1. The EG4 Experiment: A Low Q 2 Determination of the GDH Integral Sarah K. Phillips The University of New Hampshire JLab Users Group Meeting June 9, 2009 For the CLAS EG4 Collaboration

2. Introduction CLAS EG4 (E03-006 + E06-017): a measurement of the generalized GDH sum rule for the proton and neutron (deuteron) at very low Q 2 (0.015 – 0.5 GeV 2 ) The GDH Sum Rule Generalized Forward Spin Polarizabilities Inclusive Electron Scattering and Spin Structure Functions The EG4 Experiment Inclusive analysis Exclusive analysis Summary

3. The GDH Sum Rule At Q 2 = 0 (real photon limit): The GDH Sum Rule relates the difference of the two photo-absorption cross sections to the anomalous magnetic moment of the nucleon κ. Circularly polarized photons incident on a longitudinally polarized target. σ 3/2 (σ 1/2 ) denotes the photo-absorption cross section with photon helicity parallel (anti-parallel) to the target spin. Sum rules are solid theoretical predictions based on general principles. Derived in the real photon limit, but can be generalized for virtual photons.

4. The Generalized GDH Sum Rule At Q 2 = 0, the GDH sum rule is recovered. At Q 2 → ∞, the Bjorken sum rule is recovered. The first moment Γ 1 Connected to the total spin carried by the quarks. Ji and Osborne, J. Phys. G27, 127 (2001) For virtual photons, Rule can be expressed as the integral of g 1 (x,Q 2 ) Can be linked to the forward spin-dependent Compton amplitude S 1 (0,Q 2 ) by the extended GDH sum rule

5. Measurements of Γ 1 Y. Prok et al. Phys. Lett. B672 12, 2009 Measurements from EG1 (a and b), SLAC, Hermes EG4 will push to lower Q 2 Other low Q 2 data from EG1b and Hall A's E97-110 and E94-010 (on polarized 3 He)

6. Generalized Forward Spin Polarizabilities Higher moments of spin structure functions are interesting too! Additional x-weighting emphasizes the kinematic region measured at JLab. D. Drechsel et al. Phys. Rep. 378 (2003) 99 Ideal quantities to test calculations of χ PT at low Q 2 !

7. Generalized Forward Spin Polarizabilities Y. Prok et al. Phys. Lett. B672 12, 2009 However, agreement is not so great between EG1b data and χPT calculations! Same problem exists for the proton and neutron.

8. Importance of the GDH Sum Rule How can we measure this? Extract helicity-dependent inclusive cross sections, then extract the structure function g 1. At low Q 2, the behaviour of the GDH integral and Γ 1 is predicted by chiral perturbation theories Data at very low Q 2 can give an accurate test of chiral perturbation theory predictions

9. Inclusive Electron Scattering The usual definitions: Four-momentum transfer squared: Structure functions: Invariant mass squared: Bjorken variable: Spin-dependent structure functions: Unpolarized Case Polarized Case All four ( F 1, F 2, g 1, g 2 ) are needed for a complete description of nucleon structure!

10. The EG4 Experiment Spokespeople NH 3: M. Battaglieri, A. Deur, R. De Vita, M. Ripani (Contact) ND 3: A. Deur (Contact), G. Dodge, K. Slifer Ph.D. Students K. Adhikari, H. Kang, K. Kovacs The CLAS EG4 experiment is focused on the measurement of the generalized GDH sum rule for the proton and neutron (deuteron) at very low Q 2 (0.015 – 0.5 GeV 2 ) Measured polarized electrons scattered off polarized targets down to 6° scattering angles Will extract g 1 from the helicity dependent inclusive cross sections

11. EG4 Experimental Set-Up EG4 ran from February to May 2006 in Hall B using CLAS. Longitudinally polarized CLAS NH 3 and ND 3 targets at -1m w.r.t. CLAS center. Longitudinally polarized electron beam (P b ~ 80%) at low energies (1-3 GeV); outbending torus field. Cross section measurement requires uniform detection efficiency at low Q 2. New Cherenkov detector (INFN – Genova) installed in sector-6 for detecting small angle scatterings down to 6º with uniform and high efficiencies.

