1. M. Djordjevic 1 Heavy Quark Energy Loss in Nucleus-Nucleus Collisions Magdalena Djordjevic The Ohio State University

2. M. Djordjevic 2  Jet Quenching of light partons strongly suggest that QGP is discovered.  Further tests of jet tomography using heavy quarks could be decisive as a complementary test of the theory. However, single electron measurements are available. Is the QGP already discovered at RHIC? Heavy ion physics has a goal to form and observe a QGP. Heavy mesons not yet measured at RHIC.

3. M. Djordjevic 3 1997 Shuryak argued that heavy quarks will have large energy loss in QGP => large suppression of heavy mesons. 2001 Dokshitzer and Kharzeev proposed “dead cone” effect => heavy quark small energy loss What value of heavy quark suppression we can expect at RHIC? 

4. M. Djordjevic 4 Significant reduction at high pT suggest sizable energy loss! Single electron suppression measurements at RHIC V. Greene, S. Butsyk, QM2005 talksJ. Dunlop, J. Bielcik; QM2005 talks Can this be explained by the energy loss in QGP?

5. M. Djordjevic 5 Outline 1)Radiative energy loss mechanisms. 2)Heavy meson (D and B) and single electron suppression. 3)B mesons can not be neglected in the computation of single electron spectra. 4)Radiative energy loss alone can not explain the experimental data. 5)Inclusion of elastic energy loss as a solution?

6. M. Djordjevic 6 1) Initial heavy quark pt distributions 2) Heavy quark energy loss 3) c and b fragmentation functions into D, B mesons 4) Decay of heavy mesons to single e -. D, B 1) production 2) medium energy loss 3) fragmentation c, b Single electron suppression e-e- 4) decay

7. M. Djordjevic 7 To compute the initial charm and beauty pt distributions we applied the MNR code (Mangano et al. Nucl.Phys.B373,295(1992)). Parameters values from R.Vogt, Int.J.Mod.Phys.E 12,211(2003). Initial heavy quark pt distributions

8. M. Djordjevic 8 Radiative heavy quark energy loss Three important medium effects control the radiative energy loss: 1)Ter-Mikayelian effect (M. D. and M. Gyulassy, Phys. Rev. C 68, 034914 (2003)) 2)Transition radiation (M. D., to be published). 3)Energy loss due to the interaction with the medium (M. D. and M. Gyulassy, Phys. Lett. B 560, 37 (2003); Nucl. Phys. A 733, 265 (2004)) c L c 1) 2) 3)

9. M. Djordjevic 9 Ter-Mikayelian effect This is the non-abelian analog of the well known dielectric plasmon effect  (k  pl  ~ gT. In pQCD vacuum gluons are massless and transversely polarized. However, in a medium the gluon propagator has both transverse (T) and longitudinal (L) polarization parts. T L vacuum

10. M. Djordjevic 10 In order to compute the main order radiative energy loss we calculated |M rad | 2, where M rad is given by Feynman diagram: We used the optical theorem, i.e.: Where M is the amplitude of the following diagram: Dielectric Effect

11. M. Djordjevic 11 The Ter-Mikayelian effect thus tends to enhance the yield of high p T charm quarks relative to the vacuum case. Comparison between medium and vacuum 0 th order in opacity fractional energy loss  Longitudinal contribution is negligible.  The Ter-Mikayelian effect on transverse contribution is important, since for charm it leads to ~30% suppression of the vacuum radiation. CHARM

12. M. Djordjevic 12 An additional dielectric effect at 0 th order in opacity. It must be taken into account if the QGP has finite size. Transition radiation occurs at the boundary between medium and the vacuum. Transition radiation c L

13. M. Djordjevic 13 This computation was performed assuming a static medium. To compute the effect we start from work by B.G. Zakharov, JETP Lett.76:201-205,2002.

14. M. Djordjevic 14 Transition & Ter-Mikayelian for charm Two effects approximately cancel each other for heavy quarks. Transition radiation lowers Ter-Mikayelian effect from 30% to 15%.

15. M. Djordjevic 15 Transition radiation provides natural regularization of m=0 light quark energy loss. What about light quarks? Problem: Transition radiation as a solution: Infinite discontinuity

16. M. Djordjevic 16 c c L Energy loss due to the interaction with the medium To compute medium induced radiative energy loss for heavy quarks we generalize GLV method, by introducing both quark M and gluon mass m g. Neglected in further computations. Caused by the multiple interactions of partons in the medium.

