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**Haiyan Gao Duke University Durham, NC, U.S.A.**

Semi-Inclusive DIS and Transverse-Momentum Dependent Parton Distribution Functions ( SoLID Collaboration June 13-14, 2012 Haiyan Gao Duke University Durham, NC, U.S.A.

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**QCD Nucleon Structure Spin as an important knob**

Strong interaction, running coupling ~1 -- QCD: the theory of strong interaction -- asymptotic freedom (2004 Nobel) perturbation calculation works at high energy -- interaction significant at intermediate energy quark-gluon correlations -- confinement interaction strong at low energy coherent hadron -- Chiral symmetry -- theoretical tools: pQCD, OPE, Lattice QCD, ChPT E Charge and magnetism (current) distribution Spin distribution Quark momentum and flavor distribution Polarizabilities Strangeness content Three-dimensional structure C. Carlson, H. Meyer, G. Orlandini, B. Pasquini, M. Schindler, L. Tiator, A.W. Thomas, H. Wittig Spin as an important knob

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**The Incomplete Nucleon: Spin Puzzle**

[X. Ji, 1997] DIS → DΣ 0.25 RHIC + DIS → Dg« 1 → Lq Orbital angular momentum of quarks and gluons is important Understanding of spin-orbit correlations (atomic hydrogen, topological insulator…..) D. de Florian et al., PRL 101 (2008)

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**Leading-Twist TMD PDFs**

Nucleon Spin Quark Spin Quark polarization Unpolarized (U) Longitudinally Polarized (L) Transversely Polarized (T) Nucleon Polarization U L T h1 = Boer-Mulders f1 = h1L = Long-Transversity Helicity g1 = ! relate g1, f1 -> collinear w/ pT dep. Say: Noval new information on structure of nucleon, spin-orbital cor and multi-parton cor. h1 = Transversity f 1T = Sivers g1T = Trans-Helicity h1T = Pretzelosity

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**Leading-Twist TMD PDFs**

Nucleon Spin Quark Spin Quark polarization Unpolarized (U) Longitudinally Polarized (L) Transversely Polarized (T) Nucleon Polarization U L T h1 = Boer-Mulders f1 = h1L = Helicity g1 = Long-Transversity ! relate g1, f1 -> collinear w/ pT dep. Say: Noval new information on structure of nucleon, spin-orbital cor and multi-parton cor. h1 = Transversity f 1T = Sivers g1T = h1T = Pretzelosity Trans-Helicity

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**TMD PDFs: nucleon structure in 3-D momentum space**

TMD PDFs: nucleon structure in 3-D momentum space! Sivers as fixed x, Q2

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**6D Dist. 3D imaging 1D Unified View of Nucleon Structure**

Wpu(x,kT,r ) Wigner distributions d3r TMD PDFs f1u(x,kT), .. h1u(x,kT) GPDs/IPDs d2kT drz d2rT dx & Fourier Transformation 3D imaging d2kT Form Factors GE(Q2), GM(Q2) PDFs f1u(x), .. h1u(x) 1D

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**Access TMDs through Hard Processes**

proton lepton antilepton Drell-Yan BNL JPARC FNAL EIC lepton pion proton SIDIS electron positron pion e–e+ to pions Partonic scattering amplitude Fragmentation amplitude Distribution amplitude

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**Access Parton Distributions through Semi-Inclusive DIS**

Unpolarized Boer-Mulders Transversity Polarized Target Sivers Pretzelosity Polarized Beam and Target SL, ST: Target Polarization; e: Beam Polarization

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**Example: Separation of Collins, Sivers and pretzelocity effects through angular dependence**

Collins frag. Func. from e+e- collisions SIDIS SSAs depend on 4-D variables (x, Q2, z and PT ) Large angular coverage and precision measurement of asymmetries in 4-D phase space is essential.

