Spin Study at JLab: from Longitudinal to Transverse J. P. Chen, Jefferson Lab Berkeley Summer Spin Program, 2009, LBNL, California Introduction Longitudinal and transverse spin Selected results from JLab Recently completed and planned measurements 12 GeV plan

Strong Interaction and QCD Strong interaction, running coupling ~1 -- QCD: accepted theory for strong interaction -- asymptotic freedom (2004 Nobel) perturbation calculation works at high energy -- interaction significant at intermediate energy quark-gluon correlations -- interaction strong at low energy (nucleon size) confinement theoretical tools: pQCD, OPE, Lattice QCD, ChPT, … A major challenge in fundamental physics: Understand QCD in strong interaction region  Study and understand nucleon structure as E

Nucleon Structure 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% Spin: ½, quarks contribution ~30% Spin Sum Rule 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 DS = (12+-9+-14)% ! ‘spin crisis’ (Ellis-Jaffe sum rule violated) 1990s: SLAC, SMC (CERN), HERMES (DESY) DS = 20-30% the rest: gluon and quark orbital angular momentum A+=0 (light-cone) gauge (½)DS + Lq+ DG + Lg=1/2 (Jaffe) gauge invariant (½)DS + Lq + JG =1/2 (Ji) A new decomposition (X. Chen, et. al) Bjorken Sum Rule verified to <10% level 2000s: COMPASS (CERN), HERMES, RHIC-Spin, JLab, … : DS ~ 30%; DG probably small, orbital angular momentum probably significant Transversity, Transverse-Momentum Dependent Distributions Generalized Parton Distributions

Unpolarized and Polarized Structure functions

Parton Distributions (CTEQ6 and DSSV) Polarized PDFs Unpolarized PDFs CTEQ6, JHEP 0207, 012 (2002) DSSV, PRL101, 072001 (2008)

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

Jefferson Lab Hall A Experimental Setup for inclusive polarized n (3He) Experiments

Hall A polarized 3He target longitudinal, transverse and vertical Luminosity=1036 (1/s) (highest in the world) High in-beam polarization > 65% Effective polarized neutron target 12 completed experiments 1 are currently running 6 approved with 12 GeV (A/C) 15 uA

Hall B/C Polarized proton/deuteron target Polarized NH3/ND3 targets Dynamical Nuclear Polarization In-beam average polarization 70-90% for p 30-40% for d Luminosity up to ~ 1035 (Hall C) ~ 1034 (Hall B)

JLab Spin Experiments Results: Just completed: Planned Future: 12 GeV Moments: Spin Sum Rules and Polarizabilities Higher twists: g2/d2 Quark-Hadron duality Spin in the valence (high-x) region Just completed: d2p (SANE) and d2n Transversity (n) Planned g2p at low Q2 Future: 12 GeV Inclusive: A1/d2, Semi-Inclusive: Transversity, TMDs, Flavor-decomposition Review: Sebastian, Chen, Leader, arXiv:0812.3535, PPNP 63 (2009) 1

Longitudinal Spin (I) Spin in Valence (high-x) Region

Valence (high-x) A1p and A1n results Hall A E99-117, PRL 92, 012004 (2004) PRC 70, 065207 (2004) Hall B CLAS, Phys.Lett. B641 (2006) 11

pQCD with Quark Orbital Angular Momentum F. Yuan, H. Avakian, S. Brodsky, and A. Deur, arXiv:0705.1553 Inclusive Hall A and B and Semi-Inclusive Hermes BBS BBS+OAM

Projections for JLab at 11 GeV A1p at 11 GeV

Flavor decomposition with SIDIS Du and Dd at JLab 11 GeV Polarized Sea JLab @11 GeV

Longitudinal Spin (II) Quark Hadron Duality in Spin Strcuture Function

Duality in Spin-Structure: Hall A E01-012 Results A13He (resonance vs DIS) g1/g2 and A1/A2 (3He/n) in resonance region, 1 < Q2 < 4 GeV2 Study quark-hadron duality in spin structure. <Resonances> = <DIS> ? PRL 101, 1825 02 (2008)

