1. Color Glass Condensate HIM MEETING( 광주 ) Dec. 4, 2004

2. 0. Introduction 1) What is CGC? 2) Physics related to the CGC 3) Classical Theory(MV) 4) Quantum Theory 5) RGE >> From IANCU, LEONIDOV & McLERRAN (hep-ph/0202270) Try McLerran or A. Mueller for general references

3. Notation: Light Cone(LC) coordinate: Light Cone gauge: Rapidity:

4. Pseudorapidity: Feynman, Bjorken x:

5. I. What is CGC ? - Color: colored particles - Glass: a) disordered b) Solid in short time scale but Liquid in long time scale. - Condensate: highly dense, ~ 1/alpha_s

6. II. Physics Related to the CGC A. Total Cross Section of Hadron-Hadron: 1) Intrinsically non-perturbative even though E increase 2) Regge theory in 70s but not so satisfactory 3) Froissart bound: Unitarity of scattering matrix 4) Why the unitarity saturated. 5) Is this understandable from QCD?

8. B. Particle Production 1) Can we compute dN/dy even at y=0? 2) Feynman scaling: Cut the green in half (low energy) and move to red (high energy) distribution. They match!!! i.e. independent of energy  As E goes up, the small x degree of freedom fills in while the large x held fixed  Some kind of RG property shows up.

11. C. DIS(Electron-Hadron) 1) Electron emits virtual photon  fluctuate into quark-antiquark  interact with partons in hadron 2) The rapidity distribution for gluons of hadron is almost same as the distribution for produced hadrons after hadron-hadron collision(or heavy ion collision) 3) However, ZEUS data show sharp increase in rapidity distribution  SMALL-x problem.

14. 4) The saturation must be shown up!!! the saturation momentum: 5) The saturation momentum increase as E increases  Once  Weak coupling:  Hope gluon, quark distribution can be calculable.  However, it is highly dense so that perturbation cannot be applicable

16. D. Geometrical Scaling Structure functions from DIS depend on (in general) (x, Q^2/Lambda^2), but the function depend only on at x < 0.01 (HERA), i.e. independent of x.  Some kind of scaling at small x.

17. E. Universality 1) Weak universality: At sufficient high energy, physics must depend on the specific properties of hadron(nuclei) via saturation scale Q_s(x,A), i.e. With same Q_s, they have to have same properties. 2) Strong universality: Statistical sense. The behavior of correlation function is given by universal critical exponents.

18. III. Classical Theory (MV) A. Basics WHAT WE WILL SOLVE: : Classical soft gluon field : Color current of fast partons in x^+ direction sitting at x^- = 0

20. -Softer partons have larger energies(note that)  thus shorter life-times  time-independent color source in view of soft field:  treat the density as a classical random variable with some probability, weight function, as functional:  Using,

21. - The Gluon correlation functions at scale for example, - Gluon distributions: : # of gluons having longitudinal momentum between and and transverse size The gluon distribution with transverse momenta per unit rapidity:

22. To get the readable form: Consider the equation of motion in light cone gauge without source: for + component, therefore, The quantization: with the commutation relation,

23. The gluon density with Fock space operators, Using that In coordinate space, This form is gauge dependent!!!!!

24. Now inserting WILSON LINES: where the Wilson line is We choose the path such that along the horizontal line, along the vertical line, (retarded condition) IN RESULT,

25. Another interesting quantity: number of gluons per unit rapidity and transverse phase space: And for homogeneous transverse space,

26. B. Formal Solution of 가. Anticipating a solution, so A^i are pure gauge, 나. Now choose Covariant gauge: ( 가 ) 항을 이용, 다. Formal Solution

27. Thus, 라. Gauge transforming to LC-gauge Since, we get the equation with solution, 마. Classical source is dummy and ‘measure’ and ‘weight function’ are gauge invariant so that

28. C. MV approximation Independent color sources: A*N_c valence quarks Consider a tube of transverse area: The number of valence quarks in the tube:

29. 따라서, 한편, 위의 correlator 들은 ( 마 ) 항을 이용할 때 다음의 weight function 을 사용하면 유도될 수 있다,

30. Linearized Solution: gluon field 에 대한 운동방정식에서 선형항만 사용하여 풀면,

31. Exact and non-linear solution: 이 경우 다음의 correlator 계산이 필수, 여기서 기본 propagator 는 위의 correlator 를 전개한 후 위의 propagator 을 이용하여 contraction 을 계산하면,

32. 여기서, using

33. Final Solution:

34. Quantum Theory and RGE can be presented by someone who is an expert on the subject !! THANKS