Modified Fragmentation Function in Strong Interaction Matter

1. Modified Fragmentation Function in Strong Interaction Matter Enke Wang (Institute of Particle Physics, Huazhong Normal University) • Jet Quenching in QCD-based Model • Jet Quenching in High-Twist pQCD • Jet Tomography of Hot and Cold Strong Interaction Matter • Modification of Dihadron Frag. Function

2. leading particle hadrons q q hadrons leading particle A-A collision p-p collision Leading particle suppressed hadrons q p q hadrons leading particle suppressed Jet Quenching: Fragmentation Function: DGLAP Equation

3. I. Jet Quenching in QCD-based Model G-W (M. Gyulassy, X. –N. Wang) Model: Static Color-Screened Yukawa Potential

4. Feynman Rule: p-q p q p p+k p k k-q,a k,c q,b

5. Opacity Expansion Formulism (GLV) Double Born Scattering GLV, Phys. Rev. Lett. 85 (2000) 5535; Nucl. Phys. B594 (2001) 371 Elastic Scattering

6. Assumption • The distance between the source and the scattering center are large compaired to the interaction range: • The packet j(p) varies slowly over the range of the momentum transfer supplied by the potential: • The targets are distributed with the density: • Opacity: Mean number of the collision in the medium

7. First Order in opacity Correction

8. First Order in opacity Correction Induced gluon number distribution: Non-Abelian LPM Effect Medium-induced radiation intensity distribution: Induced radiative energy loss: QCD: QED:

9. Higher order in Opacity Reaction Operator Approach: (GLV) Induced gluon number distribution: Non-Abelian LPM Effect

10. Radiated Energy Loss vs. Opacity First order in opacity correction is dominant!

11. Detailed Balance Formulism (WW) B-E Enhancement Factor 1+N(k) Thermal Distribution Func. N(k) Stimulated Emission Thermal Absorption E. Wang & X.-N. Wang, Phys. Rev. Lett.87 (2001) 142301

12. Final-state Radiation Energy loss induced by thermal medium: = Net contribution: Energy gain Stimulated emission increase E loss Thermal absorption decrease E loss

13. First Order in Opacity Correction Single direct rescattering: Double Born virtual interaction: Key Point: Non-Abelian LPM Effect—destructive Interference!

14. Energy Loss in First Order of Opacity Energy loss induced by rescattering in thermal medium: Take limit: Zero Temperature Part: 2 L GLV Result Temperature-dependent Part: Energy gain

15. Numerical Result for Energy Loss • Intemediate large E, absorption is important • Energy dependence becomes strong • Very high energy E, net energy gain can be neglected

16. Parameterization of Jet Quenching with Detailed Balance Effect Average parton energy loss in medium at formation time: Energy loss parameter proportional to the initial gluon density Modified Fragmentation Function (FF) (X. -N. Wang , PRC70(2004)031901)

17. Comparison with PHENIX Data PHENIX, Nucl. Phys. A757 (2005) 184

18. DGLAP Equation at Finite Temperature J. A. Osborne, E. Wang, X.-N. Wang, Phys. Rev. D67 (2003) 094022

19. DGLAP Equation at Finite Temperature Splitting function at finite temperature:

20. Quark Energy Loss from Splitting Function The minus sign indicates that the absorptive processes in the plasma overcome the emissive processes. The net Contribution is energy loss!

21. II. Jet Quenching in High-Twist pQCD e- Frag. Func.

22. Modified Fragmentation Function Cold nuclear matter or hot QGP medium lead to the modification of fragmentation function

23. Jet Quenching in e-A DIS e- X.-N. Wang, X. Guo, NPA696 (2001); PRL85 (2000) 3591

24. Modified Frag. Function in Cold Nuclear Matter Modified splitting functions Two-parton correlation: LPM

25. Modified Frag. Function in Cold Nuclear Matter Fragmentation function without medium effect: parton hadrons are measured, and its QCD evolution E ph tested in e+e-, ep and pp collisions Fragmentation function with medium effect: Suppression of leading particles

26. Heavy Quark Energy Loss in Nuclear Medium 2) Induced gluon spectra from heavy quark is suppressed by “dead cone” effect Dead cone Suppresses gluon radiation amplitude at B. Zhang, E. Wang, X.-N. Wang, PRL93 (2004) 072301; NPA757 (2005) 493 Mass effects: 1) Formation time of gluon radiation time become shorter LPM effect is significantly reduced for heavy quark

27. Heavy Quark Energy Loss in Nuclear Medium LPM Effect 1) Larg or small : 2) Larg or small :

28. Heavy Quark Energy Loss in Nuclear Medium The dependence of the ratio between charm quark and light quark energy loss in a large nucleus The dependence of the ratio between charm quark and light quark energy loss in a large nucleus

29. III. Jet Tomography of Hot and Cold Strong Interaction Matter Energy loss E. Wang, X.-N. Wang, Phys. Rev. Lett. 89 (2002) 162301 Cold Nuclear Matter: Quark energy loss = energy carried by radiated gluon

30. Comparison with HERMES Data , , HERMES Data: Eur. Phys. J. C20 (2001) 479

31. Expanding Hot Quark Gluon Medium R. Baier et al

32. Initial Parton Density and Energy Loss jet1 jet2 R » A 15 t 2 0 Initial energy loss in a static medium with density t 0.1 fm = 0 GeV/fm Initial parton density(Energy loss) is 15~30 times that in cold Au nuclei !

33. Comparison with STAR data STAR, Phys. Rev. Lett. 91 (2003) 172302

34. d-Au Result 理论预言 实验结果 E. Wang, X.-N. Wang, Phys. Rev. Lett. 89 (2002) 162301 STAR, Phys. Rev. Lett. 91(2003) 072304

35. IV.Modification of Dihadron Frag. Function h1 h1 h2 h2 jet A. Majumder, Enke Wang, X. –N. Wang, Phys. Rev. Lett. 99 (2007) 152301 Dihadron fragmentation:

36. DGLAP for Dihadron Fragmentation h1 h1 h2 h2 h1 h2

37. Evolution of Dihadron Frag. Function

38. Evolution of Dihadron Frag. Function

39. Medium Modi. of Dihadron Frag. Function

40. Nuclear Modification of Dihadron Frag. Func. e-A DIS

41. Hot Medium Modification

42. Thank You