1. Haiyan Gao Duke University Durham, NC, U.S.A.
Semi-Inclusive DIS and Transverse-Momentum Dependent Parton Distribution Functions (
SoLID Collaboration
June 13-14, 2012
Haiyan Gao
Duke University
Durham, NC, U.S.A.

2. QCD Nucleon Structure Spin as an important knob
Strong interaction, running coupling ~1
-- QCD: the theory of strong interaction
-- asymptotic freedom (2004 Nobel)
perturbation calculation works at
high energy
-- interaction significant at
intermediate energy
quark-gluon correlations
-- confinement
interaction strong at low energy
coherent hadron
-- Chiral symmetry
-- theoretical tools:
pQCD, OPE, Lattice QCD, ChPT E
Charge and magnetism (current) distribution
Spin distribution
Quark momentum and flavor distribution
Polarizabilities
Strangeness content
Three-dimensional structure
C. Carlson, H. Meyer, G. Orlandini, B. Pasquini,
M. Schindler, L. Tiator, A.W. Thomas, H. Wittig
Spin as an important knob

3. The Incomplete Nucleon: Spin Puzzle
[X. Ji, 1997]
DIS → DΣ  0.25
RHIC + DIS → Dg« 1
→ Lq
Orbital angular momentum of quarks and gluons is important
Understanding of spin-orbit correlations (atomic hydrogen, topological insulator…..)
D. de Florian et al., PRL 101 (2008)

4. Leading-Twist TMD PDFs
Nucleon Spin
Quark Spin
Quark polarization
Unpolarized
(U)
Longitudinally Polarized (L)
Transversely Polarized (T)
Nucleon Polarization U L T
h1 =
Boer-Mulders
f1 =
h1L =
Long-Transversity
Helicity
g1 =
! relate g1, f1 -> collinear w/ pT dep.
Say: Noval new information on structure of nucleon, spin-orbital cor and multi-parton cor.
h1 =
Transversity
f 1T =
Sivers
g1T =
Trans-Helicity
h1T =
Pretzelosity

5. Leading-Twist TMD PDFs
Nucleon Spin
Quark Spin
Quark polarization
Unpolarized
(U)
Longitudinally Polarized (L)
Transversely Polarized (T)
Nucleon Polarization U L T
h1 =
Boer-Mulders
f1 =
h1L =
Helicity
g1 =
Long-Transversity
! relate g1, f1 -> collinear w/ pT dep.
Say: Noval new information on structure of nucleon, spin-orbital cor and multi-parton cor.
h1 =
Transversity
f 1T =
Sivers
g1T =
h1T =
Pretzelosity
Trans-Helicity

6. TMD PDFs: nucleon structure in 3-D momentum space
TMD PDFs: nucleon structure in 3-D momentum space! Sivers as fixed x, Q2

7. 6D Dist. 3D imaging 1D Unified View of Nucleon Structure
Wpu(x,kT,r ) Wigner distributions
d3r
TMD PDFs f1u(x,kT), .. h1u(x,kT)‏
GPDs/IPDs
d2kT drz
d2rT
dx &
Fourier Transformation
3D imaging
d2kT
Form Factors
GE(Q2),
GM(Q2)‏
PDFs
f1u(x), .. h1u(x)‏ 1D

8. Access TMDs through Hard Processes
proton
lepton
antilepton
Drell-Yan
BNL
JPARC
FNAL
EIC
lepton
pion
proton
SIDIS
electron
positron
pion
e–e+ to pions
Partonic scattering amplitude
Fragmentation amplitude
Distribution amplitude

9. Access Parton Distributions through Semi-Inclusive DIS
Unpolarized
Boer-Mulders
Transversity
Polarized
Target
Sivers
Pretzelosity
Polarized
Beam and
Target
SL, ST: Target Polarization; e: Beam Polarization

10. Example: Separation of Collins, Sivers and pretzelocity effects through angular dependence
Collins frag. Func.
from e+e- collisions
SIDIS SSAs depend on 4-D variables (x, Q2, z and PT )
Large angular coverage and precision measurement of asymmetries in 4-D phase space is essential.

