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