Nucleon Spin: Results and Challenges on both Longitudinal and Transverse Spin

Transcription

1 Nucleon Spin: Results and Challenges on both Longitudinal and Transverse Spin J. P. Chen, Jefferson Lab, Virginia Los Alamos, February 19, 009 Introduction Highlights on JLab Longitudinal Spin Program: Spin Sum Rules and Polarizabilities Higher Twists: g /d Quark-Hadron Duality Spin Structure at High x: Valence Quark Distributions Transverse Spin and TMDs Outlook: 1 GeV Energy Upgrade

2 Introduction Structure and interactions matter: atoms nuclei e+nucleons quarks interactions: strong, EM, weak, gravity Nucleon structure and strong interaction energy and mass confinement spin and angular momentum

3 QCD and Nucleon Structure Strong interaction, running coupling ~1 -- QCD: accepted theory -- asymptotic freedom (004 Nobel) perturbation calculation works at high energy -- interaction significant at intermediate energy quark-gluon correlations -- confinement interaction strong at low energy -- Chiral symmetry -- theoretical tools: pqcd, OPE, Lattice QCD, ChPT, α s Major challenges: Understand and test QCD in strong interaction region Study and understand nucleon structure Spin Structure Study: -- study QCD and nucleon structure -- very rich program: crises and puzzles E

4 Nucleon Structure Nucleon: proton =(uud) and neutron=(udd) + sea + gluons Global properties and structure Mass: 99% of the visible mass in universe ~1 GeV, but u/d quark mass only a few MeV each! Spin: ½, but total quarks contribution only ~30%! Spin Sum Rule? Magnetic moment: large part is anomalous, >150%! GDH Sum Rule Axial charge Bjorken Sum Rule Tensor charge Transverse Spin Sum Rule? Polarizabilities (E, M, Spin, Color,) Sum rules: relate global property to integral of structure information

5 Spin and Magnetic Moment (of electron) 191 Otto Stern and Walther Gerlach Ag molecular-beam passing through inhomogeneous magnetic field split into two beams Ag atom has a magnetic moment Bohr magneton of the electron: µ e =eћ/m e c 195 Uhlenbeck and Goudsmit spin: internal property, like angular momentum electron spin S e =1/ two eigenstates +- 1/ Dirac: relativistic effect: spin magnetic moment electron is point-like particle (no internal structure observed so far)

6 Anomalous Magnetic Moment (of Proton) 1933 Otto Stern Magnetic moment of the proton -- expected: µ p =eћ/m p c (since S p =1/) -- measured: µ p =eћ/m p c(1+κ p )! first spin crisis anomalous magnetic moment (a.m.m) κ p = % 1943 Nobel Prize awarded to Stern for development of the molecular beam method and the discovery of the magnetic moment of protons now: κ p = and κ n =

7 A.M.M and Its Implications Anomalous magnetic moment is an evidence for an internal structure finite size Finite size Form factors Dirac form factor: normal relativistic effect Pauli form factor: relate to a.m.m. part Finite size Excitation spectrum GDH Sum Rule relates a.m.m. to integral of excitation spectrum A.M.M < -- > related to GPDs, TMDs (quark orbital angular momentum)

8 Spin Crisis or Spin Puzzle 1980s: EMC (CERN) + early SLAC quark contribution to proton spin is very small Σ = ( )%! spin crisis (Ellis-Jaffe sum rule violated) 1990s: SLAC, SMC (CERN), HERMES (DESY) Σ = 0-30% the rest: gluon and quark orbital angular momentum A + =0 (light-cone) gauge (½) Σ + L q + G + L g =1/ gauge invariant (½) Σ + Lq + J G =1/ Bjorken Sum Rule verified to 5-10% level 000s: COMPASS (CERN), HERMES, RHIC-Spin, JLab, : Σ ~ 30%; G probably small orbital angular momentum probably significant Transversity, transverse momentum dependent distributions (TMDs)

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10 F = xf 1 g = 0

11 Unpolarized and Polarized Structure functions

12 Unpolarized Parton Distributions (CTEQ6) After 40 years DIS experiments, unpolarized structure of the nucleon reasonably well understood. High x valence quark dominating

13 NLO Polarized Parton Distributions (AAC06) Q = 1 GeV x u v (x) AAC06 GRSV BB LSS x g(x) x d v (x) AAC06 GRSV BB LSS x x q(x) Q = 1 GeV x

