# Presentation: 528577

## Spin Structure of the Nucleon

- J. P. Chen, Jefferson Lab
- Hirschegg Workshop, January 11-17, 2004

-  Introduction
-  Spin asymmetry at high x  valence quark spin distributions
-  Sum rules, moments and  polarizabilities
-  Higher twist effects, quark-gluon correlations
-  Quark-hadron duality
-  SSA  in semi-inclusive: transversity
-  Summary

##  Parton Distributions

- After 40 years DIS experiments, unpolarized structure of the nucleon reasonably well understood.
- High x  valence quark dominating

## What we’ve learned (before JLab)
Total quark contribution to nucleon spin:  20-30%
Gluon contribution is probably large 
Quark orbital angular momentum is important
Bjorken Sum Rule verified to ~5%
Ellis-Jaffe Sum Rule violated
First dedicated g2 experiment (SLAC E155x): higher twist?

What to be learn
Gluon contribution (HERMES, COMPASS, RHIC-Spin, SLAC) 
g1 at very low x (RHIC-Spin, future ELIC)
Precision measurement of  A1 at high x 
Precision measurement of g2 (higher twists)
(Generalized) GDH Sum Rule, moments of g1 and g2, polarizabilities
Quark-hadron duality in g1 and A1

Extend to semi-inclusive and exclusive
Spin-flavor decomposition 
Transversity
Quark orbital angular momentum

- Total quark contribution to nucleon spin:  20-30%
- Gluon contribution is probably large
- Quark orbital angular momentum is important
- Bjorken Sum Rule verified to ~5%
- Ellis-Jaffe Sum Rule violated
- First dedicated g2 experiment (SLAC E155x): higher twist?
- What to be learn
- Gluon contribution (HERMES, COMPASS, RHIC-Spin, SLAC)
- g1 at very low x (RHIC-Spin, future ELIC)
- Precision measurement of  A1 at high x
- Precision measurement of g2 (higher twists)
- (Generalized) GDH Sum Rule, moments of g1 and g2, polarizabilities
- Quark-hadron duality in g1 and A1
- Extend to semi-inclusive and exclusive
- Spin-flavor decomposition
- Transversity
- Quark orbital angular momentum

**Status of Spin Structure Study**

## Overview of Spin Structure Experiments  

- High Q2, DIS: SLAC, CERN, HERMES, RHIC-Spin
- <Q2> above 1 GeV2, polarized p, d and 3He
- Real Photon:
- Mainz/Bonn, JLab, LEGS, GRAAL, TUNL, SPRING-8
- Low-Intermediate Q2:
- JLab Hall A:  neutron with polarized 3He
-  A1n at high x, valence quark spin structure, Q2 range 3-5 GeV2
-  GDH*,  Q2 range 0.02 - 1 GeV2
-            g2 at x~0.2, Q2 from 0.5-1.5 GeV2, higher twist
-            Spin Duality: Q2 from 1-4 GeV2
- JLab Hall B:  proton and deuteron, Q2 range 0.2-2 GeV2
- JLab Hall C:  proton and deuteron, <Q2> ~ 1.3 GeV2
- Semi-inclusive: HERMES, JLab

## Valence Quark Spin Structure 

- A1 at high x

**Predictions for large x****Bj**

| Nucleon Model | F2n/F2p | d/u | u/u | d/d | A1n | A1p |
| --- | --- | --- | --- | --- | --- | --- |
| SU(6) | 2/3 | 1/2 | 2/3 | -1/3 | 0 | 5/9 |
| Valence Quark | 1/4 | 0 | 1 | -1/3 | 1 | 1 |
| pQCD | 3/7 | 1/5 | 1 | 1 | 1 | 1 |

- Proton Wavefunction (Spin and Flavor Symmetric)

## World Data on A1n and Models

- SU(6): A1n=0
- Valence quark models
- pQCD assuming HHC
- (hadron helicity conservation)
- PDF fits (LSS)
- Statistical model
- Chiral Soliton model
- Local duality model
- Cloudy bag model
-  Need precision data at high x

**JLab E99-117**** ****Precision Measurement of A****1****n ****at Large x****Spokespersons: J. P. Chen, Z. -E. Meziani, P. Souder, PhD Student: X. Zheng**

- First precision A1n data at high x
- Extracting valence quark spin distributions
- Test our fundamental understanding of valence quark picture
- SU(6) symmetry
- Valence quark models
- pQCD (with HHC) predictions
- Other models
- Quark orbital angular momentum
- Crucial input for pQCD fit to PDF

## JLab Hall A

## JLab Polarized 3He Target

## 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
- Crucial input for pQCD fit to PDF
- PRL 92, 012004 (2004)

## A2n results

- Obtained as a by-product
- Precision as good as the world best results

## Precision g1n and g2n results

## Pion Asymmetry

- Another by-product Inclusive pion asymmetry
- Dominated by photon production
- Awaiting theoretical calculations
-    (J. M. Laget, ...)

