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, …

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

Unpolarized and Polarized Structure functions

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

NLO Polarized Parton Distributions (BB)

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

Valence Quark Spin Structure A 1 at high-x

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)

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?

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

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

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

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?

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

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

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

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

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

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

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.

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

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

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

Color Polarizabilities

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)

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

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

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 )

Semi-inclusive Deep Inelastic Scattering Transversity, …

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)

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

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

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