14 Jefferson Lab Experimental Halls 6 GeV polarized CW electron beam Pol=85%, 180µ µa HallA: two HRS Will be upgraded to 1 GeV by ~014 Hall B:CLAS Hall C: HMS+SOS

15 Hall A polarized 3 He target Both longitudinal, transverse and vertical Luminosity=10 36 (1/s) (highest in the world) High in-beam polarization ~ 65% Effective polarized neutron target 9 completed experiments 4 are currently running 6 approved with 1 GeV (A/C)

16 Hall B/C Polarized proton/deuteron target Polarized NH 3 /ND 3 targets Dynamical Nuclear Polarization In-beam average polarization 70-80% for p 30-40% for d Luminosity up to ~ (Hall C) ~ (Hall B)

17 JLab Spin Structure Experiments Inclusive: Moments: Spin Sum Rules and Polarizabilities, n ( 3 He), p and d Higher twists: g /d, n and p Valence Quark Structure: A 1 at high-x, n, p and d Quark-Hadron duality in spin structure: n ( 3 He) and p Planned/On-going: 6 GeV: g /d, p, n and d 1 GeV: A 1 /d, p, n and d Semi-inclusive: transversity, TMDs, flavor decomposition,. Review: Sebastian, Chen, Leader, arxiv: , to appear on PPNP

18 Spin Sum Rules and Polarizabilities Moments of Spin Structure Functions

19 Gerasimov-Drell-Hearn Sum Rule Circularly polarized photon on longitudinally polarized nucleon A fundamental relation between the nucleon spin structure and its anomalous magnetic moment Based on general physics principles ( σ 1 (ν ) σ 3 (ν)) dν ν = π α EM κ M ν in Lorentz invariance, gauge invariance low energy theorem unitarity optical theorem casuality unsubtracted dispersion relation applied to forward Compton amplitude First measurement on proton up to 800 MeV (Mainz) and up to 3 GeV (Bonn) agree with GDH with assumptions for contributions from un-measured regions

20 Generalized GDH Sum Rule Many approaches: Anselmino, Ioffe, Burkert, Drechsel, Ji and Osborne: Forward Virtual-Virtual Compton Scattering Amplitudes: S 1 (Q,ν), S (Q, ν) (or alternatively, g TT (Q,ν), g LT (Q,ν)) Same assumptions: no-subtraction dispersion relation optical theorem (low energy theorem) Generalized GDH Sum Rule For v=0 G ( Q, v') v' dv' = el v' v S Q v 1 1(, ) 4 S 1 ( Q = G1 ( Q, v) dv ) 4 el v

21 Connecting GDH with Bjorken Sum Rules Q -evolution of GDH Sum Rule provides a bridge linking strong QCD to pqcd Bjorken and GDH sum rules are two limiting cases High Q, Operator Product Expansion : S 1 (p-n) ~ g A Bjorken Q 0, Low Energy Theorem: S 1 ~ κ GDH High Q (> ~1 GeV ): Operator Product Expansion Intermediate Q region: Lattice QCD calculations Low Q region (< ~0.1 GeV ): Chiral Perturbation Theory Calculations: RBχPT with, Bernard, Hemmert, Meissner; HBχPT, Ji, Kao, Osborne; Kao, Spitzenberg, Vanderhaeghen Reviews: Theory: Drechsel, Pasquini, Vanderhaeghen, Phys. Rep. 378,99 (003) Experiments: Chen, Deur, Meziani, Mod. Phy. Lett. A 0, 745 (005)

22 JLab E Neutron spin structure moments and sum rules at Low Q Spokespersons: G. Cates, J. P. Chen, Z.-E. Meziani PhD Students: A. Deur, P. Djawotho, S. Jensen, I. Kominis, K. Slifer Q evolution of spin structure moments and sum rules (generalized GDH, Bjorken and B-C sum rules) transition from quarkgluon to hadron Test χpt calculations Results published in several PRL/PLB s New results on 3 He GDH integral on neutron PRL 89 (00) 4301 Q

23 New Hall B EG1b Results: : Γ p 1 spokespersons: V. Burkert, D. Crabb, G. Dodge, S. Kuhn, R. Minehart, M. Taiuti Γ 1 p EG1b, Prok et al. arxiv: EG1a, PRL 91: 00 (003)