17. M. Djordjevic 17 This leads to the computation of the fallowing types of diagrams: + + To compute energy loss to all orders in opacity we use algebraic recursive method described in (GLV,Nucl.Phys.B594(01)).

18. M. Djordjevic 18 Final Result to Arbitrary Order in Opacity (L/ ) n M Q and m g > 0 Hard, Gunion-Bertsch, and Cascade ampl. in GLV generalized to finite M Generalizes GLV M Q = m g =0 (Nucl. Phys. B 594, 2001)

19. M. Djordjevic 19 The numerical results for induced radiative energy loss are shown for first order in opacity. For 10 GeV heavy quark (c, b) jet, thickness dependence is closer to linear Bethe-Heitler like form L 1. This is different than the asymptotic energy quadratic form characteristic for light quarks.

20. M. Djordjevic 20 light Quantitative “dead cone effect” for the heavy quark energy loss

21. M. Djordjevic 21 For 5 GeV heavy quark (c, b) jet, thickness dependence is closer to linear Bethe-Heitler like form, while light quarks are closer to quadratic form. As the jet energy increases charm and light quark energy loss become more similar, while bottom quark remains significantly different. As the jet energy increases, the dead cone effect becomes less important.

22. M. Djordjevic 22 The numerical results can be understood from: 1 st order energy loss can not be characterized only by a “Dead-cone” effect! LPM effects are smaller for heavy than for light quarks! (See Fig. E.3) Results later confirmed by two independent groups: B. W. Zhang, E. Wang and X. N. Wang, Phys.Rev.Lett.93:072301,2004; N. Armesto, C. A. Salgado, U. A. Wiedemann, Phys.Rev.D69:114003,2004.

23. M. Djordjevic 23 Pt distributions of charm and bottom before and after quenching at RHIC Before quenchingAfter quenching To compute the jet quenching we generalized the GLV method (PLB538:282,2002).

24. M. Djordjevic 24 Heavy quark suppression as a function of pt (M. D., M. Gyulassy and S. Wicks, Phys. Rev. Lett. 94, 112301 (2005); Euro Phys. J C 43, 135 (2005). ) Moderate D meson suppression ~ 0.5  0.1 at RHIC.

25. M. Djordjevic 25 Panels show single e - from FONLL (done by R. Vogt). (M. D., M. Gyulassy, R. Vogt and S. Wicks, nucl-th/0507019, to appear Phys. Lett. B (2005)) Single electrons pt distributions before and after quenching at RHIC Before quenching After quenching Bottom dominate the single e - spectrum after 4.5 GeV!

26. M. Djordjevic 26 The ratio of charm to bottom decays to electrons obtained by varying the quark mass and scale factors. Domination of bottom in single electron spectra Done by Simon Wicks.

27. M. Djordjevic 27 Single electron suppression as a function of pt red curves: b  e; blue curves: c  e; black curves: b+c  e; At pt~5GeV, R AA (e - )  0.7  0.1 at RHIC.

28. M. Djordjevic 28 Comparison with single electron data Disagreement with PHENIX preliminary data! dN g /dy=1000

29. M. Djordjevic 29 How can we solve the problem? Reasonable agreement, but the dN g /dy=3500 is not physical! dN g /dy=3500 N. Armesto et al., Phys. Rev. D 71, 054027 (2005)

30. M. Djordjevic 30 Is elastic energy loss important? Elastic and radiative energy losses are comparable! M. G. Mustafa, Phys.Rev.C72:014905,2005) E. Braaten and M. H. Thoma, Phys. Rev. D 44, 2625 (1991). M. H. Thoma and M. Gyulassy, Nucl. Phys. B 351, 491 (1991). Elastic energy loss is negligible! Conclusion was based on wrong assumptions (i.e. they used  =0.2). Early work: Recent work: Used correct  =0.3 First results indicate that the elastic energy loss may be important (see talk by Simon Wicks) Available elastic energy loss calculations can give only rough estimates to jet quenching. More work is needed!

