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

Outline of Lecture Two  BFKL Equations  DGLAP Equations

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

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

Cold spots Size of cold spot Resolution of probe Impulse approximation

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

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

DGLAP BFKL Modified DGLAP A New Equation?

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

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

Impact Space (A. H. Mueller) Evolution Kernel

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

Contributions from virtual diagrams Using the TOPT cutting rule

Integrated distribution Unintegrated distribution

Small x Physics