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. 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.