Gluon Radiation of the Heavy Quark in Nuclei

1. Gluon Radiation of the Heavy Quarkin Nuclei Ben-Wei Zhang Institute of Particle Physics Central China Normal Univeristy Weihai, Shandong --- Augest 4, 2004

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

3. parton hadrons ph E Jet Quenching Jet quenching has been observed as a new nuclear phenomenon at RHIC.

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: Dokshitzer and Kharzeev Djordjevic and Gyulassy Armesto, Salgado and Wiedemann …… • Twist Expansion approach in pQCD B.W. Zhang, E. Wang and X.N. Wang, Phys. Rev. Lett. 93(2004) in press

6. 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 parton model, for the heavy quark production we obtain :

8. Fragmentation Function • Charm quark fragmentation function in Peterson form:

9. Mutiple 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.

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

11. Generalized Factorization

12. Quark-Gluon Double Scattering

13. Collinear Approximation • Make a collinear approximation: • The tensor structure can be factorized:

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

15. Other Processes

16. Hard Partonic Part Dead-Cone effect of heavy quark propagating

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

18. Twist-4 Parton Correlation

19. Two-parton Correlation Function Twist-4 parton correlation function is in principle not calculable. With some approximations we can estimate J. Osborne and Xin-Nian Wang, NPA 710(2002)281

20. Heavy Quark Energy Loss Twist-4 correlation functions approximated as: Heavy quark energy loss can be derived as:

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

22. Nuclear Size Dependence

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

24. Conclusions • Heavy quark energy loss induced by gluon radiation is derived in terms of Modified FF with pQCD. • 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. • Heavy quark energy loss is significantly suppressed relative to a light quark due to mass effect. Thanks to my collaborators: Xin-Nian Wang and Enke Wang

25. Thank you very much! 谢谢!