## 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 or pQCD PDF fits

## Discussion

- First precision data of A1n and g1n at high x (up to 0.6)
- A1n positive above x=0.5
- Extracted u/u and d/d
- d/d stays negative!
- Provide important input for pQCD fit to spin PDF
- Consistent with pQCD fit of spin PDF to previous data
- Consistent with SU(6) breaking valence quark models
- Disagree with leading order pQCD model
- Hadron Helicity conservation assumption in question
- Quark orbital angular momentum important
- The results published in PRL 92, 012004 (2004), and also in the news:
-         AIP Physics News Update
-          Science online (Science Now)
- 	   Science News

## A1n with 12 GeV Upgrade

- One of the flagship experiments:
- complete a chapter on the valence quark structure

- use 3He target and 15 A beam
- use a new medium (wide) acceptance spectrometer for e detection

## Generalized GDH Sum Rule

- Moments and Polarizabilities

## Gerasimov-Drell-Hearn Sum Rule

- A fundamental relation between the nucleon spin structure and its anomalous magnetic moment
- Based on general physics principles
-  Lorentz invariance, gauge invariance, unitarity
-  unsubtracted dispersion relation applied to forward Compton amplitude
- First measurement on proton up to 800 MeV (Mainz) and up to 3 GeV (Bonn)
- Results agree with sum rule with assumptions for higher energy contributions
- Next: Mainz, GRAAL, SPring-8, LEGS, HIGS, JLab, SLAC
- The neutron

## Generalized GDH Sum Rule

- Dispersion relations on Virtual Compton Scattering lead to Generalized GDH sum rule valid at all Q2 (Ji and Osborne)
- Q2-evolution of GDH Sum Rule provides a bridge linking strong QCD to pQCD
- Bjorken and GDH sum rules are two limiting cases
- Operator Product Expansion of higher twists: > 1 GeV2
- Chiral Perturbation Theory: < 0.1 GeV2
- Intermediate region: Lattice QCD calculations

## Why is IGDH(Q2) interesting?

## JLab E94-010Measurement of Neutron (3He) Spin Structure Function at Low Q2, a Connection between Bjorken and GDH Sum Rules Spokespersons: G. Cates, J. P. Chen, Z.-E. Meziani  PhD Students: A. Deur, P. Djawotho, S. Jensen, I. Kominis K. Slifer

- Investigate Q2 evolution of Spin Structure Functions
- Investigate Q2 evolution of GDH and Bjorken sum rules
- Study GDH integral over transition from perturbative regime to non-perturbative regime
- First results (GDH) published in PRL89,242301 (2002)
- Second results (moments) accepted for publication in PRL

## Hall A g13He and g23He       

- First JLab experiment using polarized 3He target to study neutron spin structure functions
- Parallel and perpendicular asymmetries and cross section measurements  precision g1 and g2
- g2 ~ -g1 in the  resonance region
-     (i.e. LT ~ 0)

## First Moment of g1n

- High precision data
- Resonance contributions to the first moment significant
- Smooth transition
- Test fundamental understanding
-        ChPT at low Q2
-        Twist expansion at high Q2
-        Models
-        Future Lattice QCD

## Moments of  g1p-g1n

**Moments of  g****1****p****-g****1****n**

- 1p - 1n

- Bjorken Sum Rule
- (Verification of QCD)

- Hall B  results of moment 1p
- Resonance significant contribution
- Zero crossing

- Combine Hall A g1n
- with Hall B g1p data

- Chiral Perturbation
- Theory (PT)

## Moments of g2n

- First moment:
-         Burkhardt-Cottingham sum rule
- Same assumptions as GDH, with
-       super-convergence
- Elastic and high energy contributions
- B-C sum rule satisfied within uncertainties

- Second moment d2
-        Twist-3 matrix element
- Color polarizabilities
- ChPT (low Q2), MAID model and Lattice QCD (high Q2)
- Need intermediate Q2 data

## Forward Spin Polarizabilities

- ChPT expected to work at low Q2 (up to 0.1-0.2 GeV2?)
- 0 sensitive to resonance
- 		LT insensitive to  resonance
- Comparison with two group’s ChPT calculations
- Good agreement with MAID model predictions