11. Transversity The third PDFs in addition to f1 and g1L
h1T =
The third PDFs in addition to f and g1L
Lowest moment gives tensor charge
Fundamental property, benchmark test of Lattice QCD
A global fit to the HERMES p, COMPASS d and BELLE e+e- data by the Torino group, Anselmino et al.,
arXiv:
Solid red line : transversity
distribution, analysis at
Q2=2.4 (GeV/c)2
Solid blue line: Soffer bound
|h1T| <= (f1+g1L)/2
GRV98LO + GRSV98LO
Dashed line: helicity distribution
g1L, GRSV98LO
Test bound violations

12. Sivers Function
f 1T =
Correlation between nucleon spin with quark orbital angular momentum
Important test for factorization
Different sign with twist-3 quark-gluon corr. dis. at high PT?
T-odd final state interaction -> Target SSA
Recent developments in the evolution of Sivers function

13. Older fit shows possibly discrepancy?
Latest extraction based on
HERMES p, COMPASS d and p data by M. Anselmino et al., arXiv: taking into account TMD evolution show consistency between the HERMES and COMPASS data

16. Pretzlosity: h1T = Relativistic effect of quark PRD 78, 114024 (2008)
(in models) direct measurement of OAM PRD 58, (1998) (more previous slide)
Expect first non-zero Pretzelosity
asymmetries

17. E06-010: neutron A(U/L)T(π+K+, π-K-)
First neutron data in SIDIS SSA&DSA
Similar Q2 as HERMES experiment
Disentangle Collins/Sivers effects
Electron beam: E = 5.9 GeV
High luminosity L ~ 1036 cm-2s-1
40 cm transversely polarized 3He target
Average beam current 12 uA (max: 15 uA as in proposal)
BigBite at 30o as electron arm: Pe = 0.6 ~ 2.5 GeV/c
HRSL at 16o as hadron arm: Ph = 2.35 GeV/c e
Polarized
3He Target p
HRSL
16o g* e’
BigBite
30o
The experimental is configured as following. We have 5.9 GeV polarized electron beam incident on a 40 cm polarized 3He target.
The scattered electron was detected by the BigBite spectrometer positioned 30 degrees to the beam right. And the momentum range is …
The produced hardon was detected coincidently using the left high resolution spectrometer 16 degrees to the beam left. And the momentum setting is 2.35 GeV/c.
This setup allowed us to measure the … asymmetries in the valence range … 17

18. Effective Polarized Neutron Target!
3He Target
~90% ~1.5% ~8% S S’ D
Effective Polarized Neutron Target!
Polarized 3He ran reliably throughout the experiment, and the following three experiments.
Reached 55%-60% polarization with 15 mA beam and 20 minute spin flip! A NEW RECORD!

19. Results on Neutron Sizable Collins π+ asymmetries at x=0.34?
Sign of violation of Soffer’s inequality?
Data are limited by stat. Needs more precise data!
Negative Sivers π+ Asymmetry
Consistent with HERMES/COMPASS
Independent
demonstration of negative d quark Sivers function.
Model (fitting) uncertainties shown in blue band.
Experimental systematic uncertainties: red band
X. Qian et al, Phys. Rev. Lett. 107, (2011)

20. Double Spin Asymmetry: g1T
Worm Gear
Leading twist TMD PDFs
T-even, Chiral-even
Dominated by real part of interference between L=0 (S) and L=1 (P) states
Imaginary part -> Sivers effect
First TMDs in Pioneer Lattice calculation
arXiv: [hep-lat], Europhys.Lett.88:61001,2009
arXiv: [hep-lat] , Phys.Rev.D83:094507,2011
g1T =
TOT
g1T (1)
S-P int.
P-D int.
Light-Cone CQM by B. Pasquini
B.P., Cazzaniga, Boffi, PRD78, 2008
g1T function is sometimes referred as the “worm-gear” function, since the spin direction for quark and nucleon are perpendicular to each other
It is T-even anc Chiral-even.
It is dominated by the real part of interference of quark wavefunctions that differ by one unit of quark OAM. Using a Light-cone constituent quark model, the g1T function can be explicitly decomposed to the major contribution of S-P states and a small contribution from the P-D interference.
Effect resembles the g1T function has been recently studied using lattice QCD calculations. More studies are on-going
And it can be probed my measuring the beam-target double spin asymmetry, A_LT and look for the cos(…) modulation
Target
Spin
Beam
Helicity e e’ π X n

21. Existing ALT Results are preliminary
No measurement until 2002
Preliminary COMPASS results
ALT on proton and deuteron
Fixed beam helicity (μ beam)
Low x, small predicted asymmetry
Preliminary HERMES results
ALT on proton
New measurement needed
Different target for flavor decomposition
Higher precision at valence region
Double spin reversal to cleanly separate ALT
Proton
arXiv: [hep-ex]
Preliminary
There is no measurement on ALT until COMPASS provided the first preliminary data on deuterons and protons using a Muon beam with fixed helicity.
Very recently, HERMES collaboration also released their preliminary result on proton.
A new measurement on neutron is needed for flavor decomposition, especially for the d quark
We would like to focus on the valence region, where the models predict maximum signal
And a double spin reversal can cleanly separate ALT from other SSA terms, including both beam-SSA and target-SSA.
arXiv: [hep-ex]

