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

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

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

5. Opacity Expansion Formulism (GLV)
GLV, Phys. Rev. Lett. 85 (2000) 5535; Nucl. Phys. B594 (2001) 371
Elastic Scattering
Double Born 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)
E. Wang & X.-N. Wang, Phys. Rev. Lett.87 (2001)
Stimulated Emission
Thermal Absorption
B-E Enhancement Factor
1+N(k)
Thermal Distribution Func.
N(k)

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: L 2
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
Nucl. Phys. A757 (2005) 184

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

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
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
X.-N. Wang, X. Guo, NPA696 (2001); PRL85 (2000) 3591 e-

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

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

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

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

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

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
Initial energy loss in
a static medium with
density 15 2 A R t t =
0.1 fm
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)

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

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

36. DGLAP for Dihadron Fragmentation

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