1. M. Djordjevic 1 Open questions in heavy flavor physics at RHIC Magdalena Djordjevic The Ohio State University

2. M. Djordjevic 2 Quark Gluon Plasma Form, observe and understand Quark-Gluon Plasma (QGP). Heavy quarks (charm and beauty, M>1 GeV) are widely recognized as the cleanest probes of QGP. High Energy Heavy Ion Physics Heavy mesons not yet available, but they are expected soon! N. Brambilla et al., e-Print hep-ph/0412158 (2004).

3. M. Djordjevic 3 Significant reduction at high pT suggests sizeable heavy quark energy loss! Indirect probe- single electron suppression – is available V. Greene, S. Butsyk, QM2005 talksJ. Dunlop, J. Bielcik; QM05 talks Can this be explained by the energy loss in QGP?

4. M. Djordjevic 4 Outline  Discuss the heavy quark energy loss mechanisms:  Heavy meson and single electron suppression results that come from the above mechanisms.  Open questions that can be addressed in the future RHIC experiments.  Radiative energy loss.  Collisional energy loss.

5. M. Djordjevic 5 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 -. From production to decay D, B 1) production 2) medium energy loss 3) fragmentation c, b e-e- 4) decay

6. M. Djordjevic 6 D mesons,  ’,  A B Initial heavy quark pt distributions M. Cacciari, P. Nason and R.Vogt, Phys.Rev.Lett.95:122001,2005; MNR code (M. L. Mangano, P.Nason and G. Ridolfi, Nucl.Phys.B373,295(1992)). R.Vogt, Int.J.Mod.Phys.E 12,211(2003).

7. M. Djordjevic 7 c Medium induced radiative energy loss To compute medium induced radiative energy loss for heavy quarks we generalize GLV method, by introducing both quark M and gluon mass m g. Caused by the multiple interactions of partons in the medium. M. Djordjevic and M. Gyulassy, Nucl. Phys. A 733, 265 (2004).

8. M. Djordjevic 8 This leads to the computation of the fallowing types of diagrams: + + Final Result to Arbitrary Order in Opacity (L/ ) with M Q and m g > 0

9. M. Djordjevic 9 Thickness dependence is closer to linear Bethe-Heitler like form. This is different than the asymptotic energy quadratic form characteristic for light quarks. The numerical results for induced radiative energy loss are shown for first order in opacity, for L= 5 fm, =1 fm.

10. M. Djordjevic 10 M. D., M. Gyulassy and S. Wicks, Phys. Rev. Lett. 94, 112301 (2005). Pt distributions of charm and bottom before and after quenching at RHIC Before quenchingAfter quenching M. Gyulassy, P.Levai and I. Vitev, Phys.Lett.B538:282-288 (2002).

11. M. Djordjevic 11 Panels show single e - from FONLL M. Cacciari, P. Nason and R. Vogt, Phys.Rev.Lett.95:122001,2005 M. D., M. Gyulassy, R. Vogt and S. Wicks, Phys.Lett.B632:81-86,2006 Single electrons pt distributions Before quenching After quenching Bottom dominate the single e - spectrum above 4.5 GeV!

12. M. Djordjevic 12 Single electron suppression as a function of pt At pt~5GeV, R AA (e - )  0.7  0.1 at RHIC.

13. M. Djordjevic 13 Radiative energy loss is not able to explain the single electron data as long as realistic parameter values are taken into account! M. D. et al., Phys. Lett. B 632, 81 (2006) Can single electron suppression be explained by the radiative energy loss in QGP? Radiative energy loss predictions with dN g /dy=1000 Disagreement!

14. M. Djordjevic 14 E. Braaten and M. H. Thoma, Phys. Rev. D 44, 2625 (1991). M. H. Thoma and M. Gyulassy, Nucl. Phys. B 351, 491 (1991). Collisional energy loss is negligible! Conclusion was based on outdated assumptions (i.e. they used  =0.2), and assumed that dE/dL<0.5 GeV/fm is negligible. Early work:Recent work: Is collisional energy loss also important? Collisional and radiative energy losses are comparable! M.G.Mustafa,Phys.Rev.C72:014905,2005 A. K. Dutt-Mazumder et al.,Phys.Rev.D71:094016,2005 Will collisional energy loss still be important once finite size effects are included? Above computations are done in an ideal infinite QCD medium.

15. M. Djordjevic 15 Radiative energy lossCollisional energy loss Collisional energy loss comes from the processes which have the same number of incoming and outgoing particles: Radiative energy loss comes from the processes which there are more outgoing than incoming particles: 0 th order 1 st order 0 th order

16. M. Djordjevic 16 The main order collisional energy loss is determined from: L Collisional energy loss in a finite size QCD medium The effective gluon propagator: Consider a medium of size L in thermal equilibrium at temperature T.

17. M. Djordjevic 17 Comparison between computations of collisional energy loss in finite and infinite QCD medium Finite size effects are not significant, except for very small path-lengths. M.D., nucl-th/0603066

18. M. Djordjevic 18 Bottom quark collisional energy loss is significantly smaller than charm energy loss. M.D., nucl-th/0603066 Comparison between charm and bottom collisional energy loss

19. M. Djordjevic 19 Collisional v.s. medium induced radiative energy loss Collisional and radiative energy losses are comparable! M.D., nucl-th/0603066 Complementary approach by A. Adil et al., nucl-th/0606010: consistent results obtained.

