Neutron Transverse Spin Structure Jian-ping Chen, Jefferson Lab Transverse Workshop (GaryFest), JLab, Oct. 29, 2010 Introduction Longitudinal and Transverse Spin: Inclusive Scattering Polarized Structure, OAM, Higher-twists Transverse Spin with SIDIS Transversity and TMDs Preliminary results from 6 GeV neutron transversity experiment Future: 12 GeV and EIC

Introduction Why do we care about transverse (spin) structure? Obvious for Gary (decades ago).

Nucleon Structure and QCD Colors are confined in hadronic system Hadron: ideal lab to study QCD Nucleon = u u d + sea + gluons Mass, charge, magnetic moment, spin, axial charge, tensor charge Decomposition of each of the fundamental quantities Mass: ~1 GeV, but u/d quark mass only a few MeV each! Momentum: quarks carry ~ 50% Spin: ½, quarks contribute ~30% Spin Sum Rule Orbital Angular Momentum Relations to GPDs and TMDs Tensor charge Transverse sum rule(?) Quarks and gluon field are in-separable Multi-parton correlations are important Beyond co-linear factorization Transverse dimension is crucial for understanding nucleon structure and QCD, help understanding confinement

Four Decades of Nucleon Structure Study 1970s: SLAC DIS  Bjorken Scaling, discovery of partons (quarks) 4 decades study on unpolarized structure, 5 orders in x range and Q2 Global analyses to extract unpolarized PDFs 1980s: ‘spin crisis’, quark spin contribution to proton spin is very small 3 decades study on longitudinally polarized structure: 3 orders in x and 2 in Q2 DS ~ 30%; DG small Orbital angular momentum important, definition? 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.) 2000s:Transversity and Transverse-Momentum-Dependent Distributions Model-dependent extraction of transversity distributions Spin-orbit correlations, orbital angular momentum Multi-parton correlations, QCD dynamics, Confinement

Nucleon Spin Structure Spin, Orbit Angular Momentum, Higher-Twists: quark-gluon correlations

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

Transverse Spin in Inclusive Scattering: g2 Color Polarizability (or Lorentz Force): d2 B-C Sum Rule 2nd moment of g2-g2WW d2: twist-3 matrix element

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 preliminary 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%)

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)

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

Twist-4 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

Transversity and TMDs What have we learned?

Transversity and TMDs Momentum distributions: q(x,Q2) = q↑(x) + q↓(x) 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. 15 15

Multi-dimensional Distributions GPDs/IPDs H(x,rT),E(x,rT),.. d2kT Wpu(k,rT) “Mother” Wigner distributions d2rT d2kT TMDs f1u(x,kT), .. h1u(x,kT) quark polarization d2rT PDFs f1u(x), .. h1u(x)

Pasquini, GPD2010 GTMDs GPDs TMDs GPDs and TMDs probe the same overlap of quark LCWFs in different kinematics nucleon quark at »=0 UU UT LL TU TT TT LT TL

Separation of Collins, Sivers and pretzelocity effects through angular dependence in SIDIS

Status of Transverse Spin Study Large single spin asymmetry in pp->pX Collins Asymmetries - sizable for the 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 the deuteron (COMPASS) Sivers Asymmetries - non-zero for p+ from proton (HERMES), smaller with COMPASS data? - consistent with zero for p- from proton and for all channels from deuteron - large for K+ ? Collins Fragmentation from Belle Global Fits/models by Anselmino et al., Yuan et al., Pasquini et al., Gary and collaborators,…. Very active theoretical and experimental study RHIC-spin, JLab (6 GeV and 12 GeV), Belle, FAIR, J-PARC, EIC, …

6 GeV Transversity Experiment: E06-010 Preliminary Results

E06‑010 Experiment First measurement on n (3He) Polarized 3He Target Polarized Electron Beam ~80% Polarization Fast Flipping at 30Hz PPM Level Charge Asymmetry controlled by online feed back BigBite at 30º as Electron Arm Pe = 0.7 ~ 2.2 GeV/c HRSL at 16º as Hadron Arm Ph = 2.35 GeV/c 7 PhD Thesis Students (4 graduated this year) Beam Polarimetry (Møller + Compton) Luminosity Monitor What’s new: Neutron Target Helicity Flip -> Cancel drift/cancel false asym. Beam charge feed back -> PPM level Charge Asym

