1. Probing the Spin Structure of the Nucleon: New Experimental Results on d2 and A1 for Neutron and Proton from JLab Brad Sawatzky APS April Meeting April 13—16, 2013 1

2. SSF Measurements at JLab

3. SSF Measurements at JLab

4. Introduction: Deep Inelastic Scattering
Incident electron k
Nucleon k’
Scattered electron q
Virtual photon
Start with a polarized electron and a polarized nucleon
They exchange a virtual photon
Virtual photon probes a quasi-free quark inside nucleon
We measure the scattered electron

5. Polarized DIS cross sections

6. What are g1 and g2? The Parton Model
The “g's” play a role analogous to the “F's” in the unpolarized cross section
F encodes information about the momentum structure of the nucleon
g1 and g2 encode information about the spin structure of the target nucleon
The Parton Model
g1 is a measure of the spin distribution among the individual constituent quarks (ie. aligned parallel and anti-parallel to the nucleon spin)
g2 ???

7. g2 and Quark-Gluon Correlations
QCD allows the helicity exchange to occur in two principle ways

8. d2: A clean probe of quark-gluon correlations
d2 is a clean probe of quark-gluon correlations / higher twist effects
d2 is the 2nd moment of a sum of the spin structure functions
matrix element in the Operator Product Expansion
it is cleanly computable using Lattice QCD
Connected to the color Lorentz force acting on the struck quark (Burkardt)
same underlying physics as in SIDIS k┴ studies

9. Other Interesting Observables
Often experimentally simpler to measure Asymmetries
target polarized parallel to beam polarization
target polarized transverse to beam polarization
Asymmetry is formed by measuring the difference in yields when you flip polarization of the beam
Virtual photon asymmetries A1 and A2 can be expressed in terms of these experimental asymmetries
these are also connected to g1, g2, of course

10. Virtual Photon Asymmetries
D' is virtual photon depolarization
● gT measures spin distribution normal to the virtual photon

11. E07-003: SANE (Hall C) Spin Asymmetries of the Nucleon Experiment
Polarized NH3 target
Large acceptance detector to measure asymmetries
Focus: A1, g2, d2 for the proton

12. SANE: Experimental Layout
DNP = dynamic nuclear polarization

13. Polarized NH3 Target

14. Big Electron Telescope Array • BETA

15. World data on A║, A┴ and SANE kinematics

16. A1, A2 for the proton Preliminary General agreement with world data
somewhat above CLAS at low Q2

17. A1, A2 for the proton A1 A2 Preliminary Preliminary Asymmetry
A1 is roughly linear vs. ln(W)
minimal Q2 dependence
A2 is consistent with E143 even though E143 has much greater Q2
minimal/weak Q2 dependence for A2?
Models used in comparison
Leader, Sidorov, Stamenov LSS 2006 (Phys. Rev, D ) (target mass corrected)
AAC 2003 (Phys. Rev, D ) (target mass corrected)
CLAS fit to world data (S. Kuhn & N. Guler)
F1 from F1F209 fit to world data (Bosted, Christy)

18. g1 & g2 on the proton Preliminary Preliminary
AAC parametrization seems to perform the best
(Phys. Rev, D )

19. d2 Integrand ( ) Preliminary Integrand is negative
hint of a negative d2p, negative twist-3?

20. E06-014: The Neutron d2 (Hall A)
A measurement of the neutron d2
Polarized He3 target
Large acceptance detector to measure asyms (BigBite)
High-precision device to measure unpol. x-sec (HRS)
Focus: d2, g2 on the neutron
extracted A1, g1 as well

21. The Experiment
A 4.75 and 5.9 GeV polarized electron beam scattering off a polarized 3He target
Measure unpolarized cross section for reaction in conjunction with the parallel asymmetry and the transverse asymmetry for < x < 0.65 with 2 < Q2 < 5 GeV2.
Asymmetries measured by BigBite
Absolute cross sections measured by L-HRS
Determine d2n using the relation
This allows us to reach d2 directly from the data. We do not have to go through g1 and g2 (g2_ww) first.
phi = angle between the transverse target pol. and the scattering plane.
where,

22. Floor configuration for d2n

23. BigBite Electron Stack
BigBite detector package:
3 Multi-wire drift chambers (MWDC) Tracking
Scintillator plane Timing
Pb-glass Calorimeter (Pre-shower + Shower) Energy/PID
Gas Cherenkov PID

24. Kinematics of the measurement
Two beam energies and 5.9 GeV (4 pass, 5 pass)
provides a handle on the Q2 dependence of g2
supports rad. correction calculations
BigBite fixed at single scattering angle (θ=45°) (data divided into bins during analysis)
Avoid resonance region as much as possible.
E = 5.9 GeV
E = 4.7 GeV
Very low-x region covered by previous JLab and SLAC data.

