Topical Seminar on Frontier of Particle Physics 2004: QCD and Light Had

rons Lecture 2

Wei ZhuEast 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 equationsBjorken fram

eThe 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 probeImpulse approximation

At small x and fixed Q2, beyond impulse approximation

DGLAP amplitude (for gluon)

Impulse approximation

NQ xx

What will happen?

QCD, Parton Model, Tree Level

+ +

++

+ +……2

a b c

d e

fBeyond 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 z1 >>z2 at the LLA(1/x), we insert δ(z1 -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