Download Feng Yuan

Transverse spin and 3-D
Parton Structure of
Nucleon
Feng Yuan
Lawrence Berkeley National Laboratory
RBRC, Brookhaven National Laboratory
5/24/2017
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Exploring nucleon is of fundamental in
Science
Search for New
Physics
Fundamental
question of our
universe
Mass, energy-momentum,
Spin structure, …
Jlab, RHIC, Tevatron, LHC,…
Nucleon
Structure
How nuclei
formed from
nucleons, etc..
FRIB (RIA), Jlab, …
Study the strong
interaction physics
Partonic Structure
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QCD dynamics: confinement
Factorization, universality,…
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Feynman Parton Model

Hadronic reactions
Inclusive cross sections probe
the momentum (longitudinal)
distributions of partons inside
nucleon
ElectronIon Collider
12 GeV
JLab
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Extension to transverse
direction…

Semi-inclusive measurements
 Transverse
momentum dependent (TMD)
parton distributions

Deeply Virtual Compton Scattering and
Exclusive processes
 Generalized
parton distributions (GPD)
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Quantum phase space distribution

Wigner distributions
Ji: PRL91,062001(2003)
After integrating over r, one gets TMD
After integrating over k, one gets
Fourier transform of GPDs
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3D image of quarks at fixed-x

GPDs can be used to picture quarks in the proton
(Belitsky-Ji-Yuan, PRD 04)
Beam direction
z
fm
fm
y
x
fm
low x
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moderate x
high x
Transverse momentum
dependent parton distribution

Straightforward extension
 Spin
average, helicity, and transversity
distributions

Transverse momentum-spin correlations
 Nontrivial
distributions, STXPT, ST.PT
 In quark model, depends on S- and P-wave
interference
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Motivations…
Nucleon
Structure, spin correlation,
orbital motion of quarks and gluon
Nontrivial QCD dynamics, and
fundamental test of the factorization,
and the universality of PDFs, FFs,…
Single spin asymmetry (SSA)
phenomena
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Where can we learn TMDs
Semi-inclusive hadron production in
deep inelastic scattering (SIDIS)
 Drell-Yan lepton pair production in pp
scattering
 Di-jet (photon+jet) correlation in pp
scattering
 Relevant e+e- annihilation processes
 Many others…

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Inclusive and
Semi-inclusive DIS
JLab & EIC
Inclusive DIS:
Q
Partonic Distribution depending on
the longitudinal momentum fraction
Semi-inclusive DIS:
Q
Probe additional information for parto
transverse distribution in nucleon
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JLab & EIC


Transverse Momentum Dependent (TMD)
Parton Distributions and Fragmentations
Novel Single Spin Asymmetries
U: unpolarized beam
T: transversely polarized target
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Two major contributions

Sivers effect in the distribution
ST
kT
P

Collins effect in the fragmentation
(zk+pT)
(k,sT)

ST (PXkT)
~pTXsT
Other contributions…
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Universality of the Collins
Fragmentation
ep--> e Pi X
e+e--> Pi Pi X
pp--> jet(->Pi) X
Metz 02, Collins-Metz 02,
Yuan 07,
Gamberg-Mukherjee-Mulders 08
Meissner-Metz 0812.3783
Yuan-Zhou, 0903.4680
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Model calculations of the Collins
Effects
Metz 02, Collins-Metz 02:
Gamberg-Mukherjee-Mulders, 08
Universality of the Collins function!!
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Similar arguments for pp collisions
Yuan, 0709.3272
By using the Ward
Identity:
same Collins fun.
The Collins function is the same as e^+e^- and SIDIS
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Extend to two-gluon exchange
Universality preserved
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Key observations
Final state interactions DO NOT
provide a phase for a nonzero SSA
 Eikonal propagators DO NOT contribute
to a pole
 Ward identity is applicable to warrant
the universality arguments

