1. Heavy flavor flow from electron measurements at RHIC Shingo Sakai (Univ. of California, Los Angeles)

2. Outline Introduction Non-photonic e v 2 measurement Non-photonic e v 2 D meson v 2 Charm v 2 Outlook (B decay)

3. Elliptic flow In non-central collisions, the initial shape is anisotropic The emission pattern is influenced by mean free path  Mean free path λ = (nσ) -1 λ>> R ; isotropic λ<< R ; anisotropic RHIC ; n ~ 4 [1/fm 3 ], σ ππ = 20mb λ ～ 10 -1 fm << R(Au) ～ 6 fm  hydro model ； medium is equilibrium, pressure gradient is larger x than y, and the collective flow is developed in x. second harmonic of the azimuthal distribution => “elliptic flow” dN/d(  ) = N (1 + 2v 2 cos(2(φ))) λ >> R ; Isotropic λ << R ; anisotropic Y X Y X

4. Elliptic flow @ RHIC In low p T (p T <1.5 GeV/c), v 2 increases with p T, and show mass dependence v 2 (π)>v 2 (K)>v 2 (p) => hydro model well represents identified particle v 2 assume early time thermalization τ 0 = 0.6 fm/c Hydro;Phys. Rev. C 67 (03) 044903 v2; Phys.Rev.Lett.91 182301 (2003) PHENIX

5. 52006/5/20 v 2 already developed in partonic phase ? identified hadrons v 2 after scaling p T and v 2 number of quarks v 2 after scaling fall on same curve v 2 already formed in the partonic phase for hadrons made of light quarks (u,d,s)  charm flow => re-scattering is so intense => quark level thermalization

6. Charm study @ RHIC Electron measurement  photonic - photon conversion - Dalitz decay (π 0,η,ω ---)  nonphotonic - Ke3 decay - primarily semileptonic decay of mesons containing c & b D meson measurement => reconstructed from π,K

7. Charm quark yield Phys.Rev.Lett.94:082301,2005 (PHENIX) QM06, F. Kajihara Non-suppressed charm yield at low p T => they are initially produced and survived until the end  Non-photonic electron v 2 @ low p T does not come from energy loss => would reflect collective flow * energy loss also generate non-zero v 2

8. Radial flow of charm meson AuAu Central charm hadron AuAu Central , K, p AuAu Central strangeness hadron  Brast-wave fit to D-meson and single electron and muon from D-meson decay spectra  non-zero collective velocity  further information of charm flow obtain v 2 measurement SQM06, Y. Yifei STAR

9. Non-photonic electron v 2 measurement Non-photonic electron v 2 is given as; v 2 γ.e ; Photonic electron v 2  Cocktail method (simulation) stat. advantage  Converter method (experimentally) v 2 e ; Inclusive electron v 2 => Measure R NP = (Non-γ e) / (γ e) => Measure (1) (2)

10. Photonic e v 2 determination compare inclusive e v 2 with/without converter (converter only increase photonic component) photonic electron v 2 => cocktail of photonic e v 2 R = N X->e / N γe photonic e v 2 (Cocktail) decay v 2 (π 0 ) pT<3 ; π (nucl-ex/0608033) pT>3 ; π 0 (PHENIX run4 prelim.)

11. Non-photonic electron v 2 non-zero non-photonic electron v 2 was observed below 3 GeV/c Non-photonic electron v 2 Phys. Rev. Lett. 98, 172301 (2007) dN/d(  ) = N (1 + 2v 2 cos(2(φ)))

12. 12 Non-photonic electron v 2 (centrality dep.)  Hydro -> driving force of v 2 is pressure gradient (ΔP)  ΔP get large with impact parameter (centrality) => v 2 get large with centrality  Non-photonic electron v 2 seems like get large with impact parameter 0-20%20-40% 40-60%

13. Non-photonic electron v 2 (centrality dep.)  Non-photonic electron v 2 seems like get large with impact parameter  R AA =1 @ peripheral collisions but non-zero v 2  non-photonic e v 2 => result of collective flow 0-20%20-40% 40-60% 1