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**Transversity The third PDFs in addition to f1 and g1L**

h1T = The third PDFs in addition to f and g1L Lowest moment gives tensor charge Fundamental property, benchmark test of Lattice QCD A global fit to the HERMES p, COMPASS d and BELLE e+e- data by the Torino group, Anselmino et al., arXiv: Solid red line : transversity distribution, analysis at Q2=2.4 (GeV/c)2 Solid blue line: Soffer bound |h1T| <= (f1+g1L)/2 GRV98LO + GRSV98LO Dashed line: helicity distribution g1L, GRSV98LO Test bound violations

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Sivers Function f 1T = Correlation between nucleon spin with quark orbital angular momentum Important test for factorization Different sign with twist-3 quark-gluon corr. dis. at high PT? T-odd final state interaction -> Target SSA Recent developments in the evolution of Sivers function

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**Older fit shows possibly discrepancy?**

Latest extraction based on HERMES p, COMPASS d and p data by M. Anselmino et al., arXiv: taking into account TMD evolution show consistency between the HERMES and COMPASS data

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**Pretzlosity: h1T = Relativistic effect of quark PRD 78, 114024 (2008)**

(in models) direct measurement of OAM PRD 58, (1998) (more previous slide) Expect first non-zero Pretzelosity asymmetries

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**E06-010: neutron A(U/L)T(π+K+, π-K-)**

First neutron data in SIDIS SSA&DSA Similar Q2 as HERMES experiment Disentangle Collins/Sivers effects Electron beam: E = 5.9 GeV High luminosity L ~ 1036 cm-2s-1 40 cm transversely polarized 3He target Average beam current 12 uA (max: 15 uA as in proposal) BigBite at 30o as electron arm: Pe = 0.6 ~ 2.5 GeV/c HRSL at 16o as hadron arm: Ph = 2.35 GeV/c e Polarized 3He Target p HRSL 16o g* e’ BigBite 30o The experimental is configured as following. We have 5.9 GeV polarized electron beam incident on a 40 cm polarized 3He target. The scattered electron was detected by the BigBite spectrometer positioned 30 degrees to the beam right. And the momentum range is … The produced hardon was detected coincidently using the left high resolution spectrometer 16 degrees to the beam left. And the momentum setting is 2.35 GeV/c. This setup allowed us to measure the … asymmetries in the valence range … 17

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**Effective Polarized Neutron Target!**

3He Target ~90% ~1.5% ~8% S S’ D Effective Polarized Neutron Target! Polarized 3He ran reliably throughout the experiment, and the following three experiments. Reached 55%-60% polarization with 15 mA beam and 20 minute spin flip! A NEW RECORD!

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**Results on Neutron Sizable Collins π+ asymmetries at x=0.34?**

Sign of violation of Soffer’s inequality? Data are limited by stat. Needs more precise data! Negative Sivers π+ Asymmetry Consistent with HERMES/COMPASS Independent demonstration of negative d quark Sivers function. Model (fitting) uncertainties shown in blue band. Experimental systematic uncertainties: red band X. Qian et al, Phys. Rev. Lett. 107, (2011)

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**Double Spin Asymmetry: g1T**

Worm Gear Leading twist TMD PDFs T-even, Chiral-even Dominated by real part of interference between L=0 (S) and L=1 (P) states Imaginary part -> Sivers effect First TMDs in Pioneer Lattice calculation arXiv: [hep-lat], Europhys.Lett.88:61001,2009 arXiv: [hep-lat] , Phys.Rev.D83:094507,2011 g1T = TOT g1T (1) S-P int. P-D int. Light-Cone CQM by B. Pasquini B.P., Cazzaniga, Boffi, PRD78, 2008 g1T function is sometimes referred as the “worm-gear” function, since the spin direction for quark and nucleon are perpendicular to each other It is T-even anc Chiral-even. It is dominated by the real part of interference of quark wavefunctions that differ by one unit of quark OAM. Using a Light-cone constituent quark model, the g1T function can be explicitly decomposed to the major contribution of S-P states and a small contribution from the P-D interference. Effect resembles the g1T function has been recently studied using lattice QCD calculations. More studies are on-going And it can be probed my measuring the beam-target double spin asymmetry, A_LT and look for the cos(…) modulation Target Spin Beam Helicity e e’ π X n

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**Existing ALT Results are preliminary**

No measurement until 2002 Preliminary COMPASS results ALT on proton and deuteron Fixed beam helicity (μ beam) Low x, small predicted asymmetry Preliminary HERMES results ALT on proton New measurement needed Different target for flavor decomposition Higher precision at valence region Double spin reversal to cleanly separate ALT Proton arXiv: [hep-ex] Preliminary There is no measurement on ALT until COMPASS provided the first preliminary data on deuterons and protons using a Muon beam with fixed helicity. Very recently, HERMES collaboration also released their preliminary result on proton. A new measurement on neutron is needed for flavor decomposition, especially for the d quark We would like to focus on the valence region, where the models predict maximum signal And a double spin reversal can cleanly separate ALT from other SSA terms, including both beam-SSA and target-SSA. arXiv: [hep-ex]