24 Γ 1 of neutron and p-n neutron Γ p-n p-n EG1b JLab Hall A E94010/CLAS EG1a CLAS EG1a HERMES E143 E155 pqcd leading twist Burkert-Ioffe Soffer-Teryaev (004) EG1b (008) E94-010: PRL 9 (004) Q (GeV ) EG1b, PRD 78, (008) E EG1a: PRL 93 (004) 1001

25 Effective Coupling extracted from Bjorken Sum A. Deur, V. Burkert, J. P. Chen and W. Korsch PLB 650, 44 (007) and PLB 665, 349 (008) α s /π α s (Q)/π JLab, this paper 0.4 JLab PLB α s,g1 /π world data α s,f3 /π GDH limit pqcd evol. eq. α s,τ /π OPAL Q (GeV)

26 P N 0<X<1 :Total Integral BC Sum Rule Γ = 1 g( x) dx = 0 Brawn: SLAC E155x Red: Hall C RSS Black: Hall A E Green: Hall A E (very preliminary) Blue: Hall A E01-01 (very preliminary) 0 BC = Meas+low_x+Elastic 3 He Meas : Measured x-range low-x : refers to unmeasured low x part of the integral. Assume Leading Twist Behaviour Elastic: From well know FFs (<5%) K. Slifer Crimea07 6

27 BC Sum Rule P BC satisfied w/in errors for JLab Proton.8σ violation seen in SLAC data N BC satisfied w/in errors for Neutron (But just barely in vicinity of Q =1!) 3 He BC satisfied w/in errors for 3 He K. Slifer Crimea07 7

28 nd Moments: Generalized Spin Polarizabilities generalized forward spin polarizability γ 0 generalized L-T spin polarizability δ LT d Q Q K Q TT ), ( ), ( ) 1 ( ) ( = ν ν ν σ ν ν π γ ν dx x Q g x Q M x Q g x Q M x )], ( 4 ), ( [ = α ν ν π ν + = = ), ( ), ( [ 16 ), ( ), ( ) 1 ( ) ( x LT LT dx x Q g x Q g x Q M d Q Q Q K Q α ν ν ν σ ν ν π δ ν

29 Neutron Spin Polarizabilities δ LT insensitive to resonance RB ChPT calculation with resonance for γ 0 agree with data at Q =0.1 GeV Significant disagreement between data and both ChPT calculations for δ LT Good agreement with MAID model predictions γ 0 E94-010, PRL 93 (004) δ LT Q Q

30 Summary of Comparison with χpt I n A Γ P 1 Γ n 1 Γ p-n 1 γ p 0 γ n 0 δ n LT γ p-n 0 Q (GeV ) HBχPT poor poor good poor good good good bad poor bad bad RBχPT/ good fair fair fair good poor fair bad good bad bad Q ~0.1 GeV is too high for HBχPT? 0.05 is good? RBχPT(NL) with reasonable to Q ~ 0.1? δ LT puzzle: δ LT not sensitive to, one of the best quantities to test χpt, it disagrees with neither calculations by several hundred %! Very low Q data on n( 3 He), p and d available soon (E97-110, EG4) Need NNL O(P 5 )? Kao et al. are working on that Other reasons? A challenge to χpt theorists.

31 JLab E97-110: GDH Sum Rule and Spin Structure of 3 He and Neutron with Nearly Real Photons Spokespersons: J. P. Chen, A. Deur, F. Garibaldi; PhD Students: J. Singh, V. Sulkosky, J. Yuan Preliminary Results: zeroth moments of g 1 and g Γ n JLab E94010 JLab E97110 Preliminary HERMES SLAC E143 JLab CLAS EG1a pqcd leading twist Burkert-Ioffe Soffer-Teryaev (004) GDH slope Χpt heavy baryons Γ n E94010 (total) SLAC E155x E97110 (total) Χpt Relativistic Q (GeV ) Q (GeV )

32 Hall B EG4 Projected Results Spokespersons: M. Battaglieri, R. De Vita, A. Deur, M. Ripani Extend to very low Q of GeV Longitudinal polarization g 1p, g 1 d Data taking in 006 Analysis progress well

33 δ LT Puzzle Possible reasons for δ LT puzzle: discussions with theorists Consensus: A real challenge to (χpt) theorists! Speculations: Short range effects beyond πn? t-channel axial vector meson exchange? Isoscalar in nature? An effect of QCD vacuum structure? To help solve the puzzle and to understand the nature of the problem, more information needed, including isospin separation need measurement on proton Does the δ LT discrepancy also exists for proton? E08-07 approved to measure g p and δ LT on proton

