1. Heavy Quark Energy Loss with Twist Expansion Approach Ben-Wei Zhang Institute of Particle Physics Central China Normal Univeristy CCAST, Beijing --- Augest 10, 2004 Thanks to my collaborators: Xin-Nian Wang and Enke Wang

2. 2 ------------------------------------------- Ben-Wei Zhang @ CCAST, Beijing Outline Motivation Twist expansion approach Modified heavy quark fragmentation function Heavy quark energy loss ------ Heavy VS. Light Conclusion

3. 3 ------------------------------------------- Ben-Wei Zhang @ CCAST, Beijing Jet Quenching Jet quenching has been discovered at RHIC as a good probe of the hot/dense matter. hadrons phph parton E X.N. Wang, nucl-th/0405017

4. 4 ------------------------------------------- Ben-Wei Zhang @ CCAST, Beijing From Light to Heavy Theory: A lot of theoretical studies have been devoted to the calculations of the energy loss of a light quark. For massive quarks, the formalism of medium-induced gluon radiation is not developed to the same extent. Experiment: Open charm suppression, which can now be measured at RHIC by comparing pt distributions of D-mesons in D-Au and Au-Au collisions, is a novel probe of QGP dynamics.

5. 5 ------------------------------------------- Ben-Wei Zhang @ CCAST, Beijing Heavy Quark Energy Loss There are several theoretical calculations to obtain the heavy quark energy loss: Yu.L. Dokshitzer and D.E. Kharzeev M. Djordjevic and M. Gyulassy B.W.Zhang, E. Wang and X.N. Wang N. Armesto, C. Salgado and U. Wiedemann …… Twist Expansion approach in pQCD B.W. Zhang, E. Wang and X.N. Wang, PRL 93(2004) in press

6. 6 ------------------------------------------- Ben-Wei Zhang @ CCAST, Beijing Jet quenching with pQCD How to measure the parton energy loss? Direct measurement is impossible Particle distributions within a jet Modification to Fragmentation Function Obtain the energy loss indirectly from measuring the modification of FF hadrons phph parton E

7. 7 ------------------------------------------- Ben-Wei Zhang @ CCAST, Beijing Heavy Quark In eA DIS, for the heavy quark production we obtain : In eA DIS, for the heavy quark production we obtain :

8. 8 ------------------------------------------- Ben-Wei Zhang @ CCAST, Beijing Multiple Scattering in Nuclei In order to calculate the heavy quark energy loss induced by gluon radiation in pQCD, we should separate the ‘ hard ’ part from the ‘ soft ’ part: factorizing.

9. 9 ------------------------------------------- Ben-Wei Zhang @ CCAST, Beijing Generalized Factorization Luo, Qiu, Sterman, PLB 279(1992)377; Luo, Qiu, Sterman, PRD 49(1994)4493; PRD 50(1994)1951

10. 10 ------------------------------------------- Ben-Wei Zhang @ CCAST, Beijing Quark-Gluon Double Scattering

11. 11 ------------------------------------------- Ben-Wei Zhang @ CCAST, Beijing Tensor Structure Making a collinear approximation: The tensor structure can be factorized as:

12. 12 ------------------------------------------- Ben-Wei Zhang @ CCAST, Beijing LPM Effect LMP interference effect. The formation time of gluon radiation.

13. 13 ------------------------------------------- Ben-Wei Zhang @ CCAST, Beijing Other Processes

14. 14 ------------------------------------------- Ben-Wei Zhang @ CCAST, Beijing Hard Partonic Part Dead-cone effect of heavy quark propagating will suppress gluon radiation at small angles.

15. 15 ------------------------------------------- Ben-Wei Zhang @ CCAST, Beijing Modified FF of Heavy Quark With the generalized factorization theorem we obtain the semi- inclusive hadronic tensor: With the generalized factorization theorem we obtain the semi- inclusive hadronic tensor: The modified effective fragmentation function is

16. 16 ------------------------------------------- Ben-Wei Zhang @ CCAST, Beijing Two-parton Correlation Function Twist-4 parton correlation function is in principle not calculable. With some approximations we can estimate the twist-4 correlation functions approximated as J. Osborne and Xin-Nian Wang, NPA 710(2002)281

17. 17 ------------------------------------------- Ben-Wei Zhang @ CCAST, Beijing Heavy Quark Energy Loss Heavy quark energy loss can be derived as: Xiao-fen Guo, Xin-Nian Wang, PRL 85(2000)3591; Xin-Nian Wang, Xiao-fen Guo, NPA 696(2001) 788 Ben-Wei Zhang, Xin-Nian Wang, NPA 720(2003) 429 When M=0, we will recover the result of the light quark energy loss.

18. 18 ------------------------------------------- Ben-Wei Zhang @ CCAST, Beijing Two Distinct Limits (1) When (2) For large values of Q 2 or small x B, we have

19. 19 ------------------------------------------- Ben-Wei Zhang @ CCAST, Beijing Nuclear Size Dependence

20. 20 ------------------------------------------- Ben-Wei Zhang @ CCAST, Beijing Heavy Quark VS. Light Quark Energy loss of heavy quark is significantly suppressed due to mass effect, in particular, the dead-cone effect.

21. 21 ------------------------------------------- Ben-Wei Zhang @ CCAST, Beijing Conclusion Heavy quark energy loss induced by gluon radiation is derived in terms of Modified FF with pQCD. Two mass effects: (I) Gluon formation time of the heavy quark is reduced relative to that of a light quark: Medium size dependence of heavy quark enegy loss is found to change from a linear to a quadratic form when the initial energy and momentum scale are increasing. (II) Dead-cone effect: Heavy quark energy loss is significantly suppressed relative to a light quark.

22. 22 ------------------------------------------- Ben-Wei Zhang @ CCAST, Beijing Thank you very much! 谢谢 ! Thank you very much! 谢谢 !

23. 23 ------------------------------------------- Ben-Wei Zhang @ CCAST, Beijing Backup

24. 24 ------------------------------------------- Ben-Wei Zhang @ CCAST, Beijing Factorization of Twist-4 Luo, Qiu, Sterman, PLB 279(1992)377; Luo, Qiu, Sterman, PRD 49(1994)4493; PRD 50(1994)1951

25. 25 ------------------------------------------- Ben-Wei Zhang @ CCAST, Beijing Twist-4 Parton Correlation

26. 26 ------------------------------------------- Ben-Wei Zhang @ CCAST, Beijing Factorization of Twist-4 Matries