22. New Observable Reveals Interesting Behaviors of Quarks
Huang, et. al. PRL. 108, (2012)
Target:
polarized 3He => polarized neutron
First measurement of ALT
beam-target double-spin asymmetry
For JLab one-page highlight. Edited by Xiaodong Jiang 02/15/2012.
E06010, Hall A Neutron Transversity experiment.
Semi-inclusive deep inelastic scattering on a transversely polarized neutron (3He) target.
Curves from theory models:
WW-type: Wandzura-Wilczek, neglects higher-twist contributions, Kotzinian (2006).
LCCQM: light-cone constituent quark model, Boffi (2009), Pasquini (2008).
LCQDM: light-cone quark-diquark model, Zhu and Ma (2011).
Indications:
A non-vanishing quark “transversal helicity” distribution, reveals alignment of quark spin transverse to neutron spin direction
Quark orbital motions
J. Huang et al., PRL108, (2012)

23. SoLID-Spin: SIDIS on 3He/Proton @ 11 GeV
E : Single Spin Asymmetry on Transverse 90 days, rating A E : Single and Double Spin Asymmetry on 35 days, rating A PR : Single and Double Spin Asymmetries on Transverse Proton (conditionally approved)
International collaboration with 180
Collaborators from 8 countries
White paper
Key of SoLID-Spin program:
Large Acceptance + High Luminosity  4-D mapping of asymmetries  Tensor charge, TMDs …
Lattice QCD, QCD Dynamics, Models.

24. 3-D neutron π+/π- Collins/Sivers Asymmetries at Q2=2.0 GeV2
Collins/Sivers asymmetries vs. x and transverse momentum PT at different z at fixed Q2.
Multi-dimensional nature.
Targets: proton and neutron
Detect: positive pion and negative pions!
Torino 2008

25. Projected Data (E12-10-006) X. Qian et al in PRL 107, 072003
Total 1400 bins in x, Q2, PT and z for 11/8.8 GeV beam.
z ranges from 0.3 ~ 0.7, only one z and Q2 bin of 11/8.8 GeV is shown here.
π+ projections are shown, similar to the π- .
X. Qian et al in PRL 107,

26. Power of SOLID (example)

27. SoLID Data Projection for ALT (Partial)
E and E : Neutron ALT Projection of one out of 48 Q2-z bins for π-
Center of points:
Scale for error bars:
E Data Huang, et. al. PRL 108 (2012)
! Sign
! Will be improved

28. E12-11-007 Projection/AUL (Partial)
Projection of a single Q2-z bin for π+
Center of points:
+ bound
Scale for error bars:

29. PAC38: Conditionally approved, update submitted to PAC39
Proposal PR : Target Single Spin Asymmetry in SIDIS (e, eπ± ) Reaction on a Transversely Polarized Proton Target and SoLID
Measure SSA in SIDIS using transversely polarized proton target
Use similar detector setup as that of two approved 3He SoLID expts.
Use JLab/UVa polarized NH3 target with upgraded design of the magnet
Target spin-flip every two hours with average in-beam polarization of 70%
Two Beam energies: 11 GeV and 8.8 GeV
Polarized luminosity with 100nA current: 1035 cm-2s-1
Beamline chicane to transport beam through 5T target magnetic field (already designed for g2p expt.)
NH3
target
Spokespersons: K. Allada (Jlab), J. P. Chen (Jlab), Haiyan Gao (Contact), Xiaomei Li (CIAE), Z-E. Meziani (Temple)
PAC38: Conditionally approved, update submitted to PAC39

30. Proton 4-D Projection

31. Projected measurements in 1-D (x)
Expected improvement of Sivers function
(A. Prokudin) x
Assumption: We know the kT dependence, Q2 evolution of TMDs.
Also knowledge on TMFF  project onto 1-D in x to illustrate the power of SoLID-3He.

32. Summary
Frontiers in nucleon structure go beyond collinear, 1-D picture
TMDs
Three-dimensional description of nucleon in momentum space
Direct link with orbital motion (orbital angular momentum)
Transverse motion: spin-orbit correlations, multi-parton correlations, dynamics of confinement and QCD
10% quark tensor charge from both SSA data from SoLID provides excellent test of LQCD predictions
JLab 12-GeV upgrade will provide excellent opportunities to map out the 3-dimensional structure of the nucleon through TMDs and GPDs
SoLID will just do that!
Thanks to B. Pasquini, J. P. Chen, J. Huang, and X. Qian and others in the SoLID collaboration
Supported in part by U.S. Department of Energy under contract number DE-FG02-03ER41231