1. M. Djordjevic 1 Hard probes at RHIC and LHC Magdalena Djordjevic 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 Significant reduction at high pT suggest sizable 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?

4. M. Djordjevic 4 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)Is elastic energy loss important at LHC?

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 -. D, B 1) production 2) medium energy loss 3) fragmentation c, b Single electron suppression e-e- 4) decay To make theoretical predictions for heavy meson and single electron suppression we generalized the GLV method ( PLB538:282,2002 ).

6. M. Djordjevic 6 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

7. M. Djordjevic 7 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)

8. M. Djordjevic 8 c 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. Caused by the multiple interactions of partons in the medium.

9. M. Djordjevic 9 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)).

10. M. Djordjevic 10 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)

11. M. Djordjevic 11 The numerical results for induced radiative energy loss are shown for first order in opacity, for L= 5 fm, l =1 fm. 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.

12. M. Djordjevic 12 light Quantitative “dead cone effect” for the heavy quark energy loss

13. M. Djordjevic 13 b c u,d RHICLHC As the jet energy increases, the dead cone effect becomes less important.

14. M. Djordjevic 14 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.

15. M. Djordjevic 15 M. D., M. Gyulassy and S. Wicks, Phys. Rev. Lett. 94, 112301 (2005); Euro Phys. J C, in press (2005). Pt distributions of charm and bottom before and after quenching at RHIC Before quenchingAfter quenching

16. M. Djordjevic 16 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, press) Moderate D meson suppression ~ 0.5  0.1 at RHIC.

17. M. Djordjevic 17 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!

18. M. Djordjevic 18 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 Plot done by Simon Wicks.

19. M. Djordjevic 19 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.

20. M. Djordjevic 20 Comparison with single electron data Disagreement with PHENIX preliminary data! dN g /dy=1000

21. M. Djordjevic 21 How can we solve the problem? Reasonable agreement, but the dN g /dy=3500 is not physical! dN g /dy=3500

22. M. Djordjevic 22 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)

23. M. Djordjevic 23 Heavy quark suppression with the elastic energy loss The elastic energy loss significantly changes the charm and bottom suppression! CHARM BOTTOM Plots done by Simon Wicks.

24. M. Djordjevic 24 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. Solution: Include the geometrical fluctuations (see M. Gyulassy’s talk). Include elastic energy loss Plot done by Simon Wicks.

25. M. Djordjevic 25 Elastic v.s. radiative energy loss: Radiative energy loss dominates at high pt! Is the elastic energy loss important at LHC?

26. M. Djordjevic 26 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, inclusion of the elastic energy loss may lead to the agreement with experimental results.

27. M. Djordjevic 27 Acknowledgements: Miklos Gyulassy (Columbia University) Ramona Vogt (LBNL, Berkeley and University of California, Davis) Simon Wicks (Columbia University)