14. 14 D meson v 2 charm →D meson → non-photonic e non-photonic electron v 2 reflect D meson v 2 ? pT<1.0 GeV/c, smeared by the large mass difference p T > 1.0 GeV/c, decay electrons have same angle of the parents “non-zero” non-photonic e v 2 => indicate non-zero D meson v 2 Line ; D meson Circle ; electron Electron p T (GeV/c) simulation Phys.Lett.B597

15. D v 2 estimation π(PHENIX prelim.) p (PHENIX prelim.) k (PHENIX prelim.) D from scaling(kE T =m T -m 0 ) + ・・・ φ MC simulation (PYTHIA) e v 2 Assumptions  non-photonic electron decay from D meson  D meson v 2 ; D v 2 = a*f(p T ) f(p T ) ; D meson v 2 shape assume various shape a ; free parameter (p T independent) f(p T )  compared with measured v 2 and find “a” range (Χ 2 test)

16. 16 Fitting result fitting result χ 2 / ndf vs. a ndf = 13 χ 2 / ndf Pion shapeKaon shape Proton shape φshapescale shape χ 2 / ndf 1 1 a[%]

17. 17 Expected D meson v 2 D meson v 2 expected from non-photonic e v 2 D meson v 2 ; Max 0.09±0.03 D v 2 is smaller than pion v 2 (p T <3 GeV/c)

18. Charm flow ? R AA for non-photonic electron ； A large suppression of high p T electron yield model predict initial parton density > 3500 => high parton dense matter charm mean free path n > 7 fm -3 σ = 3 mb (pQCD) => λ charm < 0.5 fm shorter than R(Au) ~ 6 fm => would expect charm v 2 nucl-ex/0611018 (PRL) [PLB623]

19. Estimation of charm quark v 2 (1) Apply coalescence model (2) Assume universal pT dependence of v 2 for quark [PRC 68 044901 Zi-wei & Denes] Quark v 2 (3)Quarks which have same velocity coales charm u D v v m u + m c = m D m u = 0.3 & m c = 1.5 (effective mass) a,b --- fitting parameter simultaneous fit to non-γ e v 2, v 2 K, v 2 p v 2,u = a ×v 2,q v 2,c = b ×v 2,q

20. Fitting result (1) χ 2 minimum result  The best fitting (Χ 2 minimum)  a = 1, b = 0.96 (χ 2 /ndf = 21.85/27) v 2,u = a ×v 2,q v 2,c = b ×v 2,q Kaon v 2 k = 2(av 2,u (2p T,u )) proton v 2 p = 3(av 2,u (3p T,u )) Non-photonic

21. Fitting result (1) χ 2 minimum result  the coalescence model well represent low pT v 2 shape saturate point and value

22. Fitting result (2) χ 2 minimum ; a = 1, b = 0.96 (χ 2 /ndf = 21.85/27) Quark coalescence model indicate non-zero charm v 2 a ; u quark 0.96 1 v 2,u = a ×v 2,q v 2,c = b ×v 2,q

23. 23 Charm quark v 2 In the assumptions (1)Charm quark v 2 is non-zero (2)Charm quark v 2 is same as light quarks

24. Compare with models (1) Charm quark thermal + flow (2) large cross section ; ~10 mb (3) Elastic scattering in QGP [PRC72,024906] [PRC73,034913] [Phys.Lett. B595 202-208 ] models support a non-zero charm v 2

25. 25 Charm thermalization ? Theoretical calculation [PRC73 034913] assume D & B resonance in sQGP => accelerate c & b thermalization time => comparable to τ QGP ~ 5 fm/c Strong elliptic flow and suppression for nonphotonic would indicate early time thermaliation of charm

26. Bottom quark contribution  Three independent methods provide B/D @ pp  e-h azm. correlation (STAR)  e-D 0 azm. correlation (STAR)  e-h invariant mass (PHENIX)

27. Bottom quark contribution  Three independent methods provide B/D @ pp  e-h azm. correlation (STAR)  e-D 0 azm. correlation (STAR)  e-h invariant mass (PHENIX) => consistent  Bottom contribution is significant B/D = 1 above 5 GeV/c  pQCD (FONLL) calculation well represent B/D ratio as a function of p T pp 200 GeV

28. Bottom quark contribution RUN4 RUN7 min.bias  B/D = 1.0 (p T >5.0) @ pp but unclear @ AuAu  but their contribution would large at high p T @ AuAu  nonphotonic electron decay from B keeps parent direction above 3 GeV/c  high p T nonphotonic electon v 2 would provide B v 2 information  SVT will install in STAR & PHNIX

29. Summary Non-photonic electron v 2 mainly from charm decay was measured @  s = 200 GeV in Au+Au collisions at RHIC & non-zero v 2 is observed Non-photonic electron v 2 is consistent with hydro behavior Measured non-photonic electron indicate non-zero D meson v 2 Based on a quark coalescence model, the data suggest non-zero v 2 of charm quark.

