山东大学博士开题报告.pdf

Hard, Infrared safe, calculable Universal, extremely difficult (if not impossible) to calculate
Short-distance and long-distance are separately gauge invariant.
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Factorization
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Motivation
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Factorization
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Ward identities
H(n)→H(n-1)
gauge link (A+)
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Spin Dependence
Hadronic Tensor = Hard × Gauge Invariant Matrix (4×4)
Gamma Matrices × Lorentz Covariants
Calculate with Models Light-cone wave function, String, Cluster
Di-hadron correlation….
Thanks for your attention!
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Backup
Subsection
30
Fragmentation Functions
Parameterization
A usual parameterization for light hadrons,
Dih
(x,

2 0
)

Nx
(1
x)
(1

(1
x)
).
Spin dependent fragmentation function?
2012-11-20
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Motivation
Feynman Diagram
Very Clean
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Motivation
Factorization (collinear)
d H dz
3 ee
Semi-inclusive case (almost done). Collins Effect
Calculate with Models Light-cone wave function, String, Cluster
Di-hadron correlation….
2012-11-20
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i
ei2 DiH ( z, Q 2 )
zDiH (z, Q 2 )dz 1 H
d H 3 ' ' '
dz
ee
i
ei2 DiH ' ( z, Q 2 )
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Transverse polarization of quarks in hadrons, V. Barone, etc
QCD evolution of the Sivers function, Collins, Qiu, 2012
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Motivation
Parameterization (Collins Function)
u/d pi +
u/d pi +
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Transversity and Collins functions from SIDIS and e+e- data, 2007
Twist-2 Twist-3
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Twist-2
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Spin Dependence
Frame
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Spin Dependence
Cross Section
cA=0 twist-2
cos θs
sin θs
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Collinear Expansion
Framework
Perturbative Field Theory
Collinear Expansion
Not gauge invariant
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Collinear Expansion
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Fragmentation Functions
unpolarized FF
d H
dz
3 ee
i
ei2 DiH ( z, Q 2 )
1 f1 x D(x)
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Spin Dependence
Polarization
Pz
e+e-Z0qq
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Semi-inclusive
Hale Waihona Puke Semi-inclusive
Lorentz Structure
Leading twist terms
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Collinear Expansion
Wn Tr[H n (k1,..., kn ) 0 | (0) A1A2... | h h | ...An (z) | 0 ]
H(1)(x, x)× Taylor Exp.
Decomposition of A
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Qiu Jian-wei’s lectures at KITPC, 2012
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Motivation
Non-perturbative QCD Parton Distribution Functions
Fragmentation Functions
D(z) quark with momentum k hadron with momentum zk
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Semi-inclusive
Cross Section
The Lund 3P0 Mechanism
+ ···(k·S)
qq pair in 3P0 state,
Sq Sq L / 2
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X. Artru, Arxiv: 1001.1061v1 [hep-ph]
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Spin Dependence

CA0
twist-2
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sin θs cos θs
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Multi-gluon Interaction
Taylor Expansion Decomposition of A(x)
Ward Identities
Gauge Invariant
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Ellis, Inclusive DIS, Prof. Liang & Prof. Wang SIDIS
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Motivation
Non-perturbative QCD
Parton Distribution Functions
Drell-Yan
DIS
Fragmentation Functions
e+ e-
D(z) quark with momentum k hadron with momentum zk
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Page 252, PDG
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Motivation
Parameterization (collinear)
A usual parameterization for light hadrons,
Page 252, PDG Global analysis of fragmentation functions for protons and charged hadrons, 2007
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Motivation
TOPICS
Flavor dependent Polarized fragmentation functions High-twist TMD fragmentation functions High-twist evolution function
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Plan
Gauge Invariant Fragmentation Functions.
Multi-gluon exchange (collinear expansion)
The Spin-dependent Cross Section. Lorentz structure