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Nucleon Spin Structure and Sum Rules

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Nucleon Spin Structure and Sum Rules Powered By Docstoc
					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: A1 at high x
    g2, d2 and higher-twist effects (twist-3)
     g3, f2 (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:
    A1n at high-x, d2n, g3n
    SIDIS: transversity, and …
     high luminosity and large acceptance
• Polarized 3He target
    effective polarized neutron
    highest polarized luminosity
• A solenoid with detector package
    large acceptance
Valence Quark Spin Structure

      A1 at high-x
                      JLab E99-117 A1n Results


•   First precision A1n 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, 012004 (2004)
    PRC 70, 065207 (2004)
              Polarized Quark Distributions
• Combining A1n and A1p 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 10-30 times HMS+SHMS
• Low energy particles cut off (~1.7 GeV)
• PID: Gas Cherekov + Shower Counter
• Challenge: polarized 3He target inside the solenoid
• 100 hours beam time, a precision measurement of A1n at high-x
up to ~0.8
• Can do Q2 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)
  g2, d2 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 Q2 due to asymptotic freedom


• Interaction important at low to intermediate Q2
     quantify the interaction
     1st 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)
                                     t
                          
                                m
              g (Q )  
                   2
                                    t 2
                         t 2   Q
    twist t is related to (mass dimension – spin)
    mt contains twist-t matrix elements
                 Twist-2 and Twist-3




-- twist-2: parton (quark,   -- twist-3: quark-gluon
   gluon) distributions         correlations
-- no interactions           -- one gluon
                                one additional 1/Q
                  g2: twist-3, q-g correlations
• experiments: transversely polarized target
  SLAC E155x, JLab Hall A
  g2 leading twist related to g1 by Wandzura-Wilczek relation

        g 2 ( x, Q )  g 2        ( x, Q )  g 2 ( x, Q )
                    2        WW         2             2

                                                1
                                                           dy
                  ( x, Q )   g1 ( x, Q )   g1 ( y, Q )
             WW         2                   2               2
        g2
                                             x
                                                            y
• g2 - g2WW: a clean way to access twist-3 contribution
             quantify q-g correlations
                  d2: twist-3 matrix element

• 2nd moment of g2-g2WW
  d2: twist-3 matrix element
                       1
       d 2 (Q )  3 x [ g 2 ( x, Q )  g
             2             2         2        WW
                                             2     ( x, Q 2 )]dx
                       0
                   1
                   x 2 [2 g1 ( x, Q 2 )  3g 2 ( x, Q 2 )]dx
                   0

  Provide a benchmark test of Lattice QCD
  Avoid issue of low-x extrapolation (as in the lower moments)
  Needs precision data at high-x
            g2n: JLab and world data




E97-103(Q2~1 GeV2), K. Kramer et al., PRL 95, 142002 (2005)
E99-117(Q2~3-5 GeV2), X. Zheng et al., PRC70, 065207 (2004)
                       d2n: JLab and world data

•   E99-117+SLAC (high Q2)
    E94-010 (low Q2)

•   Twist-3 matrix element


•   ChPT (low Q2)
    MAID model

•   Lattice QCD (high Q2)
    other models
                g2n/d2n with the solenoid
• Transversely polarized target
     target in front of the solenoid
• Angular range 10o-22o,
• Acceptance is ~ 10-30 times higher than SHMS+HMS
     with W2 > 4 GeV2
     Q2 = 3 GeV2, x: 0.1- 0.55
          4               0.15 – 0.6
          5               0.2 - 0.65
          6               0.3 – 0.7
 In ~100 hours, map of Q2 dependence of d2n.
 Benchmark test of Lattice QCD calculations.
              JLab 12 GeV Projection for x2g2n
   Solenoid (100 hours) (W >2 GeV)
   SHMS+HMS (500 hours) (W. Korsch)
                           d2n with JLab 12 GeV
•   Projection with Solenoid, Statistical only, will be systematic limited?
   Improved Lattice Calculation (QCDSF, hep-lat/0506017)
g3: Parity Violating Spin Structure Function
     f2: twist-4,  color polarizabilities
Color “Polarizabilities”
                   f2 and Color Polarizabilities Extraction
• JLab + world n data,                 Z. Meziani et al. PLB 93 (2004) 212001
     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
•   Color polarizabilities
    cE = 0.033+-0.029
    cB = -0.001+-0.016
        g3: Parity Violating Spin Structure Function
• f2 can be directly measured from:
              1 1 2
    f 2 (Q )   x (7 g1 ( x, Q )  12 g 2 ( x, Q )  9 g3 ( x, Q ))dx
          2                    2                 2               2

              2 0
  g3 is a parity violating spin structure function.
• Never been measured so far
• g3: unpolarized beam and polarized target

   d 
    2
         d
                
                           Z Z                  Z Z
            ~ (1  y ) gV g 3  xy (2  y ) g A g1
   dxdy dxdy
               g3 in Naïve Parton Model

• Naïve Parton Model:

        g3  2 x eq ( g A ) q (q  q)
          Z

                        q

•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 Q2 – 10-4 Q2)
•Need high luminosity and large acceptance
                  Measurement of g3n

• Rate estimation with the Solenoid detector:
  polarized 3He target in front the solenoid
  1036 neutron/s luminosity, 50% target polarization
  11 GeV beam, 10o - 22o, W > 2 GeV
  x: 0.1 - 0.65, Q2: 2 – 8 GeV2,
     <x> ~ 0.25, <Q2> ~ 4 GeV2
  rate is 3.3 KHz
  1000 hours beam, statistical precision for asymmetry
   will be 1.8x10-5.
     A significant first measurement (~ a few  ?)
Semi-inclusive Deep Inelastic Scattering

             Transversity, …
                           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)
• Some characteristics of transversity:
   • δq(x) = Δq(x) for non-relativistic quarks
   • δq and gluons do not mix → Q2-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)
Collins             Sivers                   Collins               Sivers

                 HERMES (p)




                 COMPASS (d)




                JLab 6 GeV (n)




               π-                                   π+
          The errors with approved beam time will be 33% higher.
                 Collins and Sivers Asymmetries
•    Projections with MADII
     (1200 hours)                       p-    p+

• Solenoid option:
 -- Acceptance for both e
                              Collins
    and p improved by
  ~ 1 order of magnitude
 -- Total improvement
  ~ 2 orders of magnitude

•     p+ case
    Two halves different      Sivers
    baffles

•    Simulations to be done
                          Summary

• A powerful tool for inclusive DIS study at high-x
   • Improvement of a factor of 10-30 in acceptance
   • A1n at high-x
      • Crucial input to fundamental understanding of valence
         quark picture
   • d2n
      • twist-3 matrix element: q-g correlations
      • direct comparison with Lattice QCD
   • First g3n measurement
      • Twist-4 (f2n), color polarizabilities, sea-quark spin
• Even better for semi-inclusive DIS
   • An example: transversity: 2 orders of magnitude improvement