1. Probing Quark – Gluon correlations in the neutron Precision measurements of d2n and g2n Brad Sawatzky for the E Collaboration

2. The proposal for Hall C and SHMS/HMS
A polarized electron beam of GeV and new polarized 3He target
Measure , for reaction using both the SHMS and HMS running in parallel for 4 kinematic settings of 125 hours each
SHMS: (7.5 GeV/c, 11.0°), (7.0 GeV/c, 13.3°), (6.3 GeV/c, 15.5°), (5.6 GeV/c, 18.0°)
HMS: (4.3 GeV/c, 13.5°), (5.1 GeV/c, 16.4°), (4.0 GeV/c, 20.0°), (2.5 GeV/c, 25.0°)
Polarized 3He target will also be used with 12 GeV A1n, GeN experiments
Use E to commission this new target?
Determine d2n and g2n using the relations:
- Use our experiment to commission the new target and, perhaps, the new/refurbished SHMS systems.
- Our collaboration will have data from the 6GeV Hall A measurement for direct cross checks of backgrounds and systematics.
- We do not push the envelop of the new target design. Our experiment can trivially fall back to the original proposal kinematics without compromising the baseline physics goals of this measurement.
- We can also easily extend our measurement to cover a larger phase space if everything works beautifully right out of the box.
Ibeam = 30 μA
Pbeam = 0.8
Ptarg = 0.55

3. Motivation & Updated Kinematics
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)
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.
Lines of integration for d2n at Q2 = 3, 4, 5, 6 GeV2
Updated kinematics:
4 settings/arm
125 hours/setting
d2 is related to the twist three matrix element in the Operator Product Expansion (OPE) framework and is connected to the quark-gluon correlations within the nucleon. Earlier work by Ji et al. related this
quantity to a measure of how the color electric and magnetic fields responded to the polarization of the nucleon (alignment of its spin along one direction)—what he called the “color polarizabilities” [1, 2].
More recent analysis by Burkardt suggests that categorization may be too broad (i.e. by similar analogy, too many other observables would also become “polarizabilities”). He identifies d2 as a measure of
the color Lorentz force acting on the struck quark the instant after it was hit by the virtual photon [3]. That interpretation also connects the average transverse momentum of an ejected quark hk⊥i in SIDIS with the transverse impulse generated by the same color Lorentz force acting on the struck quark, chromodynamic lensing, and the average transverse momentum arising from the Sivers effect[4, 5]. This quantity has also seen thorough study in Lattice QCD and is one of the cleanest observables with which to test the theory.

4. 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.

5. Backup Slides

6. Model evaluations of d2 Note the several sigma disagreement.
Current theories self-consistent, but (almost) all get the sign wrong.
Lattice very interesting because we can compute d2 from first principles / the fundamentals of QCD.

7. Updated Kinematics Tables
Note the several sigma disagreement.
Current theories self-consistent, but (almost) all get the sign wrong.
Lattice very interesting because we can compute d2 from first principles / the fundamentals of QCD.

8. Systematic Error Contributions to g2n and d2n
Positron contamination will be directly measured (part of the 200 hours allocated to systematic studies)
Radiative correction uncertainty cross-checked with E (Spin Duality) experiment
worst case: 4.4%
Dominant uncertainties are
- He3 -> neutron correction (well understood now)
- Radiative corrections
-we measure much of the data we need during this experiment already
- correction uncertainties cross-checked with E (Spin-duality) experiments. Their worst case uncertainty was 4.4%.

9. Safe Fall Back to
Original Kinematics

10. Projected Results w/ Original Kinematics
3 settings/arm
200 hours/setting
Same beamtime allocation
Lines of integration for d2n at Q2 = 3.5, 4.5, 5.5 GeV2

11. Projected Results w/ Original Kinematics
Projected points are vertically offset from zero along lines that reflect different (roughly) constant Q2 values from 2.5—6 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)

12. Theory / Motivation

13. g2 and Quark-Gluon Correlations
QCD allows the helicity exchange to occur in two principle ways
h_t is transverse polarization density (suppressed by M_quark/M_nucleon
g1 is a measure of the spin distribution among the individual constituent quarks (ie. aligned parallel and anti-parallel to the nucleon spin). In the Feynman parton model, g1 is involved in a incoherent scattering process where the virtual photon interacts with a single quark within the nucleon.
g2 is best understood within the OPE. There it becomes associated with a t- channel helicity exchange. QCD allows this exchange to occur in two principle ways...

14. Moments of Structure Functions
(Extracted from neutron and hyperon weak decay measurements)

15. Moments of Structure Functions (continued)3
d2, f2 are computable matrix elements with this approach
a2 is second moment of g1 – connected to target mass corrections

16. Color “polarizabilities”
Lorentz Force
cB and cE represent an averaged transverse force acting on the struck quark after the system has absorbed the virtual photon.

17. Nuclear corrections
Convolution method using the impulse approximation and realistic ground state wave functions of 3He (in Bjorken limit: g13He related to g1N).
Variational Method,
C. Ciofi degli Atti & S. Scopetta, Phys. Lett. B 404 (1997) 223, for g1,
for g2 ,S. Scopetta. private communication
Faddeev
F. Bissey et al. Phys. Rev. C 64 (2001)
Finite Q2 effects (both g1N and g2N contribute to g13He and to g23He)
S.A. Kulagin and W. Melnitchouk

18. Nuclear corrections (continued)

19. From 3He to Neutron Correction large for g2 but much smaller for d2
- really closer to 8% if you work out the math
Correction large for g2 but much smaller for d2
About 5% difference between additive or convolution methods or between potential models

20. Nuclear corrections (continued)

22. How g2(x,Q2) is usually obtained

23. d2 integrand evolution from g1 and g2ww

24. Floor layout for Hall C (Original Kinematics)
One beam energy
11 GeV
Each arm measures a total cross section independent of the other arm.
Experiment split into three pairs of 200 hour runs with spectrometer motion in between.
SHMS collects data at Θ = 11°, 13.3° and 15.5° for 200 hrs each
data from each setting divided into 4 bins
HMS collects data at Θ = 13.5°, 16.4° and 20.0° for 200 hrs each