1. M. Djordjevic 1 Heavy quark energy loss puzzle 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 However, single electron measurements are available. Heavy mesons not yet measured at RHIC. N. Brambilla et al., e-Print hep-ph/0412158 (2004).

3. M. Djordjevic 3 1997 Shuryak argued (Phys.Rev.C 55, 961 (1995)) that heavy quarks will have large energy loss in QGP => large suppression of heavy mesons. (based on the assymption: ΔE charm = ΔE light =BDPS (1995)) 2001 Dokshitzer and Kharzeev proposed “dead cone” effect => heavy quark small energy loss (Phys. Lett. B 519, 199 (2001)) Motivation for studying the heavy quark energy loss 

4. M. Djordjevic 4 Significant reduction at high pT suggests sizeable heavy quark energy loss! Single electron suppression measurements at RHIC V. Greene, S. Butsyk, QM2005 talksJ. Dunlop, J. Bielcik; QM05 talks Can this be explained by the energy loss in QGP?

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 -. Single electron suppression 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 High quark mass, i.e. M>> Λ QCD Perturbative calculations of heavy quark production possible. 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 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)

8. M. Djordjevic 8 N. Armesto, C. A. Salgado, U. A. Wiedemann, Phys. Rev. D 69, 114003 (2004). Generalized BDMPS-Z-W (2000) method. Computation based on path integral formalism. c Radiative energy loss due to the interaction with the medium Caused by the multiple interactions of partons in the medium. M. D. and M. Gyulassy, Phys. Lett. B 560, 37 (2003); Nucl. Phys. A 733, 265 (2004); Generalized GLV (2000) method to compute heavy quark energy loss to all orders in opacity. B. W. Zhang, E. Wang and X. N. Wang, Phys. Rev. Lett. 93, 072301 (2004); Generalized ZW (2003) method. Derivation in terms of Modified FF with pQCD (twist expansion approach).

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. M. D. and M. Gyulassy, Nucl. Phys. A 733, 265 (2004);

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 Comparison with single electron data Disagreement with PHENIX preliminary data! Armesto et al., hep-ph/0510284M. D. et al., Phys.Lett.B632:81-86,2006

14. M. Djordjevic 14 How can we solve the problem? Reasonable agreement, but the parameters are not physical! Armesto et al., hep-ph/0511257M. D. et al., Phys.Lett.B632:81-86,2006

15. M. Djordjevic 15 Are there other energy loss mechanisms? Collisional and radiative energy losses are comparable! M.G.Mustafa,Phys.Rev.C72:014905,2005 Finite size effects significantly lower collisional energy loss S. Peigne, P.-B. Gossiaux, T. Gousset, hep- ph/0509185 The paper, however, did not make separation between elastic and part of radiative energy loss effects.

16. M. Djordjevic 16, L=5 fm Collisional energy loss in finite size QCD medium Collisional and radiative energy losses are comparable! M.D., nucl-th/0603066, L=5 fm

17. M. Djordjevic 17 Single electron suppression with the collisional energy loss Reasonable agreement with single electron data, even for dN g /dy=1000. (S. Wicks, W. Horowitz, M.D. and M. Gyulassy, nucl-th/0512076) Include collisional energy loss. 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).

18. M. Djordjevic 18 Conclusions We applied the theory of heavy quark energy loss to compute the 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, inclusion of the collisional energy loss may lead to better agreement with experimental results.

19. M. Djordjevic 19 Acknowledgements: Miklos Gyulassy (Columbia University) Ramona Vogt (LBNL, Berkeley and University of California, Davis) Simon Wicks (Columbia University)

20. M. Djordjevic 20 backup

21. M. Djordjevic 21 light Similar results obtained by Zhang-Wang-Wang (2004); Armesto-Salgado-Wiedemann (2004). Quantitative “dead cone effect” for the heavy quark energy loss

22. M. Djordjevic 22 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.

23. M. Djordjevic 23 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 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.

24. M. Djordjevic 24 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

25. M. Djordjevic 25 Transition & Ter-Mikayelian for charm Two effects approximately cancel each other for heavy quarks. Transition radiation lowers Ter-Mikayelian effect from 30% to 15%.

26. M. Djordjevic 26 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.

27. M. Djordjevic 27 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.

28. M. Djordjevic 28 R AA (e - ) / R AA (  0 ) > 2

29. M. Djordjevic 29 light Comparison with pion suppression

30. M. Djordjevic 30 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!

31. M. Djordjevic 31 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.