1. Topical Seminar on Frontier of Particle Physics 2004: QCD and Light Hadrons Lecture 2 Wei Zhu East China Normal University

2. Outline of Lecture Two  BFKL Equations  DGLAP Equations

3. 1. A simplest derivation of DGLAP equations Bjorken Frame, A + =0

9. 2. A simplest derivation of BFKL equations Bjorken frame The virtual probe has almost zero-energy and zero-longitudinal momentum, so that the momentum of the probe is mainly transverse to the nucleon direction. Resolution of probe

10. Cold spots Size of cold spot Resolution of probe Impulse approximation

11. At small x and fixed Q 2, beyond impulse approximation DGLAP amplitude (for gluon) Impulse approximation What will happen?

12. QCD, Parton Model, Tree Level ++ ++ + +…… 2 ab c d e f Beyond impulse approximation

13. DGLAP BFKL Modified DGLAP A New Equation?

14. BFKL equation We separated out the probe vertex using the W -W approximation, where the transverse momenta of initial gluons are unvanished.

15. Taking the leading logarithmic (1/x) approximation, one can get the total amplitude

16. Impact Space (A. H. Mueller) Evolution Kernel

17. Note that z 1 >>z 2 at the LLA(1/x), we insert δ(z 1 -1) and obtain the evolution equation where y = ln(1/z) and

18. Contributions from virtual diagrams Using the TOPT cutting rule

19. Integrated distribution Unintegrated distribution

20. Small x Physics