17 April 2007 DIS2007 1Spin Structure Functions at CLASK. GriffioenCollege of William & Maryfor the CLAS [email protected] by J. PierceUniversity of Virginia17 April 2007 DIS2007 2Spin Structure with CLAS• Long-standing programin Hall-B at JLab tomeasure longitudinaldouble spin asymmetriesA|| on 15NH3 and 15ND3• EG1: 0.05<Q2<3.5 GeV2– data (2001); anal (2007)• EG4: 0.01<Q2<1 GeV2– data (2006); anal (2008)• EG12: 0.5<Q2<7 GeV2– data (2012?); anal (2014)17 April 2007 DIS2007 3CEBAF Accelerator• Electron beams up to 5.7 GeV with >80% longitudinalpolarization• Beam currents of 1-50 nA in Hall B17 April 2007 DIS2007 4Polarized Target• Dynamic nuclear polarization of NH3 and ND3• Polarizations of 70-80% for p and 20-30% for d• Luminosity 1035 cm-2s-117 April 2007 DIS2007 5FormalismWe can extract A1 usinga model for A2 (small), or g1using a model for g2 (small)We can extract A1 and A2from A|| at multiple valuesof η(Ebeam)17 April 2007 DIS2007 6KinematicsEG1EG4 EG12• Overlapping colors correspond to different beam energies• CLAS measures a large range in x at each fixed Q2• Different Ebeam for fixed (x,Q2) allows separation of A1 & A217 April 2007 DIS2007 7EG1 g1p (Q2<0.7)• At low Q2 the Δ resonance drives g1 negative• Extensive x-range at fixed Q2 allows integration over x• Red curve is the EG1 model used for radiative corrections17 April 2007 DIS2007 8EG1 g1p (Q2>0.7) & g1/F1• At higher Q2, g1 becomes positive everywhere• g1/F1 falls far below the DIS extrapolation at low Q2• Red curve is the EG1 model (dashed: DIS extrapolation)17 April 2007 DIS2007 9PDFs and CLAS• Error envelopes for PDFs from LSS05 global analysis (green)• CLAS EG1 data significantly improve errors on Δu, Δd, Δx and ΔG (blue)• CLAS EG12 (12 GeV upgrade) will especially improve ΔG (red)17 April 2007 DIS2007 10EG1 Extraction of A2• Analysis is in progress to obtain both A1 and A2 from the EG1 data• Intercept gives A1• Slope gives A2• A2 is larger than EG1 model (MAID, AO) as is Hall C RSS experiment17 April 2007 DIS2007 11A1 Data from EG1xbjA1d ( D-state corrected ) HF perturbed QM World Data Parm + d WF Q2 = 4.2 GeV2 World Data parm Q2 = 10 GeV2 Spin 3/2 suppression Helicity 3/2 suppression Symmetric Q Wave function suppressionSLAC - E143SMCHERMESSLAC - E155CLAS-EG1b Q2 = 1.0 - 4.52 GeV2SU(6)pQCD-0.200.20.40.60.811.21.40 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Isgur, PRD 59, 034013 (2003)}Close and Melnitchouk, PRC68, 035210 (2003)xbjA1p HF perturbed QM World Data parm Q2 = 10 GeV2 Spin 3/2 suppression Helicity 3/2 suppression Symmetric Q Wave functionSLAC - E143SMCHERMESSLAC - E155CLAS-EG1b Q2 = 1.0 - 4.52 GeV2SU(6)pQCD-0.200.20.40.60.811.21.40 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1ProtonDeuteronW > 2; Q2 > 117 April 2007 DIS2007 12DualityΔ (1232)S11 (1535)F15 (1680)GlobalΔ (1232)S11 (1535)F15 (1680)GlobalProton Deuteron17 April 2007 DIS2007 13Higher Twist from g1•F1 from NMC fit to F2 and 1998 SLAC fit to R•g1 (leading twist) from NLO fit at high Q2•h from fit to all data, especially CLAS in the pre-asymptotic region•d2: twist-3, f2: twist-417 April 2007 DIS2007 14Bjorken Sum & Higher TwistBjorken Sum Rule: Fit Γ1p-n to powers of 1/Q2 and extract f2p-n17 April 2007 DIS2007 15Moments Γ1p,dlow Q2 fitGDH + χpTPRELIMINARY PRELIMINARY17 April 2007 DIS2007 16Forward Spin Polarizabilityreal photon pointPRELIMINARY PRELIMINARY17 April 2007 DIS2007 17Hydrogen Hyperfine Splitting17 April 2007 DIS2007 18Δ1,2 from g1,2(from EG1: too small by 1 ppm?)Nucleon structure is the largest uncertainty in calculating HFS.Better g1, g2, GM, GE data at low Q2 required to resolve discrepancy.PRL96,16300117 April 2007 DIS2007 19EG4 Expectations17 April 2007 DIS2007 20EG12 Expectations17 April 2007 DIS2007 21In ConclusionCLAS, past, present and future, provides high-quality A|| data over a large and continuous range in x and Q2 that• significantly improve global PDF fits to Δu, Δd, Δs and ΔG• precisely determine higher twists• rigorously probe duality over a wide Q2 range• quantitatively test χPT calculations at low Q2• accurately yield the polarizability correction to hydrogen hyperfine splittingsNB The scope of this talk was limited to the inclusive measurements. A number of semi-inclusiveand exclusive measurements are also in progress using the same data sets (see J. Pierce’s talkin this