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

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E Collaboration 20 Institutions 72 Physicists Spin Experts from all three halls

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Overview The inclusive nucleon SSF g 1 and g 2 are measured over wide range, but remains unmeasured below Q 2 =1.3 GeV 2. The missing piece of the JLab Spin Physics Program. Motivations 1)g 2 p is central to our understanding of nucleon structure. 2)BC Sum Rule violation suggested at large Q 2. 3)State of the Art PT calculations fail for neutron spin polarizability LT. 4)Knowledge of is a leading uncertainty in Hydrogen Hyperfine calculations. 5)Resonance Structure, in particular the ¢ (1232). 6)Also a leading uncertainty in longitudinal measurements of (Hall B EG1, EG4). This Experiment Measure in the resonance region for 0.02 < Q 2 < 0.4 using the Hall A septa and the polarized ammonia target.

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PAC33 Theory Comments

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E Conditional Status PAC31 Report No particular technical obstacles were identified Called for further justification of high Q 2 points Specific PAC31 Issues 1.Impact on the purely longitudinal measurements of in JLab Hall B. 2.Impact on ongoing calculations of the Hydrogen Hyperfine Splitting. 3.Projected results for BC Sum Rule, d 2 (Q 2 ), etc.

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Impact on Longitudinal Measurements of g 1 Q 2 =0.01Q 2 =0.05 E 0 =1.1 E 0 =1.6 E 0 =2.4 E 0 =3.2 reproduced from EG4 proposal Model Prediction for g 2 contribution Longitudinal cross section difference

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EG4 Systematic PBPTPBPT 1-2% 15 N Background1-2% L and Filling Factor 3.0% Electron Efficiency<5% Radiative Corrections5.0% Modeling of g % (Q 2 Dependent) Our measurement of g 2 p will reduce this error to less than 1% for all Q 2

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Hydrogen Hyperfine Structure NCG PRL (2006) Structure Dependent Elastic Scattering Inelastic

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

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Generalized Sum Rules Unsubtracted Dispersion Relation + Optical Theorem: Ji and Osborne, J. Phys. G27, 127 (2001) Extended GDH Sum BC Sum Rule Superconvergence relation valid at any Q 2 B&C, Annals Phys. 56, 453 (1970). GDH Sum Rule at Q 2 =0 Bjorken Sum Rule at Q 2 = 1

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Generalized Forward Spin Polarizabilities LEX of g TT and g LT lead to the Generalized Forward Spin Polarizabilities Drechsel, Pasquini and Vanderhaehen, Phys. Rep. 378, 99 (2003).

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Existing Data These integral relations allow us to test the underlying theory over a wide kinematic range and : Precision data exists even at very low Q 2 No data below Q 2 =1.3 GeV 2 Hall A SAGDH : Hall B EG1 & EG4 : There are no existing analyses or 6 GeV proposals for low Q 2 g 2 p Existing Data Ongoing/Future Analyses Hall C SANE : large Q 2 Hall B transverse : large Q 2 proposal to this PAC

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Existing Resonance g 2 Data 3 He g 2 (Jlab Hall A) g 2 ww Q2Q2 Large deviation from leading twist behaviour g 2 WW not good description of data Large deviation from leading twist behaviour g 2 WW not good description of data 3 He g < Q 2 < 0.9 GeV 2

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Existing Resonance g 2 Data 3 He g 2 (Jlab Hall A) Lowest Q 2 Existing Proton Data g 2 ww Q2Q2 (Jlab Hall C : RSS) Q 2 =1.3

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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

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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. Crucial to establish the reliability of calculations and to determine how high in Q 2 (energy) we can go Example: QCDSF Lattice group utilizes Meissner et al. ÂPT calc

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Generalized Polarizabilities Fundamental observables that characterize nucleon structure. Guichon et al. Nucl. Phys. A 591, 606 (1995). VCS observables are sensitive to the GPs Expected precision on 2000 hr MAINZ run Need additional out of plane measurements to get ° 0 which is related to the VCS GPs at Q 2 =0. No simple relation between ± LT and the VCS GPS at Q 2 =0 Measurement of ± LT complementary to the VCS GP measurements

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Forward Spin Polarizabilities PRL 93: (2004) Neutron Heavy Baryon Â PT Calculation Kao, Spitzenberg, Vanderhaeghen PRD 67:016001(2003) Relativistic Baryon Â PT Bernard, Hemmert, Meissner PRD 67:076008(2003)

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

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Status of PT calculations Â PT calc HB poor goodpoorbad RB( ¢ +VM) goodfairgoodfairgoodbad Q 2 =0.1 HB good RB( ¢ +VM) good Q 2 =0.05 ± LT : was expected to be easiest quantity for Â PT calcs ¼ + ¢ term not under control in Â PT calcs. ± LT much less sensitive to this term

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Interest from Theorists State of the Art Â PT 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 g 1 and an unknown part due to g 2 From theoretical point of view, usually easier to deal with isospin separated quantity

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The Experiment E 0 (GeV) µ (deg)Days Data Taking 15.7 Overhead 8.4 Total Days 24.1

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Beamline Chicane Tungsten calorimeter SEM BPM BCM Moller Target center Fast raster EP Slow raster 85cm 10 m 4 m 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 nA beam. Local beam dump. Hall A Septa. Major Installation

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Projected Results

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BC Sum Rule Burkhardt-Cottingham Sum Rule If it holds for one Q 2 it holds for all R. Jaffe 3¾ violation for proton seen at SLAC P. L. Anthony et al., Phys. Lett. B553, 18 (2003). But, appears to hold for neutron P. L. Anthony et al., Phys. Lett. B553, 18 (2003). Hall C proton analyses at Q 2 =1.3 underway M. Amarian et al. Phys. Rev. Lett. 92 (2004)

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

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Huge systematic from lack of g 2 p data Proton d 2 (Q 2 ) SANE

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Extended GDH Sum Sensitive to behavior which is normally masked in ¡ 1 as Q 2 0 Sensitive to behavior which is normally masked in ¡ 1 as Q 2 0

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

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g 2 p unmeasured below Q 2 =1.3 GeV days to measure g 2 p at low Q 2 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 d 2 p (Q 2 ) Extended GDH Sum Eliminate leading systematic of EG4 measurement of Hall B. Hydrogen Hyperfine Splitting g 2 is large contribution to systematic uncertainty Contribution dominated by Q 2 <0.4 State of the art Â PT calcs work well for many spin-dependent quantities up to 0.1 GeV 2 But fail for ± LT. WHY? Need isospin separation to resolve.

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Existing DIS g 2 Data SLAC: = 5 GeV 2 Jlab Hall A: x ¼ 0.2 Proton Deuteron Neutron

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Total Systematic Source(%) Cross Section5-7 Target Polarization3 Beam Polarization3 Radiative Corrections3 Parallel Contribution<1 Total7-9

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Forward Spin Polarizabilities Scaling of polarizabilities expected at large Q 2 PRL 93: (2004) Not observed yet for Neutron

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

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