## Forward Spin Polarizabilities

- Expected to scale at high Q2
- Reasonable agreement with MAID model pedictions

## JLab E97-110GDH Sum Rule and Spin Structure of 3He and Neutron with Nearly Real Photons Spokespersons: J. P. Chen, A. Deur, F. Garibaldi;  PhD Students: J. Singh, V. Sulkosky, J. Yuan

- Measured generalized GDH at Q2 near zero for 3He and neutron
-       Slope of GDH sum rule at Q2 ~ 0
-        Check ChPT
-        Extrapolation to real photon point
-        Constraints on resonance models
- Overlap with previous Hall A GDH experiment E94-010 (PRL89, 242301 (2002))
- Data acquisition completed
- Analysis underway

## Higher Twists: 

- Quark-gluon Correlations*** ***

- Quark-hadron Duality
- Transversity

## Quark-Gluon Correlations

- In simple partonic picture g2(x)=0
- Wandzura and Wilczek have shown that g2 can be written in two parts:
- twist-2 contributions given by g1
- the other originating from quark-gluon correlations (twist-3)

## Jefferson Lab Hall A Experiment E97-103

- Precision Measurement of the Neutron Spin Structure Function g2n(x,Q2):
- A Search for Higher Twist Effects

- T. Averett, W. Korsch (spokespersons)    K. Kramer (Ph.D. student)

-  Inclusive DIS of polarized electrons from a polarized 3He target.
-  Precision g2n data covering 0.57 < *Q**2 *< 1.34 GeV2 at *x* ~ 0.2.
-  Direct comparison to *twist-2* g2wwprediction using world g1n data.
-  Quantitative measurement of higher twist effects provides information on
-   nucleon structure beyond simple parton model (e.g. quark-gluon correlations.

## Jefferson Lab E97-103

- Preliminary Results

-  Measured g1n agree with NLO fit
-   to world data, evolved to our Q2.
-  Measured g2n consistently higher
-   than g2ww at low Q2.
-  E97-103 improved precision of g2n
-   by an order of magnitude.

##  Measured g1n and A1n  in the resonance region  for  1.0 < Q2 < 4.0  GeV2

**JLab E01-012**
**Measurement of neutron (****3****He) spin structure functions in the resonance region**
**Spokespersons: J. P. Chen, S. Choi, N. Liyanage;   PhD student: P. Solvignon**
*** ***Measured g1n and A1n  in the resonance region  for  1.0 < Q2 < 4.0  GeV2
-  Combined with DIS measurements:
- provide a first test of spin-flavor dependence of quark-hadron duality
- Quark-hadron duality: scaling curve seen at high Q2 is an accurate average over the resonance bumps at lower Q2  (observed for F2p)
- g1n at Q2 ~ 1 GeV2 from E94-010 shows hints of duality
- If  duality  established
-   Powerful tool to study very high ***x*** behavior

## Hint from E94-010 data: approaching duality 

- E94-010 resonance g1 data, Q2 from 0.58 to 0.9 GeV2
- Comparing with SLAC DIS g1 data, Q2 = 5 GeV2
- First hint of approaching quark-hadron duality

## E01-012: Projected results

**E01-012: Projected results**

-  **Projected results shown here (black triangles), compared to published resonance data (blue squares) and DIS data (red circles), are from one of the four kinematic settings of the experiment. **

** ****Data taken early 2003**
** ****Data analysis in progress**
** ****Preliminary results expected this Spring.**

## JLab E03-004Neutron Transversity through 3He(e,e’)Spokespersons:J.-P. Chen, X. Jiang, J.-C. Peng

- Transverse target single spin asymmetry
-  n(e,e’)X
- First transversity measurement on neutron
- high polarized luminosity
- x: 0.19-0.34, Q2: 1.8-2.7 GeV2,
-      W: 2.5-2.9 GeV
- separation of Collins and Sivers effects
- complementary to the proton data of HERNES run-II

## Summary

- JLab precision spin structure data
- A1 at high x: valence quark spin distributions
- A1n went to positive above x=0.5  SU(6) breaking,
- d/d stays negative  quark orbital angular momentum
- GDH* sum rule, moments, polarizabilities
- Bridge linking strong QCD to pQCD
- ChPT, OPE twist expansion, and Lattice QCD
- Higher twister: q-g correlations
- Quark-hadron duality
- Transversity
- Outlook: even more exciting
- Near term: several experiments planned
- Long term: 12 GeV upgrade (Friday 1/16 talk by J. P. Chen)