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Low Q 2 Measurement of g 2 and the  LT Spin Polarizability

p. Low Q 2 Measurement of g 2 and the  LT Spin Polarizability. Resubmission of E07-001 to Jefferson Lab PAC-33 Jan. 14, 2008. A. Camsonne, J. P. Chen Thomas Jefferson National Accelerator Facility Karl J. Slifer University of Virginia. E07-001 Collaboration. 72 Physicists.

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Low Q 2 Measurement of g 2 and the  LT Spin Polarizability

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  1. p Low Q2 Measurement of g2and theLT Spin Polarizability Resubmission of E07-001 to Jefferson Lab PAC-33 Jan. 14, 2008 A. Camsonne, J. P. Chen Thomas Jefferson National Accelerator Facility Karl J. Slifer University of Virginia

  2. E07-001 Collaboration 72 Physicists Spin Experts from all three halls 20 Institutions

  3. Overview The inclusive nucleon SSF g1 and g2 are measured over wide range, but remains unmeasured below Q2=1.3 GeV2. The missing piece of the JLab Spin Physics Program. Motivations • g2p is central to our understanding of nucleon structure. • BC Sum Rule violation suggested at large Q2. • State of the Art PT calculations fail for neutron spin polarizability LT. • Knowledge of is a leading uncertainty in Hydrogen Hyperfine calculations. • Resonance Structure, in particular the ¢(1232). • Also a leading uncertainty in longitudinal measurements of (Hall B EG1, EG4). This Experiment Measure in the resonance region for 0.02 < Q2 < 0.4 using the Hall A septa and the polarized ammonia target.

  4. PAC33 Theory Comments

  5. E07-001 Conditional Status PAC31 Report “No particular technical obstacles were identified” Called for further justification of high Q2 points Specific PAC31 Issues Impact on the purely longitudinal measurements of in JLab Hall B. Impact on ongoing calculations of the Hydrogen Hyperfine Splitting. Projected results for BC Sum Rule, d2(Q2), etc.

  6. Impact on Longitudinal Measurements of g1 Longitudinal cross section difference Q2=0.01 Q2=0.05 E0=1.1 E0=2.4 Model Prediction for g2 contribution E0=1.6 E0=3.2 E0=2.4 reproduced from EG4 proposal

  7. EG4 Systematic (Q2 Dependent) Our measurement of g2p will reduce this error to less than 1% for all Q2

  8. Hydrogen Hyperfine Structure NCG PRL 96 163001 (2006) Structure Dependent Inelastic Elastic Scattering

  9. Hydrogen Hyperfine Structure This experiment NCG 2006: Used CLAS model assuming 100% error Integrand of ¢2 Assuming this uncertainty is realistic we will improve this by order of magnitude But, unknown in this region: Dominated by this region due to Q2 weighting MAID Model Simula Model So 100% error probably too optimistic We will provide first real constraint on ¢2

  10. Generalized Sum Rules Ji and Osborne, J. Phys. G27, 127 (2001) Unsubtracted Dispersion Relation + Optical Theorem: Extended GDH Sum • BC Sum Rule • GDH Sum Rule at Q2=0 • Bjorken Sum Rule at Q2=1 Superconvergence relation valid at any Q2 B&C, Annals Phys. 56, 453 (1970).

  11. Generalized Forward Spin Polarizabilities Drechsel, Pasquini and Vanderhaehen, Phys. Rep. 378, 99 (2003). LEX of gTT and gLT lead to the Generalized Forward Spin Polarizabilities

  12. and : Precision data exists even at very low Q2 No data below Q2=1.3 GeV2 Existing Data These integral relations allow us to test the underlying theory over a wide kinematic range Existing Data Ongoing/Future Analyses Hall A SAGDH : Hall B EG1 & EG4 : Hall B transverse : large Q2 proposal to this PAC Hall C SANE : large Q2 There are no existing analyses or 6 GeV proposals for low Q2 g2p

  13. Existing Resonance g2 Data 3He g2 0.10 < Q2 < 0.9 GeV2 Q2 3He g2 (Jlab Hall A) g2ww Large deviation from leading twist behaviour g2WW not good description of data

  14. Existing Resonance g2 Data Q2=1.3 Q2 3He g2 (Jlab Hall A) g2ww Lowest Q2 Existing Proton Data (Jlab Hall C : RSS)

  15. Chiral Perturbation Theory Though quantum chromodynamics (QCD) is generally accepted as the underlying theory of the strong interactions, a numerical check of the theory in the confinement region is difficult due to the strong coupling constant. A plethora of models have been inspired by QCD, but none of these models can be quantitatively derived from QCD. Only two descriptions are, in principle, exact realizations of QCD, namely chiral perturbation theory and lattice gauge theory. D. Drechsel (GDH 2000), Mainz Germany, June 2000

  16. PT Calculations The implementation of PT utilizes approximations which must be tested • For example: • The order to which expansion is performed. • Heavy Baryon approximation. • How to address short distance effects. • PT now being used to extrapolate Lattice QCD to the physical region. • Quark mass: From few hundred MeV to physical quark mass. • Volume: From finite to infinite • Lattice spacing: From discrete to continuous. • Example: QCDSF Lattice group utilizes Meissner et al.ÂPT calc Crucial to establish the reliability of calculations and to determine how high in Q2 (energy) we can go

