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Heavy flavor flow from electron measurements at RHIC

Heavy flavor flow from electron measurements at RHIC. Shingo Sakai (Univ. of California, Los Angeles). Outline. Introduction Non-photonic e v 2 measurement Non-photonic e v 2 D meson v 2 Charm v 2 Outlook (B decay). Elliptic flow.

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Heavy flavor flow from electron measurements at RHIC

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

  2. Outline • Introduction • Non-photonic e v2 measurement • Non-photonic e v2 • D mesonv2 • Charm v2 • 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/fm3], σππ = 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” λ >> R ; Isotropic Y X λ << R ; anisotropic Y X dN/d() = N (1 + 2v2cos(2(φ)))

  4. Elliptic flow @ RHIC Hydro;Phys. Rev. C 67 (03) 044903 v2; Phys.Rev.Lett.91 182301 (2003)PHENIX • In low pT (pT<1.5 GeV/c), • v2 increases with pT, and • show mass dependence v2(π)>v2(K)>v2(p) => hydro model well represents identified particle v2 • assume early time • thermalization τ0 = 0.6 fm/c

  5. v2 already developed in partonic phase ? • identified hadrons v2 after scaling pT and v2 number of quarks • v2 after scaling fall on same curve • v2 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 • D meson measurement => reconstructed from π,K • Electron measurement • photonic - photon conversion - Dalitz decay (π0,η,ω ---) • nonphotonic - Ke3 decay - primarily semileptonic decay of mesons containing c & b

  7. Charm quark yield QM06, F. Kajihara Phys.Rev.Lett.94:082301,2005 (PHENIX) • Non-suppressed charm yield at low pT • => they are initially produced and survived until the end • Non-photonic electron v2 @ low pT does not come from energy loss • => would reflect collective flow • * energy loss also generate non-zero v2

  8. Radial flow of charm meson AuAu Central charm hadron AuAu Central strangeness hadron AuAu Central , K, p • 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 v2 measurement STAR SQM06, Y. Yifei

  9. Non-photonic electron v2 measurement • Non-photonic electron v2 is given as; (1) (2) v2e ; Inclusive electron v2 =>Measure RNP = (Non-γ e) / (γ e) => Measure • v2γ.e ; Photonic electron v2 • Cocktail method (simulation)stat. advantage • Converter method (experimentally)

  10. Photonic e v2 determination v2 (π0) R = N X->e/ Nγe pT<3 ; π (nucl-ex/0608033) pT>3 ; π0 (PHENIX run4 prelim.) decay • photonic electron v2 • => cocktail of photonic e v2 photonic e v2 (Cocktail) • compare inclusive e v2 • with/without converter • (converter only increase • photonic component)

  11. Non-photonic electron v2 dN/d() = N (1 + 2v2cos(2(φ))) Phys. Rev. Lett. 98, 172301 (2007) Non-photonic electron v2 • non-zero non-photonic electron v2 was observed below 3 GeV/c

  12. Non-photonic electron v2 (centrality dep.) • Hydro -> driving force of v2 is pressure gradient (ΔP) • ΔP get large with impact parameter (centrality) => v2 get large with centrality 40-60% 0-20% 20-40% • Non-photonic electron v2 seems like get large with impact parameter

  13. Non-photonic electron v2 (centrality dep.) 1 40-60% 0-20% 20-40% • Non-photonic electron v2 seems like get large with impact parameter • RAA =1 @ peripheral collisions but non-zero v2 • non-photonic e v2 => result of collective flow

  14. D meson v2 • charm →D meson →non-photonic e • non-photonic electron v2 reflect D meson v2 ? • pT<1.0 GeV/c, smeared • by the large mass difference • pT > 1.0 GeV/c, decay • electrons have same • angle of the parents • “non-zero” non-photonic e v2 => indicate non-zero D meson v2 <cos(φe - φD)> simulation Electron pT(GeV/c) Line ; D meson Circle ; electron Phys.Lett.B597 simulation

  15. D v2 estimation • Assumptions • non-photonic electron decay from D meson • D meson v2 ; D v2 = a*f(pT) • f(pT) ; D meson v2 shape • assume various shape • a ; free parameter • (pT independent) • π(PHENIX prelim.) • p (PHENIX prelim.) • k (PHENIX prelim.) • D from scaling(kET=mT-m0) • + ・・・φ f(pT) MC simulation (PYTHIA) e v2 • 　compared with measured v2 • and find “a” range (Χ2 test)

  16. Fitting result χ2 / ndf 1 Pion shape Kaon shape Proton shape a[%] χ2 / ndf • fitting result χ2 / ndf vs. a ndf = 13 1 φshape scale shape a[%]

  17. Expected D meson v2 • D meson v2 expected from non-photonic e v2 • D meson v2 ; Max 0.09±0.03 • D v2 is smaller than pion v2(pT<3 GeV/c)

  18. Charm flow ? • RAA for non-photonic electron； • A large suppression of • high pT electron yield • model predict initial parton • density > 3500 => high parton dense matter • charm mean free path n > 7 fm-3 σ = 3 mb (pQCD) => λcharm < 0.5 fm shorter than R(Au) ~ 6 fm => would expect charm v2 [PLB623] nucl-ex/0611018 (PRL)

