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Transverse spin and 3-D Parton Structure of Nucleon. Feng Yuan Lawrence Berkeley National Laboratory RBRC, Brookhaven National Laboratory. Exploring nucleon is of fundamental in Science. Search for New Physics. Fundamental question of our universe. Jlab, RHIC, Tevatron, LHC,….

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Transverse spin and 3 d parton structure of nucleon

Transverse spin and 3-D Parton Structure of Nucleon

Feng Yuan

Lawrence Berkeley National Laboratory

RBRC, Brookhaven National Laboratory

Exploring nucleon is of fundamental in science
Exploring nucleon is of fundamental in Science

Search for New Physics

Fundamental question of our universe

Jlab, RHIC, Tevatron, LHC,…

Mass, energy-momentum,

Spin structure, …

Nucleon Structure

How nuclei formed from nucleons, etc..

Study the strong interaction physics

FRIB (RIA), Jlab, …

Partonic Structure

QCD dynamics: confinement

Factorization, universality,…

Feynman parton model

Hadronic reactions

Feynman Parton Model

  • Inclusive cross sections probe the momentum (longitudinal) distributions of partons inside nucleon


Ion Collider

12 GeV


Extension to transverse direction
Extension to transverse direction…

  • Semi-inclusive measurements

    • Transverse momentum dependent (TMD) parton distributions

  • Deeply Virtual Compton Scattering and Exclusive processes

    • Generalized parton distributions (GPD)

Quantum phase space distribution
Quantum phase space distribution

  • Wigner distributions

    After integrating over r, one gets TMD

    After integrating over k, one gets Fourier transform of GPDs

Ji: PRL91,062001(2003)

3d image of quarks at fixed x
3D image of quarks at fixed-x

  • GPDs can be used to picture quarks in the proton (Belitsky-Ji-Yuan, PRD 04)

Beam direction







low x

high x

moderate x

Transverse momentum dependent parton distribution
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


  • 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

Where can we learn tmds
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…

Inclusive and semi inclusive dis
Inclusive and Semi-inclusive DIS

JLab & EIC

Inclusive DIS:

Partonic Distribution depending on

the longitudinal momentum fraction


Semi-inclusive DIS:

Probe additional information for partons’

transverse distribution in nucleon


JLab & EIC

  • Transverse Momentum Dependent (TMD) Parton Distributions and Fragmentations

  • Novel Single Spin Asymmetries

U: unpolarized beam

T: transversely polarized target

Two major contributions



Two major contributions

  • Sivers effect in the distribution

  • Collins effect in the fragmentation

  • Other contributions…






Universality of the collins fragmentation
Universality of the Collins Fragmentation

ep--> e Pi X

pp--> jet(->Pi) X

e+e--> Pi Pi X

Metz 02, Collins-Metz 02,

Yuan 07,


Meissner-Metz 0812.3783

Yuan-Zhou, 0903.4680

Model calculations of the collins effects
Model calculations of the Collins Effects

Metz 02, Collins-Metz 02:

Gamberg-Mukherjee-Mulders, 08

Universality of the Collins function!!

Similar arguments for pp collisions

By using the Ward


same Collins fun.

Similar arguments for pp collisions

Yuan, 0709.3272

The Collins function is the same as e^+e^- and SIDIS

Extend to two gluon exchange
Extend to two-gluon exchange

Universality preserved

Key observations
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

Sivers effect is different
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”


Collins, 02;



Dis and drell yan
DIS and Drell-Yan

  • Initial state vs. final state interactions

  • “Universality”: QCD prediction






Experiment SIDIS vs Drell Yan

HERMES Sivers Results

RHIC II Drell Yan Projections


Markus Diefenthaler

DIS Workshop

Munich, April 2007


0.1 0.2 0.3 x

Transverse momentum dependence

QCD Dynamics

Transverse momentum dependence

Transition from perturbative region to nonperturbative region
Transition from Perturbative region to Nonperturbative region

  • Compare different region of PT

Nonperturbative TMD

Perturbative region

Perturbative tail is calculable
Perturbative tail is calculable region

  • Transverse momentum dependence

Power counting,

Brodsky-Farrar, 1973

Integrated Parton Distributions

Twist-three functions

A unified picture
A unified picture region

Transverse momentum dependent










Yuan-Zhou, 2009

Nlo corrections to ssa
NLO corrections to SSA region

Vogelsang-Yuan, arXiv:0904.0410

  • SSA in Drell-Yan as an example,

  • Collinear factorization

Collinear functions, evolution: Kang-Qiu, 08;

Zhou-Yuan-Liang 08

Future perspective
Future perspective region

  • 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

Semi inclusive dis
Semi-Inclusive DIS region

  • Transverse Momentum Dependent (TMD) Parton Distributions and Fragmentations

  • Novel Single Spin Asymmetries

U: unpolarized beam

T: transversely polarized target

What s single spin asymmetry
What’s Single spin asymmetry? region

Transverse plane

Final state particle is

Azimuthal symmetric

Single Transverse Spin

Asymmetry (SSA)

Ssas in modern era rhic jlab hermes
SSAs in Modern era region : RHIC, JLab, HERMES, …


Central rapidity!!


Large SSA continues at DIS ep

and collider pp experiments!!

Na ve parton model fails
Naïve parton model fails region

  • 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 byαSmq/Q

  • We have to go beyond this naïve picture

Two mechanisms in qcd

S regionT


Two mechanisms in QCD

  • Spin-dependent transverse momentum dependent (TMD) function

    • Sivers 90

    • Brodsky,Hwang,Schmidt, 02 (FSI)

    • Gauge Property: Collins 02;Belitsky-Ji-Yuan,NPB03


    • Factorization: Ji-Ma-Yuan,PRD04;Collins,Metz,04

  • Twist-3 quark-gluon correlations (coll.)

    • Efremov-Teryaev, 82, 84

    • Qiu-Sterman, 91,98

Sivers function ~ ST (PXkT)



Quantum phase space distribution1
Quantum Phase Space Distribution region

  • 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
Polarized TMD Quark Distributions region









Boer, Mulders, Tangerman (96&98)

Three classes in the view of a quark model
Three classes in the view of a quark model region

  • 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.