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**New Observable Reveals Interesting Behaviors of Quarks**

Huang, et. al. PRL. 108, (2012) Target: polarized 3He => polarized neutron First measurement of ALT beam-target double-spin asymmetry For JLab one-page highlight. Edited by Xiaodong Jiang 02/15/2012. E06010, Hall A Neutron Transversity experiment. Semi-inclusive deep inelastic scattering on a transversely polarized neutron (3He) target. Curves from theory models: WW-type: Wandzura-Wilczek, neglects higher-twist contributions, Kotzinian (2006). LCCQM: light-cone constituent quark model, Boffi (2009), Pasquini (2008). LCQDM: light-cone quark-diquark model, Zhu and Ma (2011). Indications: A non-vanishing quark “transversal helicity” distribution, reveals alignment of quark spin transverse to neutron spin direction Quark orbital motions J. Huang et al., PRL108, (2012)

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**SoLID-Spin: SIDIS on 3He/Proton @ 11 GeV**

E : Single Spin Asymmetry on Transverse 90 days, rating A E : Single and Double Spin Asymmetry on 35 days, rating A PR : Single and Double Spin Asymmetries on Transverse Proton (conditionally approved) International collaboration with 180 Collaborators from 8 countries White paper Key of SoLID-Spin program: Large Acceptance + High Luminosity 4-D mapping of asymmetries Tensor charge, TMDs … Lattice QCD, QCD Dynamics, Models.

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**3-D neutron π+/π- Collins/Sivers Asymmetries at Q2=2.0 GeV2**

Collins/Sivers asymmetries vs. x and transverse momentum PT at different z at fixed Q2. Multi-dimensional nature. Targets: proton and neutron Detect: positive pion and negative pions! Torino 2008

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**Projected Data (E12-10-006) X. Qian et al in PRL 107, 072003**

Total 1400 bins in x, Q2, PT and z for 11/8.8 GeV beam. z ranges from 0.3 ~ 0.7, only one z and Q2 bin of 11/8.8 GeV is shown here. π+ projections are shown, similar to the π- . X. Qian et al in PRL 107,

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**Power of SOLID (example)**

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**SoLID Data Projection for ALT (Partial)**

E and E : Neutron ALT Projection of one out of 48 Q2-z bins for π- Center of points: Scale for error bars: E Data Huang, et. al. PRL 108 (2012) ! Sign ! Will be improved

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**E12-11-007 Projection/AUL (Partial)**

Projection of a single Q2-z bin for π+ Center of points: + bound Scale for error bars:

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**PAC38: Conditionally approved, update submitted to PAC39**

Proposal PR : Target Single Spin Asymmetry in SIDIS (e, eπ± ) Reaction on a Transversely Polarized Proton Target and SoLID Measure SSA in SIDIS using transversely polarized proton target Use similar detector setup as that of two approved 3He SoLID expts. Use JLab/UVa polarized NH3 target with upgraded design of the magnet Target spin-flip every two hours with average in-beam polarization of 70% Two Beam energies: 11 GeV and 8.8 GeV Polarized luminosity with 100nA current: 1035 cm-2s-1 Beamline chicane to transport beam through 5T target magnetic field (already designed for g2p expt.) NH3 target Spokespersons: K. Allada (Jlab), J. P. Chen (Jlab), Haiyan Gao (Contact), Xiaomei Li (CIAE), Z-E. Meziani (Temple) PAC38: Conditionally approved, update submitted to PAC39

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Proton 4-D Projection

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**Projected measurements in 1-D (x)**

Expected improvement of Sivers function (A. Prokudin) x Assumption: We know the kT dependence, Q2 evolution of TMDs. Also knowledge on TMFF project onto 1-D in x to illustrate the power of SoLID-3He.

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Summary Frontiers in nucleon structure go beyond collinear, 1-D picture TMDs Three-dimensional description of nucleon in momentum space Direct link with orbital motion (orbital angular momentum) Transverse motion: spin-orbit correlations, multi-parton correlations, dynamics of confinement and QCD 10% quark tensor charge from both SSA data from SoLID provides excellent test of LQCD predictions JLab 12-GeV upgrade will provide excellent opportunities to map out the 3-dimensional structure of the nucleon through TMDs and GPDs SoLID will just do that! Thanks to B. Pasquini, J. P. Chen, J. Huang, and X. Qian and others in the SoLID collaboration Supported in part by U.S. Department of Energy under contract number DE-FG02-03ER41231

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