20. M. Djordjevic 20 Heavy quark suppression with the collisional energy loss The collisional energy loss significantly changes the charm and bottom suppression! CHARM BOTTOM (S. Wicks, W. Horowitz, M.D. and M. Gyulassy, nucl-th/0512076)

21. M. Djordjevic 21 Most up to date single electron prediction (collisional + radiative) Inclusion of collisional energy loss leads to better agreement with single electron data, even for dN g /dy=1000. (S. Wicks, W. Horowitz, M.D. and M. Gyulassy, nucl-th/0512076) Radiative energy loss alone is not able to explain the single electron data, as long as realistic gluon rapidity density dNg/dy=1000 is considered.

22. M. Djordjevic 22 The agreement between the theory and the single electron data may still not be good enough! However, theoretical predictions depend on the underlying assumptions. How good are these assumptions? What are the open questions? How can future RHIC experiments improve our understanding of heavy flavor physics at RHIC?

23. M. Djordjevic 23  How well do we understand:  Are single electrons good probe of heavy quark energy loss? Open questions: 1)charm and bottom production at RHIC? 2)charm and bottom contributions to the single electrons? 3)the energy loss at RHIC?

24. M. Djordjevic 24 Need work by both theory and experiment to gain a better understanding! How well do we understand charm and bottom production at RHIC? Theoretical computations seem to notably underpredict the data. Theoretically: Experimentally: STAR and PHENIX data may be systematically off by factor of 2. STAR (nucl-ex/0607012) Ralf Averbeck’s talk (QM2004)

25. M. Djordjevic 25 How well do we understand charm and bottom contributions to the single electrons? Good agreement with the data if only charm contribution is taken into account. Is charm enhanced at RHIC? Need direct D and B measurements to resolve a puzzle and make stronger conclusions! (S. Wicks, W. Horowitz, M.D. and M. Gyulassy, nucl-th/0512076) Current pQCD calculations c  e/b  e  Ο(1)

26. M. Djordjevic 26 How well we understand the energy loss at RHIC? According to pQCD theory, clear hierarchy in the suppression patterns! Theoretically: Gluons are more suppressed than light quarks!Charm is more suppressed than bottom! (S. Wicks, W. Horowitz, M.D. and M. Gyulassy, nucl-th/0512076)

27. M. Djordjevic 27 Potential absence of hierarchy would challenge the pQCD energy loss mechanisms! Data may indicate the same energy loss for charm and bottom! Data may indicate the same energy loss for gluons and light quarks! However, experimentally: Need: direct D and B mesons + high accuracy pbar/p measurements STAR (nucl-ex/0606003)

28. M. Djordjevic 28 For example for RHIC we should include heavy quarks up to |y max |=2.5. 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 Upcoming D and B meson measurements at mid rapidity should resolve this issue Are single electrons good probe of heavy quark energy loss?

29. M. Djordjevic 29 How D’s and B’s should be measured in the upcoming RHIC experiments? Measure (just) D mesons directly in mid rapidity region. Subtract D’s from single electrons to get B’s. Problem: Instead of mid rapidity B’s, in this way we would get a mixture of high rapidity D’s and all rapidity B’s. NO! Measure both D and B mesons directly in central rapidity region. YES!

30. M. Djordjevic 30 Summary Radiative energy loss mechanisms alone are not able to explain the recent single electron data. Collisional and radiative energy losses are comparable, and both contributions are important in the computations of jet quenching. Inclusion of the collisional energy loss lead to better agreement with the experimental results. Future direct D and B measurements will be important to get a better understanding of heavy quark physics at RHIC.

31. M. Djordjevic 31 Backup slides

32. M. Djordjevic 32 Most up to date pion and single electron predictions (collisional + radiative) Inclusion of collisional energy loss leads to good agreement with pions and an improved agreement with single electron data at dN g /dy=1000. (S. Wicks, W. Horowitz, M.D. and M. Gyulassy, nucl-th/0512076)

33. M. Djordjevic 33 Path length fluctuations Important for gluons and consistency of electron and pion predictions. Realistic Woods-Saxon nuclear density Jets produced ~ TAA 1+1D Bjorken expantion Hierarchy of fixed lengths fit the full geometrical calculations. No a priori justification for any fixed length. (S. Wicks, W. Horowitz, M.D. and M. Gyulassy, nucl-th/0512076)

34. M. Djordjevic 34 Transition & Ter-Mikayelian effects on 0 th order radiative energy loss Transition & Ter-Mikayelian effects approximately cancel each other for heavy quarks. M.D., Phys.Rev.C73:044912,2006 CHARMBOTTOM

35. M. Djordjevic 35 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! 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.

36. M. Djordjevic 36 Radiative heavy quark energy loss Three important medium effects control the radiative energy loss: 1)Ter-Mikayelian effect (M.L.Ter-Mikayelian (1954); Kampfer-Pavlenko (2000); Djordjevic-Gyulassy (2003)) 2)Transition radiation (Zakharov (2002); Djordjevic (2006)). 3)Energy loss due to the interaction with the medium (Djordjevic-Gyulassy (2003); Zhang-Wang-Wang (2004); Armesto-Salgado-Wiedemann (2004)) c L c 1) 2) 3)

37. M. Djordjevic 37 The uncertainity band obtained by varying the quark mass and scale factors. Domination of bottom in single electron spectra M. D., M. Gyulassy, R. Vogt and S. Wicks, Phys.Lett.B632:81-86,2006 R. Vogt, talk given at QM2005

38. M. Djordjevic 38 Transition & Ter-Mikayelian for charm Two effects approximately cancel each other for heavy quarks. Transition radiation lowers Ter-Mikayelian effect from 30% to 15%.

39. M. Djordjevic 39 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.