25. Polarized 3He Target 3He is (almost) a polarized neutron target
Dominant S state has neutron carrying the spin (proton spins cancel)
~90%
~2%
~8% e-
beam
~10 atm 3He cell with trace amounts of K, Rb
Polarization achieved through optical pumping and 2-step spin exchange
K → Rb
Rb → 3He

26. A1 for 3He Several corrections still under study
Radiative Corr., Pair sym. bkgrd
3He → neutron extraction underway

27. x2g1 for 3He and Neutron Several corrections still under study
Radiative Corr.
Pair sym. bkgrd
3He → neutron extraction done using effective polarization model
more sophisticated deconvolution method in progress (Melnitchouk, et al)

28. x2g2 for 3He and Neutron Several corrections still under study
Radiative Corr.
Pair sym. bkgrd
3He → neutron extraction done using effective polarization model
more sophisticated deconvolution method in progress (Melnitchouk, et al)

29. Final d2 still to come for both p & n ...
Experimental uncertainties are in good shape so far!
Current uncertainties on d2 for 3He
<Q2> ~ 3.25 GeV2 (E=4.7 GeV)
7.7 x 10-4 (stat) x 10-4 (sys)
<Q2> ~ 4.43 GeV2 (E=5.9 GeV)
7.6 x 10-4 (stat) x 10-4 (sys)
No Q2 dep. observed within errors
can combine 4.7, 5,9 GeV datasets
Uncertainties on neutron expected to be comparable

30. Summary SANE (E07-003) Proton “d2n” (E06-014) Neutron, He3
A1, A2 in good overall agreement with world
A1 a little higher than CLAS at low Q2
A2 from SANE consistent with E143 hinting at weak Q2 dependence?
g1 and g2 in good agreement with parameterizations based on world data
data hint at a negative d2p ?
“d2n” (E06-014) Neutron, He3
A1(He3) in good agreement with world data
neutron extraction underway
g1 and g2 in agreement with world data for both He3 and (prelim) neutron extraction
final corrections and more sophisticated neutron extraction in progress
12 GeV dedicated A1n (Hall A), and d2n, g2n measurements are approved (run ~2017?)
focus on high-x and Q2 evolution
Special thanks to:
O. Rondon, W. Armstrong, H. Baghdasaryan
Special thanks to:
D. Flay, M. Posik, D. Parno
[This work is supported in part by DOE Award from Temple University #DE-FG02-94ER40844.]

31. BACKUP

32. E : d2n, g2n
Directly measure the Q2 dependence of the neutron d2n(Q2) at Q2 ≈ 3, 4, 5, 6 GeV2 with the new polarized 3He target.
The SHMS is ideally suited to this task!
Doubles number of precision data points for g2n(x, Q2) in DIS region.
Q2 evolution of g2n over (0.23 < x < 0.85)
Lines of integration for d2n at Q2 = 3, 4, 5, 6 GeV2
d2 is a clean probe of quark-gluon correlations / higher twist effects
Connected to the color Lorentz force acting on the struck quark (Burkardt)
same underlying physics as in SIDIS k┴ studies
Investigate the present discrepancy between data and theories.
Theory calcs consistent but have wrong sign, wrong value.
g2 for 3He is extracted directly from L and T spin-dependent cross sections measured within the same experiment.
Strength of SHMS/HMS: nearly constant Q2 (but less coverage for x < 0.3)

33. Projected results for E12-06-121
Projected g2n points are vertically offset from zero along lines that reflect different (roughly) constant Q2 values from 2.5—7 GeV2.
g2 for 3He is extracted directly from L and T spin-dependent cross sections measured within the same experiment.
Strength of SHMS/HMS: nearly constant Q2 (but less coverage for x < 0.3)
Q2 evolution of d2n in a region where models are thought to be accurate.
Direct overlap with 6 GeV Hall A measurement point.

34. e+/e- Ratios extracted from data