1. 1 Why GLR-MQ-ZRS equation is necessary for understanding STAR BES program? Wei Zhu East China Normal University KITPC 2012.07.

2. Nuclear suppression factor

4. =TMD Unintegrated distribution=TMD

5. Reasons 1. Integrated and unintegrated gluon distributions can not directly measured, they only can been extracted from data using QCD evolution equations. 2. 3. We need a QCD evolution equation, which includes nuclear shadowing and antishadowing effects.

7. Why not? DGLAP Equation. Nuclear shadowing and antishadowing effects are assumed in input by hand.

8. Why not BFKL equation, It works at x< and has not nonlinear corrections. BK equation=BFKL+gluon fusion. It works at x< and does not consider the antishadowing corrections..

9. JIMWLK equation Although it predicts the saturation at small x limit, however, can not describe the parton distributions at < x<1.

10. Only GLR-MQ-ZRS Equation 1983 version L.V. Gribov, E.M. Levin and M.G. Ryskin, Phys. Rep.100 (1983) 1.

12. DGLAP Corrections of Gluon Fusion to DGLAP GLR-MQ-ZRS Fusion 3

13. Abramovsky, Gribov and Kancheli, Cutting rule (1973) 2 -4 1

14. 1986 version A.H. Mueller and J. Qiu, Nucl. Phys. B268 (1986) 427.

16. 1999 version W. Zhu, Nucl. Phys. B551 (1999) 245. W. Zhu and J.H.Ruan, Nucl. Phys. B559 (1999) 378; W. Zhu and Z.Q. Shen, HEP$\&$ NP, 29 (2005) 109.

18. 18 ZRS version TOPT cutting rule

19. TOPT Cutting Rules F.E. Close, J. Qiu and R.G. Roberts, Phys. Rev. D 40 (1989) 2820. W. Zhu, Nucl. Phys. B551, 245 (1999). W. Zhu and J.H. Ruan, Nucl. Phys. B559, 378(1999). W. Zhu, Z.Q. Shen and J.H. Ruan, Nucl. Phys. B692, 417 (2004);

20. TOPT-Cutting rule 1.List all possible TOPT diagrams with different cuts. 2.The contributions of the cut diagrams have the identical integral kernel with only the following different factors R:

21. (a)The sign in the first factor is determined by the energy deficits; (b)The second factor takes a value of 1/2 if the probe-vertex inserts in the initial line; (c) function relates to the probe vertex.

26. Recombination functions

27. 4. Twist-4 level (collinear frame) CVPTgeneralize Mueller-Qiu (1986) to whole x region

28. TOPT: Zhu, Ruan (1999); Bluemlein, Ravindran, Ruan, Zhu (2001); Zhu,Shen (2004)

29. Spin-dependent gluon recombination function

30. Why yes? 1.GLR-MQ-ZRS equation has solid QCD basic. 2.LL(Q^2). 0.001<x<1. DLL(1/x,Q^2). 0.001<0.1-0.2

31. GLR-MQ-ZRS at small x

37. Cronin Effect

38. Nuclear modification factor

39. KMR Scheme

43. Nuclear shadowing and antishadowing effects A+A(for gluon)>p+A(for gluon) ~eA(for gluon)>eA(for quarks) Contributions of the gluon fusion at initial state are inescapable in RHIC and LHC physics.

44. ?

46. ??? ?

48. arXiv:1012.4224 W. Zhu, J.H. Ruan and F.Y. Hou A rapid crossover from week energy loss to strong energy loss at a universal critical energy of gluon jet Ec ∼ 10GeV

51. Predictions for higher energy data at LHC

52. Predictions

54. Predictions for low energy data at STAR Primary results (works at x<0.3)

57. Conclusions 1. We do not exclude the contributions from finite state interactions. 2. Contributions of the gluon fusion at initial state are inescapable in RHIC and LHC physics 3. Please using GLR-MQ-ZRS equation (1999 version) in your relating works.