √ (0.027 2 + 0.0002 2 ) 12-181250.0610.570.080.11 (= √ (0.107 2 + 0.02 2 ) High resolution scenario Low resolution scenario

37. 37 Analysis in 2 bins of  φ Extract number of D ± in 90º “cones”:  in-plane (-45<  φ<45 U 135<  φ<225)  out-of-plane (45<  φ<135 U 225<  φ<315)