1. 1 Topical Seminar on Frontier of Particle Physics 2004: QCD and Light Hadrons Lecture 1 Wei Zhu East China Normal University

2. 2 Outline of my three lectures 1.What is the structure function: definition and tools 2.Factorization, parton distributions and evolution equations  Definition  Time Ordered Perturbation Theory  Collinear Factorization Scheme  Parton(Scattering) and Dipole pictures  DGLAP Equations  BFKL Equations

3. 3 3.Small x physics  Introduction  Modified DGLAP Equations  JIMWLK Equation  Phenomenology of Saturation  A Geometric Nuclear Effect

4. 4 Outline of Lecture One  Time Ordered Perturbation Theory  Definition  Collinear Factorization Scheme  Parton(Scattering) and Dipole pictures

5. 5 1.Definition Leptonic tensor: Hadronic tensor:

6. 6 Structure Functions: W μν has total 16 components  Parity Invariance  Time-reversal Invariance  Current conservation W μν = W ν μ for spin-averaged symmetric W μν = W ν μ real Ə μ J μ em =0 Dimensionless Structure Functions:

7. 7 Polarized Structure Functions: longitudinal structure function transverse structure function projection operators

8. 8

9. 9 The kinematic domains probed by the various experiments, shown together with the partons that they constrain

10. 10 Coefficient function Universal parton distribution PQCD γT*γT* γT*γT*

11. 11 Many Interesting Subjects Relating to SFs  Factorization  Evolution Dynamics  Shadowing, Anti-shadowing  Saturation, Color Glass Condensation  Higher Twist Effects  Nuclear Effects  Spin Problem, Polarized SFs  Asymmetry of Quark Distributions  Diffractive SFs  Large Rapidity Gap  Generalized (skewed) Parton Distributions  ……

12. 12 Research Tools  Operator Product Expansion  Renormalization Group Theory  Covariant Perturbation Theory  Time Ordered Perturbation Theory (TOPT)  Parton (Scattering) Model  Dipole Model  Pomeron Theory  ……

13. 13 2.TOPT History Old-fashioned TOPT Feynman covariant perturbation theory ~1949

14. 14

15. 15 CVPT: CVPT TOPT After contour integral l 0 =ω (F) or =- ω (B)

16. 16

17. 17 x F t 1 2 t x B 1 2

18. 18 General Rule For TOPT

19. 19 Propagating momentum CVPT TOPT Off-mass-shell On-energy-shell On-mass-shell Off-energy-shell

20. 20 Application: Weizsäcker-Williams(equivalent particle) Approximation 1 3 1 2 2 3 1 3 2 2 1 3

21. 21 Collinear TOPT (massless) W.Zhu, H.W.Xiong and J.H.Ruan P.R.D60(1999)094006 F F F F F B suppressed finite

22. 22 F F B B k k k k

23. 23 Elementary Vertices of QCD Elementary Vertices of QED

24. 24

25. 25 Propagating Momentum is but not k ! F F B B

26. 26 Application:Eikonal approximation Emission of absorption of soft particle cause hardly any recoil to a fast moving source. The eikonal approximation origins in the application of Maxwell electromagnetism theory to geometric optics by Bruns (1895). In the quantum electrodynamics field theory, the eikonal approximation implies that the denominator of the relativistic propagator, which connecting with the soft photon can be linearized. In this case, the contributions from the soft photos to the hard source can be summed as an exponential. Therefore, the eikonal approximation is an idea tool in the treatment of the corrections of the soft gluons to the high energy processes.

27. 27 A massless quark moving along light-cone y + - direction with a large momentum. Assuming a soft gluon collinear attaches to this hard quark with the momentum k <<p. F F B P k P+k F F B P k A + =0 =0 Therefore, we can only keep the forward- and backward- components for a fast quark and soft gluon, respectively.

28. 28 A similar conclusion holds for a fast gluon F F B P P+k k α ν μ β F F F F B B B F F F F B B B A fast parton moving along the y - -direction can not collinear couple with any gluons in the light-cone gauge since the vertex with two collinear backward partons are inhibited. Wilson Line

29. 29 3. Collinear Factorization Scheme γ*γ* γ*γ* γ*γ*γ*γ*

30. 30 BB B BB BBB FFF F FF

31. 31 FF FF γ*γ* γ*γ* γ*γ* F F F F F F B k Collins, Soper, Sterman

32. 32 4. Parton(Scattering) and Dipole pictures

33. 33 The transverse coefficient function with one quark-loop correction are described by the absorptive part of the amplitudes

34. 34 Sudakov variables Transverse coefficient functions

35. 35 LLA TOPT

36. 36 p + >> q -, Figure (a)

37. 37 q - >>p +, figure (b)

38. 38