Heavy Quark Energy Loss in Nucleus-Nucleus Collisions

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

2. Heavy ion physics has a goal to form and observe a QGP. Is the QGP already discovered at RHIC? • 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. Heavy mesons not yet measured at RHIC. However, single electron measurements are available.

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

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

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

6. c, b Single electron suppression D, B e- 1) production 2) medium energy loss 3) fragmentation 4) decay 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-.

7. Initial heavy quark pt distributions 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).

8. c c L • Radiative heavy quark energy loss • Three important medium effects control the radiative energy loss: • Ter-Mikayelian effect (M. D. and M. Gyulassy, Phys. Rev. C 68, 034914 (2003)) • Transition radiation (M. D., to be published). • 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)) 1) 2) 3)

9. Ter-Mikayelian effect This is the non-abelian analog of the well known dielectric plasmon effectw(k) >wpl~ gT. In pQCDvacuumgluons are massless andtransversely polarized. However, in a medium the gluon propagator has bothtransverse(T)and longitudinal(L)polarization parts. T vacuum L

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

11. Comparison between medium and vacuum 0th order in opacity fractional energy loss CHARM • 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. The Ter-Mikayelian effect thus tends to enhance the yield of high pT charm quarks relative to the vacuum case.

12. c L Transition radiation An additional dielectric effect at 0th 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.

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

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

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

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

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

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 L1. This is different than the asymptotic energy quadratic form characteristic for light quarks.

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

21. As the jet energy increasescharm and light quark energy loss become more similar, while bottom quark remains significantly different. 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, the dead cone effect becomes less important.

22. The numerical results can be understood from: (See Fig. E.3) LPM effects are smaller for heavy than for light quarks! 1st order energy loss can not be characterized only by a “Dead-cone” effect! 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. Before quenching After quenching Pt distributions of charm and bottom before and after quenching at RHIC To compute the jet quenching we generalized the GLV method (PLB538:282,2002).

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

25. Single electrons pt distributions before and after quenching at RHIC 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)) Before quenching After quenching Bottom dominate the single e-spectrum after 4.5 GeV!

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

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

28. dNg/dy=1000 Comparison with single electron data Disagreement with PHENIX preliminary data!

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

30. Is elastic energy loss important? Early work: Recent work: E. Braaten and M. H. Thoma, Phys. Rev. D 44, 2625 (1991). M. H. Thoma and M. Gyulassy, Nucl. Phys. B 351, 491 (1991). M. G. Mustafa, Phys.Rev.C72:014905,2005) Used correct =0.3 Elastic energy loss is negligible! Elastic and radiative energy losses are comparable! Conclusion was based on wrong assumptions (i.e. they used =0.2). 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. 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. Backup slides:

33. Are there other energy loss mechanisms? Elastic v.s. radiative energy loss: (see M. G. Mustafa, Phys.Rev.C72:014905,2005) Elastic and radiative energy losses are comparable! 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. Heavy quark suppression with the elastic energy loss Done by Simon Wicks. CHARM BOTTOM The elastic energy loss significantly changes the charm and bottom suppression!

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

36. Backup slides

37. b+ce- b 0 g 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. • However, • 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- RAA.

38. RAA(e-) / RAA(0)> 2

40. Collinear factorization

41. Collinear factorization h c A a b B d

42. Ter-Mikayelian backup:

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. The momentum distribution of 0th order radiative energy loss Longitudinal contributionto the energy loss was foundto besignificant only in the low k < kDregion. (See Eq. 3.23)

45. Fig.2 shows the one loop transverse plasmon mass mg(k)√(2-k2). We see that mgstarts with the value pl=µ/√3 at low k, and that as k grows, mgasymptotically 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 mg m .

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

47. Transition radiation backup:

48. This computation was performed assuming a static medium.

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

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