31. M. Djordjevic 31 Conclusions We applied the theory of heavy quark energy loss to compute heavy meson and single electron suppression. We show that bottom quark contribution can not be neglected in the computation of single electron spectra. The recent single electron data show significant discrepancies with theoretical predictions based only on radiative energy loss. However, the elastic energy loss may have an important contribution to jet quenching.

32. M. Djordjevic 32 Backup slides:

33. M. Djordjevic 33 Elastic v.s. radiative energy loss: Are there other energy loss mechanisms? Elastic and radiative energy losses are comparable! (see M. G. Mustafa, Phys.Rev.C72:014905,2005) BT: E. Braaten and M. H. Thoma, Phys. Rev. D 44, 2625 (1991). TG: M. H. Thoma and M. Gyulassy, Nucl. Phys. B 351, 491 (1991).

34. M. Djordjevic 34 Heavy quark suppression with the elastic energy loss The elastic energy loss significantly changes the charm and bottom suppression! CHARM BOTTOM Done by Simon Wicks.

35. M. Djordjevic 35 Single electron suppression with the elastic energy loss Reasonable agreement with single electron data, even for dN g /dy=1000. (S. Wicks, W. Horowitz, M.D. and M. Gyulassy, in preparation.) However, overprediction of pion suppression results happens. Possible solution: Include the geometrical fluctuations (W. Horrowitz). Include elastic energy loss Done by Simon Wicks.

36. M. Djordjevic 36 Backup slides

37. M. Djordjevic 37 Why, according to pQCD, pions have to be at least two times more suppressed than single electrons? Suppose that pions come from light quarks only and single e - from charm only. Pion and single e - suppression would really be the same. g 00 b b+c  e - However, 1)Gluon contribution to pions increases the pion suppression, while 2) Bottom contribution to single e - decreases the single e - suppression leading to at least factor of 2 difference between pion and single e - R AA.

38. M. Djordjevic 38 R AA (e - ) / R AA (  0 ) > 2

39. M. Djordjevic 39

40. M. Djordjevic 40 Collinear factorization

41. M. Djordjevic 41 Collinear factorization c d A B ab h

42. M. Djordjevic 42 Ter-Mikayelian backup:

43. M. Djordjevic 43 Computation was done in the soft gluon limit, i.e. it was assumed that gluon momentum is much smaller than quark momentum. Additionally we assumed:  Source packet J(p) varies slowly over the range of momentum, i.e..  Spin in the problem is neglected.  Quark momentum is large, such that we can assume.

44. M. Djordjevic 44 The momentum distribution of 0 th order radiative energy loss Longitudinal contribution to the energy loss was found to be significant only in the low k < k D region. (See Eq. 3.23)

45. M. Djordjevic 45 Fig.2 shows the one loop transverse plasmon mass m g (k)  √(  2 -k 2 ). We see that m g starts with the value  pl =µ/√3 at low k, and that as k grows, m g asymptotically approaches the value of m  =µ/√2, in agreement with Rebhan A, Lect. Notes Phys. 583, 161 (2002). We can conclude that we can approximate the Ter-Mikayelian effect by simply taking m g  m .

46. M. Djordjevic 46 Contrary to the charm, for bottom quark the Ter-Mikayelian effect is negligible. BOTTOM

47. M. Djordjevic 47 Transition radiation backup:

48. M. Djordjevic 48 This computation was performed assuming a static medium.

49. M. Djordjevic 49 For massive quarks and medium thickness greater than 3 fm transition radiation becomes independent on the thickness of the medium.

50. M. Djordjevic 50 Transition radiation lowers Ter-Mikayelian effect from 30% to 15%. Can this energy loss be smaller in the medium than in the vacuum?

51. M. Djordjevic 51 medium vacuum

52. M. Djordjevic 52 We also have to include the effect of confinement in the vacuum. There are two approaches to do that: 1) Assume that gluon mass in the vacuum is not exactly zero, but it has some small value on the order of Λ QCD. 2) Assume that vacuum gluon mass is large, i.e. approximately 0.7 GeV.

53. M. Djordjevic 53 Transition radiation provides natural regularization of m=0 light quark energy loss. What about confinement in the vacuum? One phenomenological way to simulate confinement in the vacuum is to assume that gluon has a nonzero mass.

