Highlights of Spin Study at JLab Hall A: Longitudinal and Transverse J. P. Chen, Jefferson Lab Pacific-Spin2011, Cairns, Australia  Introduction  Longitudinal and transverse spin  Selected results from JLab Hall A  SSA in SIDIS: Transversity and TMDs  g 2 (d 2 ) at intermediate to high Q 2 : higher-twists, B-C sum rule  g 1 /g 2 at low Q 2 : GDH sum/spin polarizabilities  Future experiments (6 GeV and 12 GeV)

Spin Milestones (I) Nature: (  1896: Zeeman effect (milestone 1)  1922: Stern-Gerlach experiment (2)  1925: Spinning electron (Uhlenbeck/Goudsmit)(3)  1928: Dirac equation (4)  Quantum magnetism (5)  1932: Isospin(6)  1935: Proton anomalous magnetic moment  1940: Spin–statistics connection(7)  1946: Nuclear magnetic resonance (NMR)(8)  1950s: Development of magnetic devices (9)  : NMR for chemical analysis (10)  1951: Einstein-Podolsky-Rosen argument in spin variables(11)  1964: Kondo Effect (12)  1971: Supersymmetry(13)  1972:Superfluid helium-3 (14)

Spin Milestones (II)  1973: Magnetic resonance imaging(15)  :NMR for protein structure determination (16)  1978: Dilute magnetic semiconductors (17)  1980s: “Proton spin crisis or puzzle”  1988: Giant magnetoresistance(18)  1990: Functional MRI (19)  Proposal for spin field-effect transistor (20)  1991: Magnetic resonance force microscopy (21)  1996: Mesocopic tunnelling of magnetization (22)  1997: Semiconductor spintronics (23)  (Spin-polarized suprecurrents for spintronics, 1/2011)  2000s: “Nucleon transverse spin puzzle”?  ?: More puzzles in nucleon spin?  ……  ?: Breakthroughs in nucleon spin/nucleon structure study?  ……  ?: Applications of nucleon spin physics?

Nucleon Structure, Moments and Sum Rules Global properties and structure Mass: 99% of the visible mass in universe ~1 GeV, but u/d quark mass only a few MeV each! Momentum: quarks carry ~ 50% Energy-Momentum Sum Rule Spin: ½, quarks contribution ~30% Spin Sum Rule(s) Magnetic moment: large part anomalous, >150% GDH Sum Rule Axial charge Bjorken Sum Rule Angular momentum Ji’s Sum Rule Polarizabilities (Spin, Color) Tensor charge

Three Decades of Spin Structure Study 1980s: EMC (CERN) + early SLAC quark contribution to proton spin is very small  = ( )% ! ‘spin crisis’ ( Ellis-Jaffe sum rule violated) 1990s: SLAC, SMC (CERN), HERMES (DESY)  = 20-30% the rest: gluon and quark orbital angular momentum A + =0 (light-cone) gauge (½)  + L q +  G + L g =1/2 (Jaffe) gauge invariant (½)  + Lq + J G =1/2 (Ji) A new decomposition (X. Chen, et. al) What observable directly corresponds to L z ~ b x X p y ? Bjorken Sum Rule verified to <10% level 2000s: COMPASS (CERN), HERMES, RHIC-Spin, JLab, … :  ~ 30%;  G probably small, orbital angular momentum probably significant  Sum Rules at low Q 2  Higher-Twists  Transversity, Transverse-Momentum Dependent Distributions

Jefferson Lab Experimental Halls HallA: two HRS’ Hall B:CLAS Hall C: HMS+SOS 6 GeV polarized CW electron beam Pol=85%, 180  A Will be upgraded to 12 GeV by ~2014

JLab Polarized 3 He Target longitudinal, transverse and vertical Luminosity=10 36 (1/s) (highest in the world) High in-beam polarization ~ 60% Effective polarized neutron target 13 completed experiments 7 approved with 12 GeV (A/C) 15 uA