30. BackUp

31. Comparison with models; R AA & v 2 Nucl-ex/0611018 Two models describes strong suppression and large v 2 Rapp and Van Hees Elastic scattering -> small τ D HQ × 2πT ~ 4 - 6 Moore and Teaney D HQ × 2πT = 3~12 These calculations suggest that small τ and/or D HQ are required to reproduce the data.

32. Constraining  /s with PHENIX data Rapp and van Hees Phys.Rev.C71:034907,2005 Phys.Rev.C71:034907,2005  Simultaneously describe PHENIX R AA (E) and v 2 (e) with diffusion coefficient in range D HQ ×2  T ~4-6 Moore and Teaney Phys.Rev.C71:064904,2005 Phys.Rev.C71:064904,2005  Find D HQ /(  /(  +p)) ~ 6 for N f =3  Calculate perturbatively, argue result also plausible non-perturbatively Combining  Recall  +p = T s at  B =0  This then gives  /s ~(1.5-3)/4   That is, within factor of 2 of conjectured bound Rapp & Hees private communication Moore & Teaney private communication

33. Additional Remarks What does D HQ /(  /(  +p)) ~ 6 mean?  Denominator: D HQ is diffusion length ~ heavy quark diffusion length HQ  Numerator: Note that viscosity  ~ n  n = number density  = mean (thermal) momentum  = mean free path “Enthalpy”  + P ~ n  Here P is pressure So  /(  +P) = (n  / (n ) ~ Note this is for the medium, i.e., light quarks  Combining gives D HQ /(  /(  +p)) ~ HQ / Not implausible this should be of order 6 Notes  Above simple estimates in Boltzmann limit of well-defined (quasi)-particles, densities and mfp’s  The “transport coefficient”  /(  +p) is preferred by theorists because it remains well-defined in cases where Boltzmann limit does not apply (sQGP?)

34. qc & gc cross section

35. Converter method install “photon converter ” (brass ;X 0 = 1.7 %) around beam pipe increase photonic electron yield Compare electron yield with & without converter experimentally separate Non-converter ; N nc = N γ +N non-γ Converter ; N c = R  *N γ +N non-γ

36. Cocktail method estimate background electron with simulation sum up all background electrons Input  π 0 (dominant source) use measured pT @ PHENIX  other source assume mt scale of pi clear enhancement of inclusive electron w.r.t photonic electron

37. Converter method Separate non-photonic & photonic e v2 by using Non-converter run & converter run Non-converter ; N nc = N γ +N non-γ Converter ; N c = R  *N γ +N non-γ (1+R NP )v2 nc = v2 γ + R NP v2 non-γ (R  +R NP ) v2 c = R  v2 γ + R NP v2 non-γ v2 non-γ (non-photonic) & v2 γ (photonic) is “experimentally” determined ! R  --- ratio of electrons with & without converter (measured) R NP --- non-photonic/photonic ratio (measured) v2 nc --- inclusive e v2 measured with non-converter run (measured) v2 c --- inclusive e v2 measured with converter run (measured)

38. Outlook for heavy flavor v 2 study @ RHIC new reaction plane detector  good resolution => reduce error from R.P.  J/ψ v 2 & high pT non-photonic electron v 2 silicon vertex detector  direct measurement D meson v 2 [Silicon vertex detector]

39. Photonic electron subtraction Cocktail subtraction photonic electrons are calculated as cocktail of each sources. [PRL 88, 192303 (2002) ] Converter subtraction Photonic electrons are extracted experimentally by special run with additional converter (X = 0.4 + 1.7%) [PRL 94, 082301 (2005) ] 50 % of e come from non-γ @ high pT (>1.5 GeV/c)