  17. Generalized Polarizabilities Fundamental observables that characterize nucleon structure. Guichon et al. Nucl. Phys. A 591, 606 (1995). VCS observables are sensitive to the GPs Need additional out of plane measurements to get °0 which is related to the VCS GPs at Q2=0. at Q2=0 No simple relation between ±LT and the VCS GPS Measurement of±LTcomplementary to the VCS GP measurements Expected precision on 2000 hr MAINZ run

  18. Forward Spin Polarizabilities Neutron PRL 93: 152301 (2004) • Relativistic Baryon ÂPT • Bernard, Hemmert, Meissner • PRD 67:076008(2003) • Heavy Baryon ÂPT Calculation • Kao, Spitzenberg, Vanderhaeghen • PRD 67:016001(2003)

  19. Forward Spin Polarizabilities Neutron PRL 93: 152301 (2004) Add ¢ by hand: major effect for °0 but not for ±LT • Relativistic Baryon ÂPT • Bernard, Hemmert, Meissner • PRD 67:076008(2003) • Heavy Baryon ÂPT Calculation • Kao, Spitzenberg, Vanderhaeghen • PRD 67:016001(2003)

  20. Status of PT calculations ¼+¢ term not under control in ÂPT calcs. ±LT much less sensitive to this term ±LT : was expected to be easiest quantity forÂPT calcs Q2=0.1 Q2=0.05

  21. Interest from Theorists State of the Art ÂPT calculations fail to reproduce ±LT. WHY? B. Holstein, T. Hemmert, C.W. Kao, N. Kochelev, U. Meissner, M. Vanderhaeghen, C. Weiss Convergence? Working on NNLO. ¼¢ term included properly? Short range effects beyond ¼ N? Isoscalar in nature? t-channel axial vector meson exchange? An effect of the QCD vacuum structure? Isospin separation is critical to understand the nature of the problem Contains a “Bjorken-like” part due to g1 and an unknown part due to g2 From theoretical point of view, usually easier to deal with isospin separated quantity

  22. The Experiment Data Taking 15.7 Overhead 8.4 Total Days 24.1

  23. Beamline Chicane 10 m 4 m Tungsten calorimeter Slow raster SEM BPM EP 85cm BCM Moller Fast raster Target center Major Installation • Chicane Design : Jay Benesh (JLab CASA) • Two upstream Dipoles, one with vertical degree of freedom. • Reuse the dipoles from the HKS experiment. • Utilize open space upstream of target. • Minimal interference with existing beamline equipment. UVA/Jlab 5 T Polarized Target Upstream Chicane and supports Slow raster and Basel SEM. Instrumentation for 50-100 nA beam. Local beam dump. Hall A Septa.

  24. Projected Results

  25. BC Sum Rule Burkhardt-Cottingham Sum Rule 3¾ violation for proton seen at SLAC P. L. Anthonyet al., Phys. Lett. B553, 18 (2003). But, appears to hold for neutron P. L. Anthonyet al., Phys. Lett. B553, 18 (2003). M. Amarian et al. Phys. Rev. Lett. 92 (2004) 022301. Hall C proton analyses at Q2=1.3 underway “If it holds for one Q2 it holds for all” R. Jaffe

  26. LT Spin Polarizability Able to unambiguously test available calcs. Provide benchmark for any future calc.

  27. Proton d2(Q2) Huge systematic from lack of g2p data SANE

  28. Extended GDH Sum Sensitive to behavior which is normally masked in ¡1 as Q2 0

  29. Summary Measure of QCD complexity Spin Polarizability Systematic uncertainty In Measurements of Ideal place to test ÂPT calcs Hydrogen Hyperfine Structure Extended GDH SUM Resonance Structure

  30. Summary • g2p unmeasured below Q2=1.3 GeV2. • 24 days to measure g2p at low Q2 and complete the Jlab Spin Physics program. • No existing experiment or 6 GeV proposal will provide this data. • This experiment is not possible with 12 GeV. • Test Integral relations and Sum Rules • BC Sum Rule • d2p(Q2) • Extended GDH Sum • Eliminate leading systematic of EG4 measurement of Hall B. • Hydrogen Hyperfine Splitting • g2 is large contribution to systematic uncertainty • Contribution dominated by Q2<0.4 • State of the art ÂPT calcs work well for many spin-dependent quantities up to 0.1 GeV2 • But fail for ±LT. WHY? Need isospin separation to resolve.

  31. Existing DIS g2 Data Jlab Hall A: x¼0.2 SLAC: <Q2> = 5 GeV2 Proton Neutron Deuteron

  32. Total Systematic

  33. Forward Spin Polarizabilities Scaling of polarizabilities expected at large Q2 Not observed yet for Neutron PRL 93: 152301 (2004)

  34. Hydrogen Hyperfine Structure NCG 2006: Utilized CLAS model assuming 100% error CLAS model Simula model Elastic piece larger but with similar uncertainty If we assumed this uncertainty is realistic we will improve this by order of magnitude In fact, unknown in this region: 0.13 ppm of this error comes from¢2 MAID Model Simula Model So if the 100% error is realistic, we would cut error on¢POLin half So 100% error is probably too optimistic We will provide first real constraint on ¢2

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