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Numerical Method of DGLAP Evolution and Modified FFs in Medium

Numerical Method of DGLAP Evolution and Modified FFs in Medium. Wei-Tian Deng. Numerical Methods. The HOPPET (High Order Perturbative Evolution Toolkit) higher-order Runge-Kutta method x-spaces grid. Taylor Series:. Euler method:. Euler method:. Second-Order Runge-Kutta method:.

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Numerical Method of DGLAP Evolution and Modified FFs in Medium

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  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. Taylor Series: Euler method: Euler method:

  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. Final state? Quenching • Final state interactions responsible for “jet quenching” instead of initial states. hadronization 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. Z=0.2 Z=0.4 Z=0.8 Z=0.6 Suppress of FFs Vs. L E=100 GeV Q=E

  18. ˆ q Energy Loss Vs.

  19. ˆ q Energy Loss Vs. L=2 fm L=5 fm

  20. ˆ q Energy Loss Vs. L=2 fm L=5 fm

  21. Outlooks

  22. Outlook

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