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Finding The Spin of the Proton

Finding The Spin of the Proton. Douglas Fields University of New Mexico. Outline. Review of Problem Brief Review of Deep Inelastic Scattering Spin “Crisis” Spin physics at RHIC RHIC and PHENIX Measurements of Δ G “Measurements” of Δ L PHENIX upgrades and future measurements.

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Finding The Spin of the Proton

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  1. Finding The Spin of the Proton Douglas Fields University of New Mexico

  2. Outline • Review of Problem • Brief Review of Deep Inelastic Scattering • Spin “Crisis” • Spin physics at RHIC • RHIC and PHENIX • Measurements of ΔG • “Measurements” of ΔL • PHENIX upgrades and future measurements

  3. Motivation • Hadron Physics: • Understanding of the structure of the nucleon. • Understanding of nuclear interactions. • Tests of QCD. • Standard Model Tests: • Use spin as a tool to test Standard Model predictions. • Search for exotics (SUSY, PV…). • Forget all of that • Spin is as fundamental as charge or mass!

  4. NL p p NR Spin Effects • Polarized pp elastic scattering at 197MeV. • Ay ~ (NL – NR)/ (NL + NR) • Shows that the strong (nuclear) force depends strongly on the spin orientation.

  5. Protons are spin ½ objects composed of three spin ½ objects. “Naïve Quark Model” Since Quarks are fermions, total wavefunction must be antisymmetric

  6. Deltas are spin 3/2 objects composed of three spin ½ objects. Mass is ~300MeV greater than proton! Strong Spin Dependence

  7. Predictions • Baryon magnetic moments are well predicted by the Naïve Quark Model mu = md ~ 1/3mp ms given by L magnetic moment (but mu=4MeV, md=7MeV)?

  8. Caveat… • Quarks (and anti-quarks) only account for ½ of nucleon momentum and it is dependent on at what scale you observe. • I like the fractal analogy: • At low resolving power, one sees three quarks in the nucleon • At higher resolving power, one sees more and more detail of what a quark is, namely a collection of quarks, antiquarks and gluons. Resolving power (smaller scales)

  9. What Does the Proton Look Like? • The distribution of partons in the proton was not very well understood 10 years ago • Today, the picture is different… J.D. Bjorken, Collisions Of Constituent Quarks At Collider Energies SLAC-PUB-95-6949 (1995)

  10. Probing the Proton • EM interaction • Photon • Sensitive to electric charge2 • Insensitive to color charge • Strong interaction • Gluon • Sensitive to color charge • Insensitive to flavor • Weak interaction • Weak Boson • Sensitive to weak charge ~ flavor • Insensitive to color

  11. Missing Ingredients • Longitudinal momentum fraction (x) • Transverse position (b) • Intrinsic transverse momentum (kT) • Correlations of above (x┴x kT) P.H. Hägler, et. al.

  12. Dq(x,Q2)= • Gluon Distributions dq(x,Q2)= g(x,Q2)= Dg(x,Q2)= No Transverse Gluon Distribution in 1/2 Parton Distribution Functions • Quark Distributions unpolarized distribution q(x,Q2)= = helicity distribution transversity distribution

  13. Sum Rules • Momentum Sum Rule • Helicity Sum Rule: • ΔΣ measured in DIS experiments and found to be small (0.1 – 0.3)…

  14. “Spin Crisis” • “Not-so-Naïve” quark model and comparison to results Predicted from EJSR Measured in DIS

  15. Remember the more complicated possibilities… But Leptons don’t scatter off gluons (at first order) How do we probe the gluons? Not Really a Crisis…

  16. RHIC pC Polarimeters Absolute Polarimeter (H jet) BRAHMS & PP2PP PHOBOS Siberian Snakes Siberian Snakes PHENIX STAR Spin Rotators (longitudinal polarization) Spin flipper Spin Rotators (longitudinal polarization) Solenoid Partial Siberian Snake Pol. H- Source LINAC BOOSTER Helical Partial Siberian Snake AGS 200 MeV Polarimeter AGS Internal Polarimeter Rf Dipole AGS pC Polarimeters Strong AGS Snake RHIC Spin