JLab Polarized Proton/Deuteron Target Polarized NH 3 /ND 3 targets Dynamical Nuclear Polarization In-beam average polarization 70-90% for p 30-40% for d Luminosity up to ~ (Hall C/A) ~ (Hall B)

JLab Spin Experiments Results: SSA in SIDIS: Transversity (n)/ TMDs g 2 /d 2: Higher twists, B-C sum rule Spin Moments: Spin Sum Rules and Polarizabilities Quark-Hadron duality Spin in the valence (high-x) region Planned g 2 p at low Q 2 Future: 12 GeV Inclusive: A 1 /d 2, Semi-Inclusive: Transversity, TMDs, Flavor-decomposition Review: Sebastian, Chen, Leader, arXiv: , PPNP 63 (2009) 1

Single Target-Spin Asymmetries in SIDIS Transversity and TMDs

Transversity Three twist-2 quark distributions: Momentum distributions: q(x,Q 2 ) = q ↑ (x) + q ↓ (x) Longitudinal spin distributions: Δq(x,Q 2 ) = q ↑ (x) - q ↓ (x) Transversity distributions: δq(x,Q 2 ) = 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 2 : δq, f 1T ┴ (x, k ┴,Q 2 ), … Fragmentation functions depends on z, p ┴ and Q 2 : D, H 1 (x,p ┴,Q 2 ) Measured asymmetries depends on x, z, P ┴ and Q 2 : Collins, Sivers, … (k ┴, p ┴ and P ┴ are related)

Leading-Twist TMD PDFs f 1 = f 1T  = Sivers Helicity g 1 = h1 =h1 = Transversity h1 =h1 =Boer-Mulders h 1T  = Pretzelosity h 1L  = Worm Gear (Kotzinian-Mulders) : Survive trans. Momentum integration Nucleon Spin Quark Spin g 1T = Worm Gear

Leading-Twist TMD PDFs f 1 = f 1T  = Sivers Helicity g 1 = h1 =h1 = Transversity h1 =h1 =Boer-Mulders h 1T  = Pretzelosity g 1T = Worm Gear h 1L  = Worm Gear (Kotzinian-Mulders) : Probed by E Nucleon Spin Quark Spin

Separation of Collins, Sivers and pretzelocity effects through angular dependence

Current Status Large single spin asymmetry in pp->  X Collins Asymmetries - sizable for proton (HERMES and COMPASS ) large at high x,  - and  has opposite sign  unfavored Collins fragmentation as large as favored (opposite sign)? - consistent with 0 for deuteron (COMPASS) Sivers Asymmetries - non-zero for  + from proton (HERMES), consistent with zero (COMPASS)? - consistent with zero for  - from proton and for all channels from deuteron - large for K + ? Very active theoretical and experimental study RHIC-spin, JLab (Hall A 6 GeV, CLAS12, HallA/C 12 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 12 GeV Unprecedented precision with high luminosity and large acceptance

E06 ‑ 010 Experiment First measurement on n ( 3 He) Polarized 3 He Target Polarized Electron Beam, 5.9 GeV – ~80% Polarization – Fast Flipping at 30Hz BigBite at 30º as Electron Arm – P e = 0.7 ~ 2.2 GeV/c HRS L at 16º as Hadron Arm – P h = 2.35 GeV/c – Excellent PID for  /K/p 7 PhD Thesis Students (5 graduated) 16 Beam Polarimetry (Møller + Compton) Luminosity Monitor

History of Figure of Merit of Polarized 3 He Target High luminosity: L(n) = cm -2 s -1 Record high in-beam ~ 60% polarization with 15  A beam with automatic spin flip every 20 minutes Performance of 3 He Target In-beam 3 He pol %

3 He Target Single-Spin Asymmetry in SIDIS 3 He Sivers SSA: negative for π +, 3 He Collins SSA small Non-zero at highest x for  + Blue band: model (fitting) uncertainties Red band: other systematic uncertainties arXiv: , submitted to PRL

Results on Neutron Collins asymmetries are not large, except at x=0.34 Sivers negative Blue band: model (fitting) uncertainties Red band: other systematic uncertainties