Duality in Spin-Structure: Partial Moment Results G1 resonance comparison with pdfs

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

Bjørken Sum Rule gA: axial vector coupling constant from neutron b-decay CNS: Q2-dependent QCD corrections (for flavor non-singlet) A fundamental relation relating an integration of spin structure functions to axial-vector coupling constant Based on Operator Product Expansion within QCD or Current Algebra Valid at large Q2 (higher-twist effects negligible) Data are consistent with the Bjørken Sum Rule at 5-10 % level

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 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 New measurements from LEGS, MAMI(2), …

Generalized GDH Sum Rule Many approaches: Anselmino, Ioffe, Burkert, Drechsel, … Ji and Osborne (J. Phys. G27, 127, 2001): Forward Virtual-Virtual Compton Scattering Amplitudes: S1(Q2,n), S2(Q2, n) Same assumptions: no-subtraction dispersion relation optical theorem (low energy theorem) Generalized GDH Sum Rule

Connecting GDH with Bjorken Sum Rules Q2-evolution of GDH Sum Rule provides a bridge linking strong QCD to pQCD Bjorken and GDH sum rules are two limiting cases High Q2, Operator Product Expansion : S1(p-n) ~ gA  Bjorken Q2  0, Low Energy Theorem: S1 ~ k2  GDH High Q2 (> ~1 GeV2): Operator Product Expansion Intermediate Q2 region: Lattice QCD calculations Low Q2 region (< ~0.1 GeV2): Chiral Perturbation Theory Calculations: HBcPT: Ji, Kao, Osborne, Spitzenberg, Vanderhaeghen RBcPT: Bernard, Hemmert, Meissner Reviews: Theory: Drechsel, Pasquini, Vanderhaeghen, Phys. Rep. 378,99 (2003) Experiments: Chen, Deur, Meziani, Mod. Phy. Lett. A 20, 2745 (2005)

Q2 evolution of neutron spin structure moments JLab E94-010 (Hall A) Neutron spin structure moments and sum rules at Low Q2 GDH integral on neutron Q2 evolution of neutron spin structure moments (sum rules) with pol. 3He transition from quark-gluon to hadron Test cPT calculations Results published in several PRL/PLB’s Q2 PRL 89 (2002) 242301

First Moment of g1p and g1n : G1p and G1n Test fundamental understanding ChPT at low Q2, Twist expansion at high Q2, Future Lattice QCD G1p G1n E94-010, from 3He, PRL 92 (2004) 022301 E97-110, from 3He, preliminary EG1a, from d-p EG1b, arXiv:0802.2232 EG1a, PRL 91, 222002 (2003)

G1 of p-n EG1b, PRD 78, 032001 (2008) E94-010 + EG1a: PRL 93 (2004) 212001

Effective Strong Coupling A new attempt at low Q2 Experimental Extraction from Bjorken Sum

The strong coupling constant from pQCD as (Q) is well defined in pQCD at large Q2. Can be extracted from data (e.g. Bjorken Sum Rule). Not well defined at low Q2, diverges at LQCD

Definition of effective QCD couplings G. Grunberg, PLB B95 70 (1980); PRD 29 2315 (1984); PRD 40 680(1989). Prescription: Define effective couplings from a perturbative series truncated to the first term in as. Generalized Bjorken sum rule: Use to define an effective asg1. Process dependent. But can be related through “Commensurate scale relations” S.J. Brodsky & H.J Lu, PRD 51 3652 (1995)‏ S.J. Brodsky, G.T. Gabadadze, A.L. Kataev, H.J Lu, PLB 372 133 (1996)‏ Extend it to low Q2 down to 0: include all higher twists.

