Heavy Quark Energy Loss with Twist Expansion Approach

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. Outline • Motivation • Twist expansion approach • Modified heavy quark fragmentation function • Heavy quark energy loss ------ Heavy VS. Light • Conclusion

3. parton hadrons ph E Jet Quenching Jet quenching has been discovered at RHIC as a good probe of the hot/dense matter. X.N. Wang, nucl-th/0405017

4. 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. 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. parton hadrons ph E 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

7. Heavy Quark • In eA DIS, for the heavy quark production we obtain :

8. 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. Generalized Factorization Luo, Qiu, Sterman, PLB 279(1992)377; Luo, Qiu, Sterman, PRD 49(1994)4493; PRD 50(1994)1951

10. Quark-Gluon Double Scattering

11. Tensor Structure • Making a collinear approximation: • The tensor structure can be factorized as:

12. LPM Effect • LMP interference effect. • The formation time of gluon radiation.

13. Other Processes

14. Hard Partonic Part Dead-cone effect of heavy quark propagating will suppress gluon radiation at small angles.

15. The modified effective fragmentation function is Modified FF of Heavy Quark • With the generalized factorization theorem we obtain the semi- inclusive hadronic tensor:

16. 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. When M=0, we will recover the result of the light quark energy loss. 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 Heavy Quark Energy Loss Heavy quark energy loss can be derived as:

18. Two Distinct Limits (1) When (2) For large values of Q2 or small xB, we have

19. Nuclear Size Dependence

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

21. 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. Thank you very much! 谢谢!

23. Backup

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

25. Twist-4 Parton Correlation

26. Factorization of Twist-4 Matries