Asymmetry A LT Result 3 He A LT Positive for  - To leading twist: Preliminary

–Corrected for proton dilution, f p –Predicted proton asymmetry contribution < 1.5% (π + ), 0.6% (π - ) –Dominated by L=0 (S) and L=1 (P) interference Consist w/ model in signs, suggest larger asymmetry Neutron A LT Extraction Preliminary

JLab 12 GeV Era: Precision Study of TMDs From exploration to precision study with 12 GeV JLab Transversity: fundamental PDFs, tensor charge TMDs: 3-d momentum structure of the nucleon  Quark orbital angular momentum Multi-dimensional mapping of TMDs 4-d (x,z,P ┴,Q 2 ) Multi-facilities, global effort Precision  high statistics high luminosity and large acceptance

Solenoid detector for SIDIS at 11 GeV Also for PVDIS at 11 GeV Approved SIDIS experiments: E & E SSA in SIDIS Pion Production Transversely/ Longitudinally Polarized 3 He Target at 8.8 and 11 GeV. Large acceptance: >100 msr High luminosity : > 10 36

Mapping of Collins/Siver Asymmetries with SoLID Both  + and  - For one z bin ( ) Will obtain many z bins ( ) Upgraded PID for K+ and K-

Map Collins and Sivers asymmetries in 4-D (x, z, Q 2, P T )

Worm-gear functions: Dominated by real part of interference between L=0 (S) and L=1 (P) states No GPD correspondence Lattice QCD -> Dipole Shift in mom. space. Model Calculations -> h 1L  =? -g 1T. h 1L  = g 1T = Worm Gear Center of points:

Discussion Unprecedented precision 4-d mapping of SSA Collins and Sivers  +,  - and K +, K - New proposal polarized proton with SoLID Study factorization with x and z-dependences Study P T dependence Combining with the 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 study Q 2 evolution Global efforts (experimentalists and theorists), global analysis much better understanding of multi-d nucleon structure and QCD Longer-term future: EIC to map sea and gluon SSAs

Inclusive Transverse Spin g 2 Structure Function and Moments Burkhardt - Cottingham Sum Rule

g 2 : twist-3, q-g correlations experiments: transversely polarized target SLAC E155x, (p/d) JLab Hall A (n), Hall C (p/d) g 2 leading twist related to g 1 by Wandzura-Wilczek relation g 2 - g 2 WW : a clean way to access twist-3 contribution quantify q-g correlations

Precision Measurement of g 2 n (x,Q 2 ): Search for Higher Twist Effects Measure higher twist  quark-gluon correlations. Hall A Collaboration, K. Kramer et al., PRL 95, (2005)

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

BC Sum Rule P N 3 He BC satisfied w/in errors for 3 He BC satisfied w/in errors for Neutron (But just barely in vicinity of Q 2 =1!) BC satisfied w/in errors for JLab Proton 2.8  violation seen in SLAC data very prelim

Results on  2 n : E and E94-010

Higher-Twist Extraction and Comparison Extract Higher-Twist part of  2 DIS Compare with higher-twist estimated from E data

Color Polarizability (Lorentz Force): d 2 2 nd moment of g 2 -g 2 WW d 2 : twist-3 matrix element d 2 and g 2 -g 2 WW : clean access of higher twist (twist-3) effect: q-g correlations Color polarizabilities     are linear combination of d 2 and f 2 Provide a benchmark test of Lattice QCD at high Q 2 Avoid issue of low-x extrapolation Relation to Sivers and other TMDs

Measurements on neutron: d 2 n

d 2 (Q 2 ) E “g2p” SANE “d2n” new in Hall A 6 GeV Experiments Sane: new in Hall C “g2p” in Hall A, 2011 projected

Spin Sum Rules: Moments of SFs Moments of Spin Structure Functions  Sum Rules Global Property