54. M. Djordjevic 54 Medium induced energy loss backup:

55. M. Djordjevic 55 In addition to the assumptions used to compute the Ter -Mikayelian effect, we used:  Interaction in a deconfined QGP can be modeled by static color screened Yukawa potentials. The Fourier and color structure of the potential is assumed to be where is the location of n th (heavy) target parton, and  All are distributed with the same density where  The distance between the source and scattering centers is large comparing to the interaction range, i.e..

56. M. Djordjevic 56 Difference between net medium and vacuum energy loss

57. M. Djordjevic 57 Energy loss dependence on dN g /dy

58. M. Djordjevic 58 B D Suppression for different coupling parameters

59. M. Djordjevic 59 “Dead cone” effect for the 0 th and 1 st order energy loss

60. M. Djordjevic 60 Single electrons:

61. M. Djordjevic 61 light Comparison with pion suppression

62. M. Djordjevic 62 Charm and Beauty pt distributions in p+p Charm and Beauty pt distributions in Au+Au Initial Charm and Beauty pt distributions

63. M. Djordjevic 63 Panels show single e - from MNR (done by R.Vogt). Red curves show total single e - ; Blue (green) curves show contribution from Charm (Beauty). Single electrons at RHIC Beauty dominate the single e - spectrum after 4.5 GeV!

64. M. Djordjevic 64 R AA for single electrons at RHIC Red solid curve: Raa for non-photonic single e -. Blue (Green) dashed curves: Raa for single e - from Charm (Beauty) quarks. We predict small single e- suppression of ~ 0.7 MNR

65. M. Djordjevic 65 Comparison with experiment Our predictions do not agree with PHENIX preliminary data.

66. M. Djordjevic 66 How to explain this puzzle? From the current model this would be hard to explain because of: 1)Bottom contribution to single electrons 2)Gluon contribution to pions PHENIX preliminary data suggest single electron suppression similar to pion suppression! Therefore, to explain the data, we need a model which would eliminate bottom contribution from single electrons + eliminate gluon contribution from pions!

67. M. Djordjevic 67 Problems with single electrons I No centrality dependence

68. M. Djordjevic 68 Consistency between electron data sets STAR systematically (slightly) above PHENIX beware: error bars are meant to be taken seriously! (Slide adapted from Xin Dong, 21st Winter Workshop on Nuclear Dynamics) Single electron results can be different by an order of magnitude Maybe single electrons are not good probe of Heavy quark energy loss?

69. M. Djordjevic 69 Charm and beauty content in the single electrons is very sensitive to their fragmentation functions Problems with single electrons II Simon Wicks (Columbia U.) MNR Single electrons suppression is strongly dependent on (unknown) charm and beauty fragmentation functions

70. M. Djordjevic 70 For example for RHIC we should include heavy quarks up to |y max |=2.5. For LHC |ymax| could be significantly larger than 3! Single electron distributions are VERY sensitive to the rapidity window (Ramona Vogt) At high rapidity, nonperturbative effects may become important! + Single electron suppression could be influenced by nonpertutbative effects We need D mesons!

71. M. Djordjevic 71 p T [GeV/c] R AA M. Djordjevic et al., hep-ph/0410372 N. Armesto et al. hep-ph/0501225 Single electrons from Charm only reproduce Armesto et al. plots Comparison with results by Armesto et al.

72. M. Djordjevic 72 Elliptic flow:

73. M. Djordjevic 73 x y z x pypy pxpx y y x pypy pxpx coordinate-space-anisotropy  momentum-space-anisotropy What is elliptic flow? x y pTpT

74. M. Djordjevic 74 Single e 10% Central Au-Au data can be explained by two different approaches: Hydro PYTHIA pQCD The answer to this question can give us the measurement of v2 for charm at RHIC. Observation of the elliptic flow which is much larger than the one predicted by jet quenching, would mean that charm flows at RHIC. What value of elliptic flow we expect from heavy quark jet quenching? DOES THE CHARM FLOW AT RHIC? S. Batsouli, S. Kelly, M. Gyulassy, J.L. Nagle Phys.Lett.B 557 (2003) 26

75. M. Djordjevic 75 We have estimated v 2 for minimum bias case. Here, we have assumed 1+1D Bjorken longitudinal expansion. According to our estimates, at RHIC we expect charm quark v 2 between 0.02 and 0.08. Shingo Sakai, QM2004 PHENIX preliminary c

76. M. Djordjevic 76