  17. PHENIX Detector • Philosophy: • High resolution at the cost of acceptance • High rate capable DAQ • Excellent trigger capability for rare events • Central Arms: • ||<0.35, =2900 • Charged particle ID and tracking; photon ID. EM Calorimetry. • Muon Arm: 1.2<||<2.4 Muon ID and tracking. • Global Detectors • Collision trigger • Collision vertex characterization • Relative luminosity • Local Polarimetry

  18. “Measurements” of ΔG • Example: • choose channel with high statistics • p + p → π0 + X • Complicated mixture of amplitudes • Compare with:

  19. Solution • Factorization between hard and soft physics • Example: q + g → π0 + X • Soft: • q(x), Δq(x), D(z) • Hard: • NLO pQCD cross-sections – spin dependent • Missing ingredients: • Δg(x) • beam polarization Soft Physics from universal fits to data Hard Physics σ ~ momenta and helicities D

  20. Status of Ingredients • Status of Pol. PDFs (2004) • Valence quark fairly well determined from DIS • ΔG and sea quarks poorly known

  21. pQCD Check pp0 X : PRD76,051106 • Next step: Measure cross-section as a test for perturbative QCD at • Run 6, pushes p0 cross-section to 20 GeV/c. • Agreement with pQCD over broad range of pT. • Does this mean that QCD works for spin sorted in this same range?

  22. Where Are We So Far? • Factorization between hard and soft physics • Example: q + g → π0 + X • Soft: • q(x), Δq(x), D(z) • Hard: • NLO pQCD cross-sections – spin dependent • Missing ingredients: • Δg(x), P – beam polarization ☺ ☺ ☺ Soft Physics from universal fits to data ☺ Hard Physics σ ~ momenta and helicities D ☺

  23. π0 ALL arXiv:0810.0694 • Put all ingredients into a NLO pQCD calculation with assumed values of ΔG, Monte Carlo the results with the detector acceptance, and compare to data to determine allowed values of ΔG.

  24. From ALL to G (with GRSV model) Generate g(x) curves for different (with DIS refit) Compare ALL data to curves (produce 2vs G) arXiv:0810.0694 Calculate ALL for each G

  25. Update to Pol. PDFs • Using the π0 results from PHENIX, one can recalculate allowed values of the pol. PDFs. • Much improved limits on ΔG.

  26. ΔL • ΔG is appearing to be small (although it may be enough to solve the Spin Crisis) • What is next? • ΔL… • Theory tells us it should be there anyway. • Anomalous magnetic moment • Sivers Effect

  27. SP kT,q p p Sivers Effect • Non-Zero Sivers function means that there is a left/right asymmetry in the kT of the partons in the nucleon • For a positive Siver’s function, there will be net parton kT to the left (relative to direction of proton, assuming spin direction is up). FSI : SIDIS ISI : Drell-Yan

  28. How can you get a net kT? • Nice conceptual picture from D. Sivers (talk given at UNM/RBRC Workshop on Parton Orbital Angular Momentum). • Summary: • Sivers effect requires orbital motion. • Is process dependent. • I would like to just follow this conceptual picture to see where it may lead.

  29. Sivers Effect No Sivers Effect without interaction with absorber.

  30. Fields Effect • Think of rotating (longitudinal) water balloons, or…

  31. Origin of Jet kT Net transverse momentum of a di-hadron pair in a factorization ansatz kT Another Possibility: • Spin-correlated transverse momentum – partonic orbital angular momentum • Can examine the helicity dependence of each term: Di-hadron pT • initial – e.g., fermi motion of the confined quarks or gluons, initial-state gluon radiation… • hard – final-state radiation (three-jet)… • frag – fragmentation transverse momentum jT

