Perspective for the measurement of D + v 2 in the ALICE central barrel

1. Perspective for the measurement of D+ v2 in the ALICE central barrel Elena Bruna, Massimo Masera, Francesco Prino INFN – Sezione di Torino ECT*, Heavy Flavour workshop, Trento, September 8th 2006

2. Physics motivation

3. Experimental observable: v2 • 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. OUT OF PLANE IN PLANE Sources of charmed meson v2 • 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

5. 130 GeV Au+Au (0-10%) D from PYTHIA D from Hydro B from PYTHIA B from Hydro e from PYTHIA e from Hydro 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 v2 as a “smoking gun” for hydrodynamic flow of charm

6. Charm flow and coalescence • Hadronization via coalescence of constituent quarks successfully explains observed v2 of light mesons and baryons at intermediate pT • hint for partonic degrees of freedom • Applying to D mesons: • Coalescence of quarks with similar velocities • Charm quark carry most of the D momentum • v2(pT ) rises slower for asymmetric hadrons ( D, Ds ) • Non-zero v2 for D mesons even for zero charm v2 (no charm thermalization)  Lin, Molnar, Phys. Rev. C68 (2003) 044901

7. OUT OF PLANE IN PLANE Sources of charmed meson v2 • 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 v2 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. What to learn from v2 of D mesons? Large pT (> 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 Low/iterm. pT (< 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  Greco, Ko, Rapp PLB 595 (2004) 202 other effects dominant

9. Simulation strategy for D+ v2 in ALICE

10. Unknown reaction plane Event plane resolution Measurement of v2 • 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: • Yn = Event plane (nth harmonic) = estimator of the unknown reaction plane • Calculate particle distribution relative to the event plane • Correct for event plane resolution • Resolution contains the unknown YRP • Can be extracted from sub-events

11. Motivation and method • GOAL: Evaluate the statistical error bars for measurements of v2 for D± mesons reconstructed from their Kpp decay • v2 vs. centrality (pT integrated) • v2 vs. pT in different centrality bins • TOOL: fast simulation (ROOT + 3 classes + 1 macro) • Assume to have only signal • Generate ND±(Db, DpT) events with 1 D± per event • For each event • Generate a random reaction plane (fixed YRP=0) • Get an event plane (according to a given event plane resolution) • Generate the D+ azimuthal angle (φD) according to the probability distribution p(φ)  1 + 2v2 cos [2(φ-YRP)] • Smear φDwith the experimental resolution on D± azimuthal angle • Calculate v′2(D+), event plane resolution and v2(D+)

12. D± statistics (I) • ALICE baseline for charm cross-section and pT 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 scc between MRST HO and CTEQ5M • Binary scaling + shadowing (EKS98) to extrapolate to p-Pb and Pb-Pb

13. D± statistics (II) • Nevents for 2·107 MB triggers • Ncc = number of c-cbar pairs • MNR + EKS98 shadowing • Shadowing centrality dependence from Emelyakov et al., PRC 61, 044904 • D± yield calculated from Ncc • Fraction ND±/Ncc ≈0.38 • Geometrical acceptance and reconstruction efficiency • Extracted from 1 event with 20000 D± in full phase space • B. R. D± Kpp = 9.2 % • Selection efficiency • No final analysis yet • Assume e=1.5% (same as D0)

14. PPR chap 6.4 Our simulation 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

15. Event plane resolution scenario • Event plane resolution depends on v2 and multiplicity Ntrack = number of p, K and p in AliESDs of Hijing events with b = <b> Hadron integrated v2 input values (chosen ≈ 2  RHIC v2)

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. Simulated results for D+ v2

18. v2 vs. centrality 2·107 MB events • 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

19. v2 vs. pT 2·107 MB events

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

21. First conclusions about D+ v2 • Large stat. errors on v2 of D± → Kpp in 2·107 MB events • How to increase the statistics? • Sum D0→Kp and D±→Kpp • Number of events roughly 2 → error bars on v2 roughly /√2 • Sufficient for v2 vs. centrality (pT integrated) • Semi-peripheral trigger • v2 vs. pT that would be obtained from 2·107 semi-peripheral events ( 6<b<9 )

22. How to deal with the background

23. Combinatorial background • Huge number (≈1010 without PID) of combinatorial Kpp triplets in a HIJING central event • ≈108 triplets in mass range 1.84<M<1.90 GeV/c2 (D± peak ± 3s ) • Final selection cuts not yet defined • Signal almost free from background only for pT > 6 GeV/c • At lower pT need to separate signal from background in v2 calculation 1 HIJING central event 1 HIJING central event

24. D+ Dφ y D meson momentum as reconstructed from the Kpp triplet φ Event plane (estimator of the unknown reaction plane) Y2 x produced particles (mostly pions) First ideas for background • Sample candidate Kpp triplets in bins of azimuthal angle relative to the event plane (Dφ= φ-Y2) • Build invariant mass spectra of Kpp triplets in Dφ bins • Extract number of D± in Dφ bins from an invariant mass analysis • Quantify the anisotropy from numbers of D± in the Dφ bins

25. Analysis in 2 bins of Dφ • Non-zero v2 difference between numbers of D ± in-plane and out-of-plane • Extract number of D± in 90º “cones”: • in-plane (-45<Dφ<45 U 135<Dφ<225) • out-of-plane (45<Dφ<135 U 225<Dφ<315)

26. 0<b<3 3<b<6 6<b<9 v2 values and error bars compatible with the ones obtained from <cos(2Dφ)> Analysis in more bins of Dφ • 16 Δφ bins • Fit number of D± vs. Dφ with K[1 + 2v2cos(2Dφ) ]

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

28. Backup

29. y x y x x z Flow in the transverse plane • 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: pT (mT) 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 )

30. Ds+ K+K-p+ : motivation I. Kuznetsova and J. Rafelski • Ds probe of hadronization: • String fragmentation: Ds+ (cs) / D+ (cd) ~ 1/3 • Recombination: Ds+ (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 (gs>1) is a signature of deconfinement • Ds v2 important test for coalescence models • Molnar, J. Phys. G31 (2005) S421.

31. Glauber calculations (I) • N-N c.s.: • scc from HVQMNR • + shadowing • Pb Woods-Saxon

32. Glauber calculations (II) • N-N c.s.: • scc from HVQMNR • + shadowing • Pb Woods-Saxon

33. Shadowing parametrization • Eskola et al., Eur. Phys. J C 9 (1999) 61. • Emel’yanov et al., Phys. Rev. C 61 (2000) 044904. Rg(x~10-4,Q2=5 GeV2) = 65% from EKS98

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. Elliptic flow coefficient: v2>0 In plane elliptic flow v2<0 Out of plane elliptic flow In-plane vs. out-of-plane Isotropic V2=10% V2= - 10%

36. More details on v2 error bars High resolution scenario Low resolution scenario

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