1. Numerical Method of DGLAP Evolution and Modified FFs in Medium
Wei-Tian Deng

2. Numerical Methods
The HOPPET (High Order Perturbative Evolution Toolkit)
higher-order Runge-Kutta method
x-spaces grid.

3. Euler method:
Euler method:
Taylor Series:

4. Second-Order Runge-Kutta method:

5. Fourth-Order Runge-Kutta method:

6. X-spaces Grid
PDFs
Piecewise interpolating polynomials

7. X-spaces Grid
convolution
DGLAP evolution
Evolution operator

8. Relative Accuracy

9. Relative Accuracy
The more denser grids, the better relative accuracy

10. HOPPET vs. KKP (vacuum)

11. Quenching
Final state interactions responsible for “jet quenching” instead of initial states.
hadronization
Final state?
shower
Splitting function

12. DGLAP The DGLAP evolution function of (FFs):
The splitting functions in vacuum:

13. Modified Splitting Functions

14. Modified FFs

15. Modified FFs

16. Suppress of FFs Vs. L

17. Suppress of FFs Vs. L
E=100 GeV
Q=E
Z=0.2
Z=0.4
Z=0.6
Z=0.8

18. Energy Loss Vs. ˆ q

19. Energy Loss Vs. ˆ q
L=2 fm
L=5 fm

20. Energy Loss Vs. ˆ q
L=2 fm
L=5 fm

21. Outlooks

22. Outlook