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Longitudinal Gluon Polarization in RHIC Double-Spin Asymmetries

This paper discusses the longitudinal gluon polarization in RHIC double-spin asymmetries, focusing on partonic spin physics and factorized cross sections. It explores the constraints of ΔG, quark model QCD, and the axial anomaly, as well as the role of gluons, interaction, and loops.

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Longitudinal Gluon Polarization in RHIC Double-Spin Asymmetries

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  1. Longitudinal Gluon Polarization in RHIC Double-Spin Asymmetries Stefan Kretzer Brookhaven National Laboratory & RIKEN-BNL Collaboration with:B. Jäger, M. Stratmann, and W. Vogelsang (PRL 2004)

  2. Catalogue of partonic spin physics: R. Jakob

  3. … and that is not the end … … plus a similar structural wealth for fragmentation.

  4. Every distribution is one component of a field-theoretic decomposition of nucleon structure collinear part:

  5. Of particular importance, for physical (“axial anomaly”) and historical (“spin crisis”) reasons, is G :

  6. Quark Model QCD ? • Gluons • Interaction • Loops: • Axial anomaly • Renormalization

  7. In inclusive DIS … LO NLO … gluons are sub-dominant.

  8. Evolution … Q2 +  Q2 Q2 … is a weak effect in polarized data.

  9. ΔG is constraint by not much else than positivity:|ΔG(x)| < g(x) Blümlein & Böttcher G=0.184±0.103G=0.100±0.075

  10. In hadronic collisions (RHIC) … LO … gluons are “leaders”.

  11. The double-spin asymmetry for the reactionpp→ π(p⊥) X

  12. Factorized cross section pp→π(pT) X “Add” polarization (double-spin asymmetry) p p π π a a c c b b p p

  13. Sanity check: The unpolarized cross section.

  14. NLO pQCD and unpolarized RHIC pp data PHENIX central rapidity STAR forward rapidity

  15. Predictions for ALL are all positive. Is this accidental or is ALL bounded from below? The upper bound on ALL depends on the scale at which positivity |Δg(x,μ)| ≤ g(x,μ)is saturated.

  16. 2→2 channels:

  17. Partonometry of inclusive pion production in unpolarized proton-proton collisions at RHIC cms energy The following is a technical decomposition into parton processes

  18. Fractional contributions from initial/final state partons Central Rapidity Forward Rapidity gq qg+gq qq initial gg qq gg qg Dq Dq final Dg Dg E [GeV] P? [GeV]

  19. Bunce & Saito & Soffer & Vogelsang Parton level double-spin asymmetries (“analyzing powers”)

  20. 2→2 channels: • Only (ii) has a negative asymmetry at parton level. • (i) >> (ii) by about a factor 160! • Does this mean that ALL has to be positive? • No: Polarized parton densities may oscillate!

  21. Taking Moments, e.g.turns the non-local (xa ≠ xb) convolution into a local (in N) product The minimum [by variation δ(Δσ)/δ(Δg)=0] is at

  22. Inverted (from N to x)bounds Δσfrom below:

  23. In the previous slides, compared to the true experimental situation (PHENIX) I have been cheating on the observable rapidity range. However, the distribution of |xa – xb| over the rapidity / longitudinal phase space proves the “cheat is conservative”. • The (quasi-)analytical observation that Δσ is (basically) positive definite in pQCD (for pT not too large) is confirmed by global analysis.

  24. ALL is bounded by: • Positivity • Underlying parton dynamics The upper bound holds up to dependence on the scale where positivity is saturated. The lower bound is obtained under low p? approximations. The order of magnitude must be correct in both cases if the dynamics are:

  25. (Instead of conlusions:) I have to head back to WG D in hope to have raised your appetite for the exciting data and a glimpse on ∆G in the following presentations by PHENIX and STAR …

  26. ***** Backup Slides *****

  27. Introduction:Partonic Spin Physics

  28. Factorized cross section pp→(pT) X p p π π a a c c b b p p

  29. “Add” polarization (double-spin asymmetry) p p π π a a c c b b p p

  30. Average Scaling Variables • Symmetric / asymmetric kinematics for central / forward rapidity • Large z fragmentation is probed. The largest z are probed by the forward rapidity data where quarks with very large xare probed as well. • Note: There is a difference in scale as well: It varies from small to large for central rapidity, whereas it’s small throughout for forward rapidity. Central Rapidity P? [GeV] Forward Rapidity E [GeV]

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