**RHIC Spin Report for DOE: Outline of Gluon Section 2.3.2**

(each major heading represents \~1 paragraph; some of the figures will
likely appear in other sections of the report)

**A. Experimental approaches to determining gluon helicity preferences
in p+p**

1.  Advantages of p+p: direct gluon involvement at LO; sizable pQCD spin
    sensitivity via A~LL~.

2.  Goals: improve statistical precision on *∆g(x)* by at least a factor
    \~2 vis-à-vis DIS analyses, for *x*\~0.1; reduce interpretation
    uncertainties via direct sensitivity; extend measurements to as low
    *x* as possible, to permit constraint on integral *∆g.*

3.  Demonstrate robustness of *∆g(x)* extraction, evaluate
    interpretation uncertainties by comparing: results for different
    channels, with differing experimental/ interpretation issues;
    results for same *x* range probed at different *p~T~* (evolution
    sensitivity); results with different constraints on flavor and
    *x-*range of colliding partner parton; quark polarizations extracted
    from p+p with those from DIS.

4.  **Figure:** LO Feynman diagrams relevant to jet, photon and heavy
    flavor production.

**B. Abundant probes: inclusive jet and pion *A~LL~***

1.  Advantages: large cross sections; NLO success for π^0^ cross
    sections; significant *∆g* sensitivity.

2.  Disadvantages: competition among LO subprocesses; combination of
    linear and quadratic sensitivity to *∆g*, and *p~T~*-dependent
    dilution from qq contributions; sensitivity to fragmentation
    functions and convolution over significant range of partonic *p~T~*
    scales; possible jet trigger biases; averaging over substantial
    *x*-range.

3.  π^0^ and jet reconstruction efficiencies in PHENIX, STAR

4.  Projected timeline and achievable uncertainties, compared to models
    consistent with DIS database. **Figures:** PHENIX π^0,±^ A~LL~
    results and projections; STAR jet A~LL~ projections for run 5.

**C. Dijet and dihadron correlations**

1.  Measure A~LL~ as function of *p~T~* and *∆η*: exploit unpolarized
    PDF differences and quark vs. gluon fragmentation differences to
    vary partonic subprocess sensitivities in controlled way.

2.  **Figure:** from Les, to indicate subprocess sensitivity for
    different rapidity intervals in di-hadron measurements (?)

**D. Inclusive direct photon production**

1.  Advantages: dominance of QCD Compton at LO; direct measurement of
    *p~T~* for partonic subprocess (modulo *k~T~* uncertainties).

2.  Interpretation issues: NLO difficulties for cross sections;
    fragmentation photon contributions, and the effect of experimentally
    achievable isolation cuts on analysis; how low in *p~T~* is analysis
    robust?

3.  Experimental issues: low cross section; π^0^ background suppression;
    need to develop isolation cuts in association with theorists; γ
    reconstruction efficiency.

4.  **Figures:** γ ID from PHENIX; projected A~LL~ uncertainties for 200
    pb^-1^ delivered, 70% beam polarizations, 200 GeV, compared to
    models consistent with DIS database.

**E. Photon-jet and photon-leading hadron coincidences**

1.  Advantages: comparable statistical sensitivity to inclusive photon;
    event-by-event constraints on colliding parton kinematics permit
    systematic study of sensitivity to cuts, variation of asymmetries
    with *x* of collision partner, etc.

2.  Disadvantages: jet reconstruction may impose more stringent low-end
    limit than photon detection on *p~T~* extent of useful measurements.

3.  Projected timeline and achievable uncertainties and *x*-range
    compared to DIS, COMPASS, SMC, HERMES.

4.  **Figure:** STAR simulations of A~LL~, *x∆g(x)* LO extraction,
    scaled for 200 pb^-1^ delivered at 200 GeV, for estimated γ
    reconstruction efficiency and for *p~T~* \> 5 GeV/c.

**F. Heavy flavor production**

1.  Features: independent channel to cross-check results; emphasizes g-g
    fusion, quadratic sensitivity to *∆g*; small *x* accessible via
    forward lepton detection.

2.  Interpretation issues: how well understood are charm production
    cross sections? How cleanly can different contributions be separated
    in inclusive lepton channels?

3.  Experimental issues: can displaced vertex cut with improved inner
    tracking improve heavy flavor ID significantly without too much
    sacrifice in yield?

4.  **Figure:** PHENIX projection of open charm A~LL~.

**G. Importance of measurements at 2 energies**

1.  Approaches to extending to lower *x*: raising energy; increasing
    forward coverage (subject to *p~T~* limit for interpretability);
    need to get beyond maximum in *x∆g(x)* to constrain integral *∆g*.

2.  Need for 200 GeV: gives overlap with COMPASS, etc. sensitivity;
    constrains *x∆g(x)* where uncertainties from DIS analysis are
    largest.

3.  Need for 500 GeV: permits sensitivity down to *x~g~* \~ 0.01;
    permits test of evolution and robustness of analysis, by comparison
    of results at similar *x*, different *p~T~*.

4.  **Figure:** Projection of STAR *∆g(x)/g(x)* uncertainties achievable
    with 200 pb^-1^ (delivered) at 200 GeV and 500 pb^-1^ (delivered) at
    500 GeV, compared to models consistent with DIS database, COMPASS
    achieved & projected, etc.

###