34 E08-07: Proton g and δ LT p g : central to knowledge of Nucleon Structure but remains unmeasured at low Q Critical input to Hydrogen Hyperfine Calculations n Violation of BC Sum Rule suggested at large Q State-of-Art χpt calcs fail dramatically for δ LT J.P. Chen, A. Camsonne, K. Slifer Septa Magnets for low Q Polarized Proton Target BC Sum Rule δ LT Spin Polarizability K. Slifer Crimea07 34

35 g, d : Higher Twists Quark-gluon Correlations and Color Polarizabilities

36 g : twist-3, q-g correlations experiments: transversely polarized target SLAC E155x, (p/d) JLab Hall A (n), Hall C (p/d) g leading twist related to g 1 by Wandzura-Wilczek relation g - g WW : a clean way to access twist-3 contribution quantify q-g correlations + = + = ), ( ), ( ), ( ), ( ), ( ), ( x WW WW y dy Q y g Q x g Q x g Q x g Q x g Q x g

37 Jefferson Lab Hall A E Precision Measurement of g n (x,q ): Search for Higher Twist Effects T. Averett, W. Korsch (spokespersons) K. Kramer (Ph.D. student) Improve g n precision by an order of magnitude. Measure higher twist quark-gluon correlations. Hall A Collaboration, K. Kramer et al., PRL 95, 1400 (005)

38 E results: g n vs. Q measured g n consistently higher than g ww : positive twist-3 higher twist effects significant below Q =1 GeV Models (color curves) predict small or negative twist-3 Bag Model Soliton Models

39 Color Polarizability: d (twist-3) nd moment of g -g WW d : twist-3 matrix element d ( Q ) = 3 x [ g( x, Q ) g ( x, Q )] dx = x g ( x, Q ) + d and g -g WW : clean access of higher twist (twist-3) effect: q-g correlations WW Color polarizabilities χ Ε,χ Β are linear combination of d and f Provide a benchmark test of Lattice QCD at high Q Avoid issue of low-x extrapolation 0 [ 1 3g( x, Q )] dx

40 Measurement on proton: d p (Hall C and SLAC) RSS and SANE: O. Rondon et al. d p Q

41 Measurements on neutron: d n (Hall A and SLAC)

42 d (Q ) Proton MAID Model Neutro n BRAND NEW DATA! Very Preliminary RED : RSS. (Hall C, NH 3,ND 3 ) K. Slifer, O. Rondon et al. in preparation BLUE: E (Hall A, 3 He) courtesy of P. Solvignon GREEN: E (Hall A, 3 He) courtesy of V. Sulkosky stat only K. Slifer Crimea07 4

43 d (Q ) E08-07 gp projected SANE Upcoming 6 GeV Experiments Sane: Fall < Q < 6 GeV gp in Hall A, < Q < 0.4 GeV dn in Hall A, 009 Q = 3 GeV K. Slifer Crimea07 43

44 Planned d n with JLab 6 GeV and 1 GeV Projections with planned 6 GeV and 1 GeV experiments Improved Lattice Calculation (QCDSF, hep-lat/ )

45 Quark-hadron Duality in Spin Structure

46 0.005 Duality in Spin-Structure: Hall A E01-01 Results Spokesperson: N. Liyanage, J. P. Chen, S. Choi; PhD Student: P. Solvignon g 1 /g and A 1 /A ( 3 He/n) in resonance region, 1 < Q < 4 GeV Study quark-hadron duality in spin structure. PRL 101, (008) Γ 1 resonance vs. pdfs 3 He A 1 3He (resonance vs DIS) ~ Γ neutron BB GRSV AAC LSS JLab E This work Q (GeV/c) x Q x

47 Valence Quark Spin Structure A 1 at high x and flavor decomposition

48 JLab E Precision Measurement of A 1n at Large x Spokespersons: J. P. Chen, Z. -E. Meziani, P. Souder, PhD Student: X. Zheng First precision A 1n data at high x Extracting valence quark spin distributions Test our fundamental understanding of valence quark picture SU(6) symmetry Valence quark models pqcd (with HHC) predictions Quark orbital angular momentum Crucial input for pqcd fit to PDF PRL 9, (004) PRC 70, (004)

