Probing small x gluon with low mass Drell-Yan dilepton

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Topical Seminar on Frontier of Particle
Physics 2004 QCD and Light Hadrons Lecture 1
Wei Zhu East China Normal University
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Outline of my three lectures

• What is the structure function
• definition and tools

• Definition
• Time Ordered Perturbation Theory
• Collinear Factorization Scheme
• Parton(Scattering) and Dipole pictures

• Factorization, parton distributions
• and evolution equations

• DGLAP Equations
• BFKL Equations

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• Small x physics

• Introduction
• Modified DGLAP Equations
• JIMWLK Equation
• Phenomenology of Saturation
• A Geometric Nuclear Effect

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Outline of Lecture One

• Definition

• Time Ordered Perturbation Theory

• Collinear Factorization Scheme

• Parton(Scattering) and Dipole pictures

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1.Definition
Leptonic tensor
Hadronic tensor
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Structure Functions
Wµ? has total 16 components

• Parity Invariance

Wµ? W? µ for spin-averaged symmetric

• Time-reversal Invariance

Wµ? W? µ real

• Current conservation

? µJ µem 0
Dimensionless Structure Functions
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Polarized Structure Functions
transverse structure function
longitudinal 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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Many Interesting Subjects Relating to SFs

• Factorization

• Evolution Dynamics

• Shadowing, Anti-shadowing

• Saturation, Color Glass Condensation

• Higher Twist Effects

• Nuclear Effects

• Spin 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.TOPT
History
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CVPT
CVPT
TOPT
After contour integral l0? (F) or -
? (B)
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General Rule For TOPT
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Propagating momentum
Off-mass-shell On-energy-shell
CVPT
On-mass-shell Off-energy-shell
TOPT
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Application Weizsäcker-Williams(equivalent
particle) Approximation
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3
3
3
1
1
1
1
2
2
2
2
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Collinear TOPT (massless) W.Zhu, H.W.Xiong and
J.H.Ruan P.R.D60(1999)094006
finite
suppressed
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Elementary Vertices of QCD
Elementary Vertices of QED
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Propagating Momentum is but not k !
B
F
F
B
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ApplicationEikonal 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.
Assuming a soft gluon collinear attaches to this
hard quark with the momentum k ltltp.
A0
F
F
F
B
Pk
Pk
P
P
B
k
F
k
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 gluon
F
F
µ
?
P
Pk
a
k
B
ß
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 Scheme
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?
?
?
F
F
F
k
B
F
F
F
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 gtgt q-, Figure (a)
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q-gtgtp, figure (b)
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