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Open Questions in Heavy Flavor Physics at RHIC

This presentation discusses the energy loss mechanisms of heavy quarks in Quark-Gluon Plasma (QGP) and explores the results and future possibilities of heavy meson and single electron suppression experiments at RHIC.

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Open Questions in Heavy Flavor Physics at RHIC

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

  2. Quark Gluon Plasma High Energy Heavy Ion Physics 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. N. Brambilla et al., e-Print hep-ph/0412158 (2004). Heavy mesons not yet available, but they are expected soon!

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

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

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

  8. + + This leads to the computation of the fallowing types of diagrams: Final Result to Arbitrary Order in Opacity (L/) with MQ and mg> 0

  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, =1fm.

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

  11. Single electrons pt distributions 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 Before quenching After quenching Bottom dominate the single e-spectrum above 4.5 GeV!

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

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

  14. Is collisional energy loss also 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). 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. 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. Radiative energy loss Collisional energy loss Radiative energy loss comes from the processes which there are more outgoing than incoming particles: Collisional energy loss comes from the processes which have the same number of incoming and outgoing particles: 0th order 0th order 1st order

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

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

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

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

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

  21. Most up to date single electron prediction (collisional + radiative) 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. Inclusion of collisional energy loss leads to better agreement with single electron data, even for dNg/dy=1000. (S. Wicks, W. Horowitz, M.D. and M. Gyulassy, nucl-th/0512076)

  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. Open questions: • How well do we understand: • Are single electrons good probe of heavy quark energy loss? charm and bottom production at RHIC? charm and bottom contributions to the single electrons? the energy loss at RHIC?

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

  25. ce/be  Ο(1) Current pQCD calculations 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)

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

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

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

  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 bothD and B mesons directly in central rapidity region. YES!

  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. Backup slides

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

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

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

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

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

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

  38. 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.

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