49 Polarized Quark Distributions Combining A 1n and A 1p results Valence quark dominating at high x u quark spin as expected d quark spin stays negative! Disagree with pqcd model calculations assuming HHC (hadron helicity conservation) Quark orbital angular momentum Consistent with valence quark models and pqcd PDF fits without HHC constraint ( u+ u )/(u+u ) ( d+ d )/(d+d ) E99117 HERMES x

50 Projections for JLab at 11 GeV A n 1 at 11 GeV A 1 p at 11 GeV A n Solenoid (Apar only), 00 hours HMS+SHMS, DIS, 1800 hours E14 E154 HERMES E x

51 Semi-inclusive Deep Inelastic Scattering N(e,e π)x Transversity and TMDs

52 Transversity and TMDs Three twist- quark distributions: Momentum distributions: q(x,q ) = q (x) + q (x) Longitudinal spin distributions: q(x,q ) = q (x) - q (x) Transversity distributions: δq(x,q ) = q (x) - q (x) It takes two chiral-odd objects to measure transversity Semi-inclusive DIS Chiral-odd distributions function (transversity) Chiral-odd fragmentation function (Collins function) TMDs: (without integrating over P T ) Distribution functions depends on x, k and Q : δq, f 1T (x,k,q ), Fragmentation functions depends on z, p and Q : D, H 1 (x,p,q ) Measured asymmetries depends on x, z, P and Q : Collins, Sivers, (k, p and P are related)

53 Leading-Twist TMD Quark Distributions Nucleon Quark Unpol. Unpol. Long. Trans. f 1 = f 1T = 1 Long. g 1L = g 1T = Trans. h 1 = h 1L = h 1T = h 1T =

54 sin(φ+φ S ) π UT π + A UT sin(φ) from transv. pol. H target Simultaneous fit to sin(φ + φ s ) and sin(φ - φ s ) `Collins moments III HERMES PRELIMINARY virtual photon asymmetry amplitudes not corrected for acceptance and smearing sin(φ-φ S ) UT π π + `Sivers moments III HERMES PRELIMINARY not corrected for acceptance and smearing sin(φ+φ S ) π UT π - 6.6% scale uncertainty sin(φ-φ S ) UT π π - 6.6% scale uncertainty x z P h [GeV] Non-zero Collins asymmetry Assume δq(x) from model, then H 1 _unfav ~ -H 1 _fav Need independent H 1 (BELLE) x z P h [GeV] Sivers function nonzero (π + ) orbital angular momentum of quarks Regular flagmentation functions

55 Current Status Large single spin asymmetry in pp->πx Collins Asymmetries - sizable for proton (HERMES and COMPASS) large at high x, large for π - π - and π+ has opposite sign unfavored Collins fragmentation as large as favored (opposite sign)? - consistent with 0 for deuteron (COMPASS) Sivers Asymmetries - non-zero for π + from proton (HERMES), consistent with zero (COMPASS)? - consistent with zero for π - from proton and for all channels from deuteron - large for K +? Very active theoretical and experimental study RHIC-spin, JLab (Hall A 6 GeV, CLAS1, HallA/C 1 GeV), Belle, FAIR (PAX) Global Fits/models by Anselmino et al., Yuan et al. and First neutron measurement from Hall A 6 GeV (E06-010) Solenoid with polarized 3 He at JLab 1 GeV Unprecedented precision with high luminosity and large acceptance

56 Transversity Distributions A global fit to the HERMES p, COMPASS d and BELLE e+e- data by the Torino group (Anselmino et al.). Need neutron data. Need precision multi-dimension data.

57 E06-010/ Single Target-Spin Asymmetry in Semi-Inclusive n (e,e π +/- ) Reaction on a Transversely Polarized 3 He Target Spokespersons: X. Jiang, J. P. Chen, E. Cisbani, H. Gao, J.-C. Peng Collins 7 PhD Students: Successfully Completed data taking, exceeded PAC approved goal Sivers

58 Hall-A Transversity: en e πx en e ΚX Polarized 3He: effective polarized neutron target World highest polarized luminosity: New record in polarization: >70% without beam ~65% in beam and with spin-flip (proposal 4%) HRSL for hadrons (p+- and K+-), new RICH commissioned BigBite for electrons, 64 msr, detectors performing well