  32. Peripheral Collisions Larger Peripheral Collisions Larger Central Collisions Smaller Like Helicity(Positive on Positive Helicity) Measure jet Integrate over b, left with some residual kT

  33. Central Collisions Larger Peripheral Collisions Smaller Un-like Helicity(Positive On Negative Helicity) Integrate over b, left with some different residual kT

  34. Like Helicity kPR kTR Un-like Helicity kPR kTR Integrating over Impact Parameter Drell-Yan pair production in polarized p+p collisions. (Meng Ta-Chung et al. Phys. Rev. D 1989) Averaging over D(b): Integrating over impact parameter b:

  35. Measuring jet kT– di-hadron correlation o- h±azimuthal correlation Trigger on a particle, e.g. o, with transverse momentum pTt. Measure azimuthal angular distribution w.r.t. the azimuth of associated (charged) particle with transverse momentum pTa. The strong same and awayside peaks in p-p collisions indicate di-jet origin from hard scattering partons.

  36. How does PHENIX measure kt? near • Zero kT • Non-Zero kT Intra-jet pairs angular width : near jT Inter-jet pairs angular width : far jT  kT far Drawings by A. Zimmerman

  37. Jet Kinematics For details, see: Phys. Rev. D 74, 072002 (2006)

  38. Correlation Function • Red – real (raw Δφ) • Blue – background (mixed events)

  39. Fit Function • Blue – real (raw Δφ) • Red – Fit from above equation

  40. Spin sorted dihadron correlations • Fit Results • Red – Like helicity (++ & --) • Blue – Unlike helicity (+- & -+)

  41. Need <zt> and xh <k2T> asymmetry results are not sensitive to this xh and <zt> values – only needed to set the scale. ^ ^ xh and <zt> are determined through a combined analysis of the π° inclusive cross section and using jet fragmentation function measured in e+e- collisions. Ref. PRD 74, 072002 (2006)

  42. kT results for unpolarized case kT = 2.88 +/- 0.02 (stat) +/- 0.12 (syst) GeV jT = 607.5 +/- 0.8 (stat) +/- 0.3 (syst) MeV

  43. Preliminary Results • Take the difference Like – Unlike helicities. • Normalized by beam polarizations. • <j2T > asymmetry small (-6 ± 6 MeV out of ~607 MeV for unpolarized). • <k2T > asymmetry also small (-8 ± 90 MeV out of ~2.9 GeV for unpolarized).

  44. Interpretation • The small asymmetry in jT verifies our assumption that the third term is suppressed. • The second term may be constrained from current knowledge of the π0 ALL.

  45. Interpretation • The first term can be related in the “Meng conjecture” to partonic transverse momentum: where cij give the initial state weights and Wij give the impact parameter weighting. • Since PYTHIA studies show that the final state studied here is dominated by gg scattering (~50%), • We can interpret this as a constraint on the gluon orbital angular momentum. • Consistent with previous (Sivers) measurements, and complimentary, since one naïvely needs no initial or final state interactions.

  46. What Next?

  47. PHENIX VTX Detector Upgrade • Main physics goal to discriminate heavy-flavor production via displaced vertices. • I would like to use it to better determine jet kT. • Needs simulation and study.

  48. Summary • We have an analysis tool – di-hadron azimuthal correlations - that allows us to measure kT. • We are studying this in helicity-sorted collisions to see if there is a spin-dependent, coherent component of kT. • In our kinematic range, we find jTRMS = -6 ± 6 MeV, and kTRMS = -8 ± 90 MeV. • While this is consistent with other measurements related to gluon OAM, the connection to parton OAM needs theoretical guidance!

  49. Summary • Our group has made significant contributions to the RHIC Spin program and to the PHENIX experiment. • We are currently leading the investigation of an interesting, albeit speculative, physics analysis. • We will continue significant contributions to the PHENIX upgrade plan with an eye on our research thrust. • I look forward to an invigorated nuclear/particle group with the addition of active theorists.

  50. Backups

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