topical seminar on frontier of particle physics 2004: qcd and light hadrons lecture 1
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Topical Seminar on Frontier of Particle Physics 2004: QCD and
Light Hadrons Lecture 1
Wei ZhuEast China Normal University
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Outline of my three lectures
1. What is the structure function: definition and tools
2. Factorization, parton distributions and evolution equations
Definition Time Ordered Perturbation TheoryCollinear Factorization Scheme Parton(Scattering) and Dipole pictures
DGLAP Equations BFKL Equations
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3. Small x physics
Introduction Modified DGLAP Equations JIMWLK Equation Phenomenology of Saturation A Geometric Nuclear Effect
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Outline of Lecture One
Time Ordered Perturbation Theory
Definition
Collinear Factorization Scheme
Parton(Scattering) and Dipole pictures
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1.Definition
EE
m
Q
qp
Qx
EEqQ
22
02
sin4
22
222
WLE
E
Q
eM
E
E
dEd
d
42
42
2
2
1616
1
Leptonic tensor:
)(2 2
2
gkkkkkk
eL
Hadronic tensor:
,)()(,
2
1
4
1 4 pzJzJpzedW ziq
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Structure Functions:
Wμν has total 16 components
Parity Invariance
Time-reversal InvarianceCurrent conservation
Wμν= Wν μ for spin-averaged symmetric
Wμν= Wν μ real
Ə μJ μem =0
22
212
,2
1
2
1, QxW
xqp
xqpQxW
q
qqgW
Dimensionless Structure Functions:
2
22
2
21
21
,,
,,
QxqWpQxF
QxWQxF
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Polarized Structure Functions:
longitudinal structure function
transverse structure function
projection operators
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The kinematic domains probed by the various experiments, shown together with the partons that they constrain
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fCF 2
Coefficient function
Universal parton distribution
PQCD
γT*
γT*
PQCD
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Many Interesting Subjects Relating to SFsFactorizatio
nEvolution DynamicsShadowing, Anti-shadowingSaturation, Color Glass CondensationHigher Twist EffectsNuclear EffectsSpin Problem, Polarized SFs
Asymmetry of Quark Distributions
Diffractive SFs
Large Rapidity Gap
Generalized (skewed) Parton Distributions
……
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Research Tools
Operator Product Expansion
Renormalization Group Theory
Covariant Perturbation Theory
Time Ordered Perturbation Theory (TOPT)
Parton (Scattering) Model
Dipole Model
Pomeron Theory
……
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2.TOPTHistory
Old-fashioned TOPT
Feynman covariant perturbation theory~1949
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CVPT:
0
),(2
0
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l
lll
il
lld
CVPT
TOPT
After contour integral
l0=ω (F)
or =- ω (B)
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17
)(2
ˆ
21
3
EE
kkd
x
F
t
12
t
x
B1
2
)(2
ˆ
21
3
EE
kkd
220 kk
),(ˆ kk
0ˆ2 k
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General Rule For TOPT
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Propagating momentum
CVPT
TOPT
k
k̂
Off-mass-shellOn-energy-shell
On-mass-shellOff-energy-shell
TOPTCVPT
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Application: Weizsäcker-Williams(equivalent particle) Approximation
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1
2 2
3
13
2 2
13
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Collinear TOPT (massless)W.Zhu, H.W.Xiong and J.H.Ruan P.R.D60(1999)094006
F F
F
F
F
B
suppressed finite
22
F
F
B
B
k
k
k
k
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Elementary Vertices of QCD
Elementary Vertices of QED
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Propagating Momentum is but not k !k̂
FF
B
B
y
y
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Application:Eikonal approximation
Emission of absorption of soft particle cause hardly any recoil to a fast moving source.
The eikonal approximation origins in the application of Maxwell electromagnetism theory to geometric optics by Bruns (1895).
In the quantum electrodynamics field theory, the eikonal approximation implies that the denominator of the relativistic propagator, which connecting with the soft photon can be linearized. In this case, the contributions from the soft photos to the hard source can be summed as an exponential. Therefore, the eikonal approximation is an idea tool in the treatment of the corrections of the soft gluons to the high energy processes.
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A massless quark moving along light-cone y+- direction with a large momentum.nPP
Assuming a soft gluon collinear attaches to this hard quark with the momentum k <<p.
F F
BP
k
P+k
F
F
B
P P+k
k
A+=0
=0
Therefore, we can only keep the forward- and backward-components for a fast quark and soft gluon, respectively.
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A similar conclusion holds for a fast gluonF F
B
P P+k
k
α
νμ
β
y
y
F
F
F
F
B
B
B
F
F
F
F
B
B
B
A fast parton moving along the y--direction can not collinear couple with any gluons in the light-cone gauge since the vertex with two collinear backward partons are inhibited.
Wilson Line
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3. Collinear Factorization Schemeγ
*γ*
γ* γ*
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B B
B
BB
B B B
F F F
F
F F
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F FF F
γ* γ* γ*
F
F
F
F
F
FB
knxpknxp
nxp
nxp
nxp
knxp
Collins, Soper, Sterman
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4. Parton(Scattering) and Dipole pictures
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The transverse coefficient function with one quark-loop correction are described by the absorptive part of the amplitudes
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Sudakov variables
Transverse coefficient functions
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LLA
TOPT
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p+ >> q-, Figure (a)
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q->>p+, figure (b)
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