Generalized GDH Sum Rule Connecting GDH with Bjorken Sum Rules Q 2 -evolution of GDH Sum Rule provides a bridge linking strong QCD to pQCD Bjorken and GDH sum rules are two limiting cases High Q 2, Operator Product Expansion : S 1 (p-n) ~ g A  Bjorken Q 2  0, Low Energy Theorem: S 1 ~  2  GDH High Q 2 (> ~1 GeV 2 ): Operator Product Expansion Intermediate Q 2 region: Lattice QCD calculations Low Q 2 region (< ~0.1 GeV 2 ): Chiral Perturbation Theory Calculations: HB  PT: Ji, Kao, Osborne, Spitzenberg, Vanderhaeghen RB  PT:  Bernard, Hemmert, Meissner Reviews: Chen, Deur, Meziani, Mod. Phy. Lett. A 20, 2745 (2005) J.P. Chen, Int. J. Mod. Phys. E19, 1893 (2010).

JLab E and E Genaralized GDH sum on neutron at Low Q < Q 2 < 1 GeV 2, resonance region PRL 89 (2002) Q2Q2 E Q2Q2 E < Q 2 < 0.3 GeV 2, resonance region

First Moment of g 1 p :  1 p EG1b, arXiv: EG1a, PRL 91, (2003) 1p1p Test fundamental understanding ChPT at low Q 2, Twist expansion at high Q 2, Future Lattice QCD

First Moment of g 1 n :  1 n E94-010, PRL 92 (2004) E97-110, preliminary EG1a, from d-p 1n1n

 1 of p-n EG1b, PRD 78, (2008) E EG1a: PRL 93 (2004)

Effective Coupling Extracted from Bjorken Sum s/s/ A. Deur, V. Burkert, J. P. Chen and W. Korsch PLB 650, 244 (2007) and PLB 665, 349 (2008)

Spin Polarizabilities Higher Moments of Spin Structure Functions at Low Q 2

Higher Moments: Generalized Spin Polarizabilities generalized forward spin polarizability  0 generalized L-T spin polarizability  LT

Neutron Spin Polarizabilities   LT insensitive to  resonance RB ChPT calculation with resonance for  0 agree with data at Q 2 =0.1 GeV 2 Significant disagreement between data and both ChPT calculations for  LT Good agreement with MAID model predictions  0  LT Q2 Q2 Q2 Q2 E94-010, PRL 93 (2004)

Preliminary Results from E Significant disagreement between data and both ChPT calculations for  LT Good agreement with MAID model predictions  0  LT Q2 Q2 Q2 Q2

Axial Anomaly and the  LT Puzzle N. Kochelev and Y. Oh; arXiv: v1

E : Proton g 2 Structure Function Fundamental spin observable has never been measured at low or moderate Q 2 BC Sum Rule : violation suggested for proton at large Q 2, but found satisfied for the neutron & 3 He. Spin Polarizability : Major failure (>8  of  PT for neutron  LT. Need g 2 isospin separation to solve. Hydrogen HyperFine Splitting : Lack of knowledge of g 2 at low Q 2 is one of the leading uncertainties. Proton Charge Radius : also one of the leading uncertainties in extraction of from  H Lamb shift. BC Sum Rule Spokespersons: Camsonne, Crabb, Chen, Slifer(contact), 6 PhD students, 3 postdocs Scheduled to run 11/2011-5/2012 Spin Polarizability  LT

Summary Spin structure study full of surprises and puzzles A decade of experiments from JLab: exciting results first neutron transversity/TMD measurement precision measurements of g 2 /d 2 : high-twist spin sum rules and polarizabilities test  PT calculations,  ‘  LT puzzle’ valence spin structure, quark-hadron duality Bright future complete a chapter in spin structure study with 6 GeV JLab 12 GeV Upgrade will greatly enhance our capability Precision determination of the valence quark spin structure Precision multi-d map of TMDs/transverse spin/tensor charge Precision extraction of GPDs, 3-d structure EIC: precision determination of sea and gluon in multi-d Goal: a full understanding of nucleon structure and QCD Lead to breakthrough in strong interaction?