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Study Neutron Spin Structure with a Solenoid Jian-ping Chen, Jefferson Lab Hall A Collaboration Meeting June 22-23, 2006 Inclusive DIS: Valence quark spin structure: A 1 at high x g 2, d 2 and higher-twist effects (twist-3) g 3, f 2 (twist-4) Semi-inclusive DIS Example: transversity. Acknowledgement: E. Chudakov (simulation), X. Zheng, W. Korsch, Z. Meziani, K. Kumar, P. Souder, …

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Introduction DIS provided rich information on quark-gluon structure of the nucleon and the strong interaction (QCD) High energy: asymptotic freedom perturbative QCD calculation works, QCD well tested parton distributions functions (PDFs) extracted from DIS data quark-parton models large-x region, spin-flavor decomposition Low-to-intermediate energy: confinement quark-gluon correlations: higher twists test QCD in the strong interaction (non-perturbative) region? Semi-inclusive DIS a new window to study nucleon structure and QCD

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Unpolarized and Polarized Structure functions

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

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NLO Polarized Parton Distributions (BB)

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Neutron Spin Structure with JLab 12 GeV DIS program on neutron spin structure: A 1 n at high-x, d 2 n, g 3 n SIDIS: transversity, and … high luminosity and large acceptance Polarized 3 He target effective polarized neutron highest polarized luminosity A solenoid with detector package large acceptance

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Valence Quark Spin Structure A 1 at high-x

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JLab E A 1 n Results First precision A 1 n data at x > 0.3 Comparison with model calculations SU(6) symmetry Valence quark models pQCD (with HHC) predictions Other models: Statistical model, Chiral Soliton model, PDF fits, … Crucial input for pQCD fit to PDF PRL 92, (2004) PRC 70, (2004)

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Polarized Quark Distributions Combining A 1 n and A 1 p 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 x high enough?

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Solenoid Option with 11 GeV beam Acceptance times HMS+SHMS Low energy particles cut off (~1.7 GeV) PID: Gas Cherekov + Shower Counter Challenge: polarized 3 He target inside the solenoid 100 hours beam time, a precision measurement of A 1 n at high-x up to ~0.8 Can do Q 2 study for high-x up to 0.75 Definitive measurements to shed lights on valence quark picture

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Solenoid, 200 hours HMS+SHMS, 1800 hours (X. Zheng)

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g 2, d 2 and higher-twist twist-3: quark-gluon correlations

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Nucleon Structure Beyond Simple Parton Models Naïve quark-parton models no interactions between quarks reasonable at high Q 2 due to asymptotic freedom Interaction important at low to intermediate Q 2 quantify the interaction 1 st step beyond parton distributions: quark-gluon correlations how to measure q-g correlations?

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Operator Product Expansion In QCD framework: Operator Product Expansion 1/Q expansion (twist expansion) twist is related to (mass dimension – spin) contains twist- matrix elements

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Twist-2 and Twist-3 -- twist-2: parton (quark, gluon) distributions -- no interactions -- twist-3: quark-gluon correlations -- one gluon one additional 1/Q

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g 2 : twist-3, q-g correlations experiments: transversely polarized target SLAC E155x, JLab Hall A 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

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d 2 : twist-3 matrix element 2 nd moment of g 2 -g 2 WW d 2 : twist-3 matrix element Provide a benchmark test of Lattice QCD Avoid issue of low-x extrapolation (as in the lower moments) Needs precision data at high-x

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E97-103(Q 2 ~1 GeV 2 ), K. Kramer et al., PRL 95, (2005) E99-117(Q 2 ~3-5 GeV 2 ), X. Zheng et al., PRC70, (2004) g 2 n : JLab and world data

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d 2 n : JLab and world data E SLAC (high Q 2 ) E (low Q 2 ) Twist-3 matrix element ChPT (low Q 2 ) MAID model Lattice QCD (high Q 2 ) other models

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g 2 n /d 2 n with the solenoid Transversely polarized target target in front of the solenoid Angular range 10 o -22 o, Acceptance is ~ times higher than SHMS+HMS with W 2 > 4 GeV 2 Q 2 = 3 GeV 2, x: – – 0.7 In ~100 hours, map of Q 2 dependence of d 2 n. Benchmark test of Lattice QCD calculations.

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JLab 12 GeV Projection for x 2 g 2 n Solenoid (100 hours) (W >2 GeV) SHMS+HMS (500 hours) (W. Korsch)

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d 2 n with JLab 12 GeV Projection with Solenoid, Statistical only, will be systematic limited? Improved Lattice Calculation (QCDSF, hep-lat/ )

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g 3 : Parity Violating Spin Structure Function f 2 : twist-4, color polarizabilities

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Color Polarizabilities

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f 2 and Color Polarizabilities Extraction JLab + world n data, 4 = ( )M 2 Twist-4 term 4 = (a 2 +4d 2 +4f 2 )M 2 /9 extracted from 4 term f 2 = Color polarizabilities = B = Z. Meziani et al. PLB 93 (2004)

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g 3 : Parity Violating Spin Structure Function f 2 can be directly measured from: g 3 is a parity violating spin structure function. Never been measured so far g 3 : unpolarized beam and polarized target

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g 3 in Naïve Parton Model Naïve Parton Model: Provide a clean way to measure sea-quark spin Asymmetry expected to be at the same level as the other DIS parity asymmetry (~10 -5 Q 2 – Q 2 ) Need high luminosity and large acceptance

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Measurement of g 3 n Rate estimation with the Solenoid detector: polarized 3 He target in front the solenoid neutron/s luminosity, 50% target polarization 11 GeV beam, 10 o - 22 o, W > 2 GeV x: , Q 2 : 2 – 8 GeV 2, ~ 0.25, ~ 4 GeV 2 rate is 3.3 KHz 1000 hours beam, statistical precision for asymmetry will be 1.8x A significant first measurement (~ a few )

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Semi-inclusive Deep Inelastic Scattering Transversity, …

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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) Some characteristics of transversity: δq(x) = Δq(x) for non-relativistic quarks δq and gluons do not mix Q 2 -evolution different Chiral-odd not accessible in inclusive DIS It takes two chiral-odd objects to measure transversity Semi-inclusive DIS Chiral-odd distributions function (transversity) Chiral-odd fragmentation function (Collins function)

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JLab 6 GeV Projections (n) and World Data (p, d) π- π+ The errors with approved beam time will be 33% higher. COMPASS (d) HERMES (p) JLab 6 GeV (n) Collins Sivers

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Collins and Sivers Asymmetries Projections with MADII (1200 hours) Solenoid option: -- Acceptance for both e and improved by ~ 1 order of magnitude -- Total improvement ~ 2 orders of magnitude + case Two halves different baffles Simulations to be done - + Collins Sivers

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Summary A powerful tool for inclusive DIS study at high-x Improvement of a factor of in acceptance A 1 n at high-x Crucial input to fundamental understanding of valence quark picture d 2 n twist-3 matrix element: q-g correlations direct comparison with Lattice QCD First g 3 n measurement Twist-4 (f 2 n ), color polarizabilities, sea-quark spin Even better for semi-inclusive DIS An example: transversity: 2 orders of magnitude improvement

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