12. EG4 Kinematics NH 3 target (P t = 80 – 90 %)ND 3 target (P t = 30 – 45 %) Good coverage of the resonance region

13. EG4 Analysis Flowchart EG4 Experiment E03-006 run Feb.-May 2006 Cooked Ntuples (Pass 1) Run and file quality checks Event selection, basic cuts Extracted Asymmetries Cross Sections Radiativ e Correcti ons Accepta nce Correctio ns g 2 model or data Extended GDH Sum Rule and polarizabilities PbPt and Dilution Factors Calibrati ons Fiducial Cuts Raster correcti ons Momentum Corrections (inclusive done) Combining Runs

14. Cherenkov Detector Performance New Cherenkov detector features nearly uniform efficiency within limited φ range (±10°) Fiducial cuts on sector 6 Cherenkov counter θ and φ in the projected PMT plane, study underway (H. Kang)

15. Electron Selection 10 x nphe To separate electrons from background particles, we use a set of six cuts (Osipenko cuts) Electrons in elastic ep scattering events used to study Cherenkov efficiency Inefficiency study underway by H. Kang

16. Momentum Corrections (K. Adhikari, S. Kuhn) Electron correction for inclusive analysis completed Pion correction for exclusive analysis underway and nearing completion Uses elastic events and assumes that angles are correctly detected.

17. PbPt Determination Elastic e-p events are used to extract PbPt for the E = 3.0 GeV NH3 data set. Dilution factor is evaluated from 12 C target data. Preliminary results agree with Moller (Pb = 80%) and target NMR (Pt=75- 76%) PbPt extraction for the deuteron data underway (S.K. Phillips, K. Kovacs)

18. Simulations E = 1.339 GeV, NH 3 data Preliminary Packing fraction obtained from fitting experimental data by simulations Points represent experimental data; the solid line is the preliminary fitting. (V. Drozdov and M. Ripani) Packing Fraction Cross section E' (GeV) θ = 14.5˚ – 15˚ θ = 19.5˚ – 20˚

19. Physics Topics Inclusive analysis going well But there is more!

20. Exclusive Channel Analysis In addition to the inclusive analysis, an exclusive analysis is underway to extract the pion electroproduction asymmetries in the nucleon resonance region. (X. Zheng) Observables in pion electroproduction Cross section: Three independent asymmetries: Single-beam Single-target Double beam-target

21. EG4 Exclusive Channel Analysis This analysis will extract A t and A et from EG4 data for These results will help to constrain models and chiral perturbation theory predictions at low Q 2 NH3 target: ND3 target: and

22. Electron identification similar to inclusive analysis Particle Selection and Missing Mass Cut A ToF cut of (-1, 1) ns is used to select the pion Missing mass cut: (0.85, 1.05) GeV (X. Zheng)

23. Dilution Factor The dilution factor measures the fraction of events from polarized nucleons (p in NH3 and D in ND3) Use low missing mass region to line up carbon with NH3 Use neutron peak to calculate dilution f (X. Zheng)

24. Preliminary Asymmetries Asymmetries not corrected for contribution from unpolarized nucleons in target Data indicates about 20% of events are from polarized protons in the NH3 target Models are scaled by 0.2 to compare with data (X. Zheng)

25. Expected Results on the Generalized GDH Sum Rule

26. Summary Extract the proton and the neutron GDH sums at very low Q 2 ; Extract pion electroproduction asymmetries A t and A et ; Both will compare to Chiral Perturbation Theory calculations. Analysis on the EG4 data is well underway! EG4 will Preliminary exclusive channel asymmetry results from the 3GeV NH3 data are very promising; Stay tuned for our new results!

28. Calorimeter (EC) Cuts (K. Adhikari)

29. (H. Kang)

30. New Resources for the EG4 Analysis New analysis work space on Hall B analysis work disk (replaced pdisks) EG4 also has a new disk server for ntuples and rootfiles Provided by INFN, 8.4 TB of space Cost about $40,000 ($20,000 for the infn1 partition currently dedicated to EG4) 0.5 TB of work space at /work/clas/claseg4/

31. Calibration Status Detector calibration and pass0 (8 iterations) done.

32. Analysis Status Pass1 ongoing.

33. World Data Well KnownPretty Well Known

34. The Hall A g 2 p Experiment (E08-027) EG4: g1p E08-027 : g 2 p Inclusive measurement at forward angle of the proton spin-dependent cross sections to determine g 2 p in the resonance region for 0.02 < Q 2 < 0.4 GeV 2. Can evaluate the BC sum and the longitudinal-transverse polarizability δ LT from these data. Will run in 2011

35. Hydrogen Hyperfine Structure The hyperfine splitting of hydrogen has been measured to a relative accuracy of 10 -13, but calculations are only accurate to a few ppm. Due to lack of knowledge of nucleon structure at low Q 2 ! Q 2 weighting of Δ 1 and Δ 2 ensures low momentum transfer region dominates integrals Precise measurements of g 1, g 2 at low Q 2 needed! Fermi energy Proton structure correction Nazaryan, Carlson, and Griffioen, Phys.Rev.Lett 96:163001 (2006)