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

“Comparison” with theory ↔ Fisher et al. Bloch et al. Maris-Tandy Bhagwat et al. Cornwall Godfrey-Isgur: Constituant Quark Model Furui & Nakajima: Lattice Schwinger -Dyson Furui & Nakajima

Transverse Spin (I): Inclusive g2 Structure Function and Moments Burkhardt - Cottingham Sum Rule

g2: twist-3, q-g correlations experiments: transversely polarized target SLAC E155x, (p/d) JLab Hall A (n), Hall C (p/d) g2 leading twist related to g1 by Wandzura-Wilczek relation g2 - g2WW: a clean way to access twist-3 contribution quantify q-g correlations

Precision Measurement of g2n(x,Q2): Search for Higher Twist Effects Measure higher twist  quark-gluon correlations. Hall A Collaboration, K. Kramer et al., PRL 95, 142002 (2005)

BC Sum Rule BC = Meas+low_x+Elastic P N 3He 0<X<1 :Total Integral P Brawn: SLAC E155x Red: Hall C RSS Black: Hall A E94-010 Green: Hall A E97-110 (preliminary) Blue: Hall A E01-012 (very preliminary) N very prelim BC = Meas+low_x+Elastic “Meas”: Measured x-range 3He “low-x”: refers to unmeasured low x part of the integral. Assume Leading Twist Behaviour Elastic: From well know FFs (<5%)

BC Sum Rule P N 3He BC satisfied w/in errors for JLab Proton 2.8 violation seen in SLAC data N BC satisfied w/in errors for Neutron (But just barely in vicinity of Q2=1!) very prelim 3He BC satisfied w/in errors for 3He

BC Sum Rule What can BC tell us about Low-X? P N 3He Unmeasured Low-X Measured x 0<x<1 What can BC tell us about Low-X? P N Unmeasured Low-X very prelim “DIS” = -(RES+ELAS) 3He

Spin Polarizabilities Higher Moments of Spin Structure Functions at Low Q2

Higher Moments: Generalized Spin Polarizabilities generalized forward spin polarizability g0 generalized L-T spin polarizability dLT

Neutron Spin Polarizabilities dLT insensitive to D resonance RB ChPT calculation with resonance for g0 agree with data at Q2=0.1 GeV2 Significant disagreement between data and both ChPT calculations for dLT Good agreement with MAID model predictions g0 dLT E94-010, PRL 93 (2004) 152301 Q2 Q2

CLAS Proton Spin Polarizability g0p g0p Q6 EG1b, Prok et al. arXiv:0802.2232 Large discrepancies with ChPT! Only longitudinal data, model for transverse (g2) g0 sensitive to resonance

Summary of Comparison with cPT IAn G1P G1n G1p-n g0p g0n dLTn Q2 (GeV2) 0.1 0.1 0.05 0.1 0.05 0.16 0.05 0.05 0.1 0.1 HBcPT poor poor good poor good good good bad poor bad RBcPT/D good fair fair fair good poor fair bad good bad dLT puzzle: dLT not sensitive to D, one of the best quantities to test cPT, it disagrees with neither calculations by several hundred %! A challenge to cPT theorists. Very low Q2 data g1/g2 on n(3He) (E97-110) g1 on p and d available soon (EG4) Recently approved: g2 on proton E08-027

New Experiment: Proton g2 and LT g2 : central to knowledge of Nucleon Structure but remains unmeasured at low Q2 E08-027 : A- rating by PAC33 K. Slifer, A. Camsonne, ,J. P. Chen Critical input to Hydrogen Hyperfine Calculations Violation of BC Sum Rule suggested at large Q2 State-of-Art PT calcs fail dramatically for LT Septa Magnets for low Q2 Transverse bPolarized Proton Target n LT Spin Polarizability BC Sum Rule

Color Polarizabilities Higher Moments of Spin Structure Functions at High Q2

Color Polarizability (or Lorentz Force): d2 2nd moment of g2-g2WW d2: twist-3 matrix element d2 and g2-g2WW: clean access of higher twist (twist-3) effect: q-g correlations Color polarizabilities cE,cB are linear combination of d2 and f2 Provide a benchmark test of Lattice QCD at high Q2 Avoid issue of low-x extrapolation Relation to Sivers and other TMDs?