JLab polarized 3He target longitudinal, transverse and vertical Luminosity=1036 (1/s) (highest in the world) High in-beam polarization ~ 65% Effective polarized neutron target 13 completed experiments 6 approved with 12 GeV (A/C) 15 uA

Performance of 3He Target High luminosity: L(n) = 1036 cm-2 s-1 Record high 65% polarization (preliminary) in beam with automatic spin flip / 20min

Preliminary Asymmetry ALT Result To leading twist: Preliminary 3He ALT - Systematic uncertainty is still under work - Projected neutron ALT stat. uncertainty : 6~10% Physics meaning If Non zero on neutron -> existence of angular momentum?

Future: 12 GeV, EIC Precision 4-d mapping

Solenoid detector for SIDIS at 11 GeV FGEMx4 LGEMx4 LS Gas Cherenkov HG Aerogel GEMx2 SH PS Z[cm] Y[cm] Yoke Coil 3He Target

4-d Mapping of Collins/Sivers Asymmetries 12 GeV With SOLID (L=1036) Both p+ and p- For one z bin (0.5-0.55) Will obtain 8 z bins (0.3-0.7) Upgraded PID for K+ and K-

Power of SOLID

EIC phase space 12 GeV: from approved SoLID SIDIS experiment Lower y cut, more overlap with 12 GeV 0.05 < y < 0.8 SoLID spectrometer at high x and low Q2 Here we show a example of the phase space we can reach. If change the s To have overlap with 12gev, 2 factors, 1.s 2. y cut. Lower y or lower s 30

EIC projection: Proton π+ (z = 0.3-0.7) 4 D mapping of the kinematics variables projection 31

Summary Spin: from longitudinal to transverse Why transverse spin and transverse structure? Complete understanding of nucleon structure, spin-orbit correlations Transverse momentum dependence - strong quark-gluon correlations Key to understanding QCD in all regions, including confinement region What have we learned? Just a beginning Non-zero Collins and Sivers asymmetries for pions and Kaons Non-favored Collins fragmentation functions as important as favored ones Model dependent extractions of transversity, Sivers and Collins functions Preliminary results from 6 GeV neutron transversity experiment First measurements of Collins ,Sivers, ALT asymmetries on the neutron Future12 GeV and EIC? Precision 4-d (x,z,PT, Q2)mapping of TMDs Ultimate coverage in kinematics, complete 4-d (x,z,PT,Q2) mapping Precision determination of tensor charge (LQCD) Lead to breakthroughs in full understanding of nucleon structure and QCD

Definitions, Indirect Evidences, Experimental Observables, Models Quark Orbital Angular Momentum Definitions, Indirect Evidences, Experimental Observables, Models

Orbital Angular Momentum “”`Spin Crisis’ -> “DS ~ 30%; DG small so far Orbital angular momentum important from indirect experimental evidences Proton Form Factor A1 at high-x N-D transition … Definitions: 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.) Ji’s sum rule -> GPDs (DVCS measurements), LQCD calculation TMDs, Pretzelocity, Worm-gears, Sivers/Boer-Mulders. Model calculations What observable directly corresponds to Lz~ bx X py Model independent relations?

Distribution in x of Orbital Angular Momentum Pasquini, GPD2010 Distribution in x of Orbital Angular Momentum Definition of Jaffe and Manohar: contribution from different partial waves TOT up down Lz=0 Lz=-1 Lz=-1 Lz=+2 Comparison between the results with the Jaffe-Manohar definition and the results with the Ji definition (total results for the sum of up and down quark contribution) Jaffe-Manohar Ji

Orbital Angular Momentum Pasquini/Yuan Orbital Angular Momentum Definition of Jaffe and Manohar: contribution from different partial waves = 0 ¢ 0.62 + (-1) ¢ 0.14 + (+1) ¢ 0.23 + (+2) ¢ 0.018 = 0.126 Definition of Ji: [BP, F. Yuan, in preparation] [scalar diquark model: M. Burkardt, PRD79, 071501 (2009)]