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Sivers effect is different
It is the final state interaction
providing a phase to the nonzero SSA
 Ward identity is not easy to apply
 Non-universality in general
 Only in special case, we have
“Special Universality”

Brodsky,Hwang,Schmidt 02
Collins, 02;
Ji,Yuan,02;
Belitsky,Ji,Yuan,02
DIS and Drell-Yan

Initial state vs. final state interactions
*
*
Drell-Yan
DIS
HERMES

“Universality”: QCD prediction
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Experiment SIDIS vs Drell Yan
HERMES Sivers Results
RHIC II Drell Yan Projections
0
0
Markus Diefenthaler
DIS Workshop
Munich, April 2007
0.1
0.2
0.3 x
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http://spin.riken.bnl.gov/rsc/
QCD Dynamics
TRANSVERSE MOMENTUM
DEPENDENCE
Transition from Perturbative region
to Nonperturbative region

Compare different region of PT
Nonperturbative TMD
Perturbative region
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Perturbative tail is calculable

Transverse momentum dependence
Power counting,
Brodsky-Farrar, 1973
Integrated Parton Distributions
Twist-three functions
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A unified picture
Transverse
momentum
dependent
Collinear/
longitudinal
QCD
PT
<<
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PT
<<
Q
Ji-Qiu-Vogelsang-Yuan,2006
Yuan-Zhou, 2009
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NLO corrections to SSA
Vogelsang-Yuan, arXiv:0904.0410

SSA in Drell-Yan as an example,

Collinear factorization
Collinear functions, evolution: Kang-Qiu, 08;
Zhou-Yuan-Liang 08
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Future perspective
Current and planed experiments will
have more and more data on various
transverse spin observables
 Recent developments have laid solid
theoretical ground to apply QCD theory
to study the relevant nucleon structure

 Quark
transversity
 Orbital motion of quarks and gluon
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Semi-Inclusive DIS


Transverse Momentum Dependent (TMD)
Parton Distributions and Fragmentations
Novel Single Spin Asymmetries
U: unpolarized beam
T: transversely polarized target
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What’s Single spin asymmetry?
Transverse plane
Final state particle is
Azimuthal symmetric
Single Transverse Spin
Asymmetry (SSA)
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SSAs in Modern era : RHIC, JLab,
HERMES, …
STAR
Central rapidity!!
BRAHMS
Large SSA continues at DIS ep
and collider pp experiments!!
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Naïve parton model fails

If the underlying scattering mechanism is
hard, the naïve parton model generates a
very small SSA: (G. Kane et al, 1978),
 It

is in general suppressed by αSmq/Q
We have to go beyond this naïve picture
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Two mechanisms in QCD

Spin-dependent transverse momentum
dependent (TMD) function
S
k
T
 Sivers
T
Sivers function ~ ST (PXkT)
90
.
P
 Brodsky,Hwang,Schmidt, 02 (FSI)
 Gauge Property: Collins 02;Belitsky-Ji-Yuan,NPB03
Boer-Mulders-Pijlman,03
 Factorization: Ji-Ma-Yuan,PRD04;Collins,Metz,04

Twist-3 quark-gluon correlations (coll.)
 Efremov-Teryaev,
82, 84
 Qiu-Sterman, 91,98
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Quantum Phase Space Distribution

Wigner operator

Wigner distribution: “density” for quarks having
position r and 4-momentum k (off-shell)
a la Saches
7-dimensional distribtuion
No known experiment can measure this!
Polarized TMD Quark Distributions
Nucleon
Unpol.
Long.
Trans.
Quark
Unpol.
Long.
Trans.
Boer, Mulders, Tangerman
33 (96&98)
Three classes in the view of a
quark model

S-wave
 Unpolarized,

helicity, transversity
S-P interference
 g1T,
h1L
 f1T┴, h1┴

P-P or S-D interference
 h1T┴

Miller 07, Burkardt 07, Avakian et al 08.
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