Measurements on neutron: d2n (Hall A and SLAC)

d2(Q2) BRAND NEW DATA! Very Preliminary Proton MAID Model RED : RSS. (Hall C, NH3,ND3) BLUE: E01-012. (Hall A, 3He) Neutron very prelim GREEN: E97-110. (Hall A, 3He) stat only

d2(Q2) Sane: just completed in Hall C “g2p” in Hall A, 2011 E08-027 “g2p” SANE 6 GeV Experiments Sane: just completed in Hall C “g2p” in Hall A, 2011 projected “d2n” just completed in Hall A

Planned d2n with JLab 12 GeV Projections with 12 GeV experiments Improved Lattice Calculation (QCDSF, hep-lat/0506017)

Color “Polarizabilities”

f2 Extraction and Color Polarizabilities JLab + world n data, m4 = (0.019+-0.024)M2 Twist-4 term m4 = (a2+4d2+4f2)M2/9 extracted from m4 term f2 = 0.034+-0.005+-0.043 f2 can be measured from g3 Color polarizabilities cE = 0.033+-0.029 cB = -0.001+-0.016 Proton and p-n f2= -0.160+-0.179 (p), -0.136+-0.109 (p-n) PLB 93 (2004) 212001

Transverse Spin (II): Single Spin Asymmetries in SIDIS Transversity and TMDs

Transversity Three twist-2 quark distributions: Momentum distributions: q(x,Q2) = q↑(x) + q↓(x) Longitudinal spin distributions: Δq(x,Q2) = q↑(x) - q↓(x) Transversity distributions: δq(x,Q2) = 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 PT) Distribution functions depends on x, k┴ and Q2 : δq, f1T┴ (x,k┴ ,Q2), … Fragmentation functions depends on z, p┴ and Q2 : D, H1(x,p┴ ,Q2) Measured asymmetries depends on x, z, P┴ and Q2 : Collins, Sivers, … (k┴, p┴ and P┴ are related)

“Leading-Twist” TMD Quark Distributions Nucleon Unpol. Long. Trans. Quark Unpol. Long. Trans. 55 55

Current Status Large single spin asymmetry in pp->pX Collins Asymmetries - sizable for proton (HERMES and COMPASS) large at high x, p- and p+ has opposite sign unfavored Collins fragmentation as large as favored (opposite sign)? - consistent with 0 for deuteron (COMPASS) Sivers Asymmetries - non-zero for p+ from proton (HERMES), consistent with zero (COMPASS)? - consistent with zero for p- 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 3He at JLab 12 GeV Unprecedented precision with high luminosity and large acceptance

E06-010 Single Target-Spin Asymmetry in Semi-Inclusive n↑(e,e′π+/-) Reaction on a Transversely Polarized 3He Target First neutron measurement 7 PhD Students Completed data taking in Feb. Exceeded PAC approved goal Collins Sivers

Hall-A Transversity: en→e’pX en→e’KX Polarized 3He: effective polarized neutron target World highest polarized luminosity: 1036 New record in polarization: >70% without beam ~65% in beam and with spin-flip (proposal 42%) HRSL for hadrons (p+- and K+-), new RICH commissioned BigBite for electrons, 64 msr, detectors performing well

Target Performance Online Preliminary Online preliminary EPR/NMR analysis shows a stable 65% polarization with 15 mA beam and 20 minute spin flip Cell: Astral Cell: Maureen Online Preliminary

Projections of g1T First Neutron (3He) Measurement With Fast Beam Helicity Flip (30Hz) Projected Uncertainties (Stat. Only): 2.3% at low x 3.4% at high x