  19. Estimation of charm quark v2 (1) Apply coalescence model (2) Assume universal pT dependence of v2 for quark (3)Quarks which have same velocity coales charm D v Quark v2 v2,u = a ×v2,q v2,c = b ×v2,q v u [PRC 68 044901 Zi-wei & Denes] • mu + mc = mD • mu = 0.3 & mc = 1.5 (effective mass) • a,b --- fitting parameter • simultaneous fit to non-γ e v2 , v2K, v2p

  20. Fitting result (1) χ2 minimum result proton v2p = 3(av2,u(3pT,u)) Non-photonic Kaon v2k = 2(av2,u(2pT,u)) • The best fitting (Χ2 minimum) • a = 1, b = 0.96 (χ2/ndf = 21.85/27) v2,u = a ×v2,q v2,c = b ×v2,q

  21. Fitting result (1) χ2 minimum result • the coalescence model well represent • low pT v2 shape • saturate point and value

  22. Fitting result (2) v2,u = a ×v2,q v2,c = b ×v2,q 0.96 a ; u quark 1 • χ2 minimum ; a = 1, b = 0.96 (χ2/ndf = 21.85/27) • Quark coalescence model indicate non-zero charm v2

  23. Charm quark v2 • In the assumptions • Charm quark v2 is non-zero • Charm quark v2 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 [Phys.Lett. B595 202-208] [PRC72,024906] [PRC73,034913] • models support a non-zero charm v2

  25. Charm thermalization ? • Theoretical calculation • [PRC73 034913] • assume D & B resonance • in sQGP => accelerate c & b thermalization time => comparable to τQGP~ 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-D0 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-D0 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 pT pp 200 GeV

  28. RUN4 RUN7 min.bias Bottom quark contribution • B/D = 1.0 (pT>5.0) @ pp but unclear @ AuAu • but their contribution would large at high pT @ AuAu • nonphotonic electron decay from B keeps parent direction • above 3 GeV/c • high pT nonphotonic electon v2 would provide B v2 information • SVT will install in STAR & PHNIX

  29. Summary • Non-photonic electron v2 mainly from charm decay was measured @ s = 200 GeV in Au+Au collisions at RHIC & non-zero v2 is observed • Non-photonic electron v2 is consistent with hydro behavior • Measured non-photonic electron indicate non-zero D meson v2 • Based on a quark coalescence model, the data suggest non-zero v2 of charm quark.

  30. BackUp

  31. Comparison with models; RAA & v2 Nucl-ex/0611018 • Two models describes strong suppression and large v2 • Rapp and Van Hees • Elastic scattering -> small τ • DHQ × 2πT ~ 4 - 6 • Moore and Teaney • DHQ × 2πT = 3~12 • These calculations suggest that small τ and/or DHQare required to reproduce the data.

  32. Constraining h/s with PHENIX data Rapp & Hees private communication • Rapp and van Hees Phys.Rev.C71:034907,2005 • Simultaneously describe PHENIX RAA(E) and v2(e) with diffusion coefficient in range DHQ ×2pT ~4-6 • Moore and Teaney Phys.Rev.C71:064904,2005 • Find DHQ/(h/(e+p)) ~ 6 for Nf=3 • Calculate perturbatively, argue result also plausible non-perturbatively • Combining • Recall e+p = T s at mB=0 • This then gives h/s ~(1.5-3)/4p • That is, within factor of 2 of conjectured bound Moore & Teaney private communication

  33. Additional Remarks • What does DHQ/(h/(e+p)) ~ 6 mean? • Denominator: • DHQ is diffusion length ~ heavy quark diffusion length lHQ • Numerator: • Note that viscosity h ~ n <p> l • n = number density • <p> = mean (thermal) momentum • l = mean free path • “Enthalpy” e + P ~ n <p> • Here P is pressure • So h/(e+P) = (n <p> l) / (n <p> ) ~ l • Note this l is for the medium, i.e., light quarks • Combining gives DHQ/(h/(e+p)) ~ lHQ / l • 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” h/(e+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 ;X0 = 1.7 %) around beam pipe • increase photonic electron yield • Compare electron yield with & without converter • experimentally separate • Non-converter ; Nnc = Nγ+Nnon-γ • Converter ; Nc = R *Nγ+Nnon-γ

  36. Cocktail method • estimate background electron with simulation • sum up all background electrons • Input • π0(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 ; Nnc = Nγ+Nnon-γ Converter ; Nc = R *Nγ+Nnon-γ (1+RNP)v2nc = v2γ + RNPv2non-γ (R+RNP) v2c = Rv2γ + RNPv2non-γ v2non-γ(non-photonic) & v2γ(photonic) is “experimentally” determined ! R --- ratio of electrons with & without converter (measured) RNP --- non-photonic/photonic ratio (measured) v2nc --- inclusive e v2 measured with non-converter run (measured) v2c --- inclusive e v2 measured with converter run (measured)

  38. Outlook for heavy flavor v2 study @ RHIC • new reaction plane detector • good resolution => reduce error from R.P. • J/ψ v2 & high pT non-photonic electron v2 • silicon vertex detector • direct measurement D meson v2 [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)

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