59 Precision Study of Transversity and TMDs From exploration to precision study Transversity: fundamental PDFs, tensor charge TMDs provide 3-d structure information of the nucleon Laboratory to study QCD Learn about quark orbital angular momentum Multi-dimensional mapping of TMDs 3-d (x,z,p ) Q dependence multi facilities, global effort Precision high statistics high luminosity and large acceptance

60 Measurement of Tensor Charge Tensor charge is a fundamental quantity; LQCD prediction A plan for a measurement of the tensor charge As much model independent as possible Valence phenomena: u and d quarks dominant To determine δu, δd, H 1u, H d 1 Need at least 4 measurements at each kinematical point SIDIS of π +- on both proton and neutron Kinematical region: most contributions in 0.1 < x < GeV JLab idea for this measurement CLAS1 with proton and a new Solenoid with polarized neutron ( 3 He) Issues: factorization, Q evolution, NLO, higher-twists, sea quarks e+e- (Belle), pp (RHIC, FAIR, ), ep (EIC) global fit

61 Solenoid detector for SIDIS at 11 GeV Proposed for PVDIS at 11 GeV GEMs

62 3-D Mapping of Collins/Siver Asymmetries at JLab 1 GeV With A Large Acceptance Solenoid Detector Both π+ and π- For one z bin ( ) Will obtain 4 z bins ( ) Upgraded PID for K+ and K-

63 3-D Projections for Collins and Sivers Asymmetry (π + )

64 Discussion Unprecedented precision 3-d mapping of SSA Collins and Sivers π +, π - and K +, K - Study factorization with x and z-dependences Study P T dependence Combining with CLAS1 proton and world data extract transversity and fragmentation functions for both u and d quarks determine tensor charge study TMDs for both valence and sea quarks study quark orbital angular momentum Combining with world data, especially data from high energy facilities study Q evolution Global efforts (experimentalists and theorists), global analysis much better understanding of 3-d nucleon structure and QCD

65 Summary Spin structure study full of surprises and puzzles A decade of experiments from JLab: exciting results Spin sum rules and polarizabilities: test χpt calculations δ LT puzzle g /d : higher-twist effects and q-g correlations, LQCD Spin-duality: transition and link between hadrons and quark-gluons A 1 at high-x: valence structure, flavor decomposition, quark OAM Bright future Complete a chapter in longitudinal spin structure study Transversity and TMDs: new dimensions Upgrades (1 GeV, large acceptance) greatly enhance our capability Together with other world facilities, experiments and theoretical efforts will lead to breakthrough in our understanding of STRONG QCD.

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67 Flavor decomposition with SIDIS u and d at JLab 11 GeV Polarized Sea GeV

68 Leading-Twist Quark Distributions ( A total of eight distributions) f 1 = No K dependence g = 1L g 1T = h 1T = K - dependent, T- odd f 1T = h 1 = K - dependent, T- even h 1L = h 1T =

69 CLAS A 1p and A 1d results CLAS collaboration, Phys.Lett. B641 (006) 11 d A 1 ( D-state corrected ) This work HERMES SMC SLAC - E155 SLAC - E143 pqcd SU(6) x

70 pqcd with Quark Orbital Angular Momentum F. Yuan, H. Avakian, S. Brodsky, and A. Deur, arxiv: Inclusive Hall A and B and Semi-Inclusive Hermes BBS BBS+OAM

71 Spin Polarizability γ 0 : Isospin Separation Deur et al. arxiv:080.3 γ p-n 0 (10-4 fm 4) Bernard et al. MAID γ 0 sensitive to resonance, but p-n not sensitive to Still large discrepancy with ChPT γ p+n 0 (10-4 fm 4) Kao et al. Bernard et al. MAID -4 Kao et al Q (GeV )

72 CLAS Proton Spin Polarizability γ 0 p γ 0 p Q 6 EG1b, Prok et al. arxiv:080.3 Large discrepancies with ChPT! Only longitudinal data, model for transverse (g ) γ 0 sensitive to resonance

73 New Hall A 3 He Results Q evolution of moments of 3 He spin structure functions Test Chiral Perturbation Theory predictions at low Q need χpt calculations for 3 He K. Slifer, et al.,prl 101, 0303 (008) I A (Q ) [µb] GDH integral I A 0.03 E94010 E DIS GDH Sum Rule MAID + Q.E. Γ 1 (Q ) Γ 1 E94010 E DIS SLAC GDH slope MAID Q (GeV ) Q (GeV )