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 Learn about quark orbital angular momentum Multi-dimensional mapping of TMDs 3-d (x,z,P┴ ) Q2 dependence Multi-facilities, global effort Precision  high statistics high luminosity and large acceptance

Upgrade magnets and power supplies Add new hall 12 11 6 GeV CEBAF Upgrade magnets and power supplies CHL-2 Enhance equipment in existing halls INFO FOR ME, BUT DO NOT SAY UNLESS ASKED!!!!! Cost range (from Mission Needs Statement) $170M-$250M This includes $30-50 M that could come from redirection of the present JLab Ops budget, and ~$20M that might come from foreign contributors (if they match what they did for the original project) About $47M of the total could come from a redirection of present operating funds over the duration of the project."

12 GeV Upgrade Kinematical Reach Reach a broad DIS region Precision SIDIS for transversity and TMDs Experimental study/test of factorization Decisive inclusive DIS measurements at high-x Study GPDs

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

3-D Mapping of Collins/Siver Asymmetries at JLab 12 GeV With A Large Acceptance Solenoid Detector Both p+ and p- For one z bin (0.5-0.6) Will obtain 4 z bins (0.3-0.7) Upgraded PID for K+ and K-

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

Discussion Unprecedented precision 3-d mapping of SSA Collins and Sivers p+, p- and K+, K- Study factorization with x and z-dependences Study PT dependence Combining with CLAS12 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 Q2 evolution Global efforts (experimentalists and theorists), global analysis much better understanding of 3-d nucleon structure and QCD

Spin Structure with the Solenoid at JLab 12 GeV Program on neutron spin structure with polarized 3He and solenoid Polarized 3He target effective polarized neutron highest polarized luminosity: 1036 A solenoid with detector package (GEM, EM calorimeter+ Cherenkov large acceptance: ~700 msr for polarized (without baffles)  high luminosity and large acceptance Inclusive DIS: improve by a factor of 10-100 A1 at high-x: high precision d2 at high Q2: very high precision parity violating spin structure g3/g5 : first significant measurement SIDIS: improve by a factor of 100-1000 transversity and TMDs, spin-flavor decomposition (~2 orders improvement) Unpolarized luminosity: 5x1038 , acceptance ~ 300 msr (with baffles) Parity-Violating DIS Boer-Mulders function

Single Spin Asymmetries in (Qausi-)Ealstic Two-photon Exchange and GPDs

E05-015: Target Single Spin Asymmetry Ay Inclusive quasi-elastic electron scattering on vertically polarized 3He target Target Single Spin Asymmetry Ay=0 in one-photon approximation, two-photon exchange gives non-zero Ay. Elastic contribution is well-known, inelastic response provides a new way to access the Generalized Parton Distributions.

E05-015 Projection Measurements at Q2=0.5, 1.0 GeV2 (and 2 GeV2). Neutron data provide unique new constraints on GPDs. Measurements at Q2=0.5, 1.0 GeV2 (and 2 GeV2). GPD model prediction and expected uncertainty (~2x10-3) at Q2=1.0 GeV2. Data taken competed two weeks ago, exceeded approved goal. First clear non-zero asymmetry measurement @ 10s level  Established quantitatively the 2-photon-exchange mechanism.  Established it as a tool to precisely probe hadron structure. Blue curve = elastic contrib. Black curve = inelastic contrib. Red point = total contrib.

Summary Spin structure study full of surprises and puzzles A decade of experiments from JLab: exciting results valence spin structure, quark-hadron duality spin sum rules and polarizabilities test cPT calculations,  ‘dLT puzzle’ precision measurements of g2/d2: high-twist first neutron transversity measurement first quasi-elastic target SSA: 2-photon to probe GPDs JLab played a major role in recent experimental efforts shed light on our understanding of STRONG QCD lead to breakthrough? Bright future complete a chapter in spin structure study with 6 GeV JLab 12 GeV Upgrade will greatly enhance our capability Goal: a full understanding of nucleon structure and strong interaction