1. Duality in the polarized structure functions
H.P. Blok
(Vrije Universiteit / NIKHEF)
Introduction
Experiments and results
Conclusions and outlook
Review polarized case
Intro: general remarks duality
polarized
relation GDH
Data: SLAC, Hermes, JLab
vnl. g1, beetje g2
Try to formulate conclusions from existing data, some ideas, and look forward to new data from JLab
H.P. Blok, Duality workshop, June 6, 2005

2. H.P. Blok, Duality workshop, June 6, 2005
Resonance averaged = (which) scaling ?
Relevance
theoretical: QCD structure, higher twist
experimental: higher x
Belief or hold?
p vs. n, L vs. T, s3/2 vs. s1/2 , semi-incl., excl.?
global, local?
resonance vs. background
Scaling: how account for different Q2?
include evolution
include TMC
more?
polarized: duality in A1 or in g1?
High x: local duality needed
In past sometimes:
believe in duality (yes/no)?
(vgl. EU vote)
More: where does it hold to what accuracy?
then look at different cases
contribution res. drops with Q2
Close (+Isgur, Melnitchouk)
H.P. Blok, Duality workshop, June 6, 2005

3. H.P. Blok, Duality workshop, June 6, 2005
Polarized
Lepton asymmetries measured
Deduce photon asymmetries A1 and A2
H.P. Blok, Duality workshop, June 6, 2005

4. H.P. Blok, Duality workshop, June 6, 2005
Relation to spin structure functions g1 and g2
g2 = Q2/n2 = 4M2x2/Q2
H.P. Blok, Duality workshop, June 6, 2005

5. H.P. Blok, Duality workshop, June 6, 2005
For proton: A1 ( g1) > 0 at high Q2
At low Q2 negative values in the resonance region, especialy for the D
 Duality must fail for Q2  0
(GDH sum rule < 0; Ellis-Jaffe sum rule > 0)
g2: Burkhardt-Cottingham sum rule:
H.P. Blok, Duality workshop, June 6, 2005

6. H.P. Blok, Duality workshop, June 6, 2005
High Q2 data for g1
As reminder: g1 at large Q2
Proton: positive (small at high x due to F1
Neutron: negative, but indication for positive for x>0.4
H.P. Blok, Duality workshop, June 6, 2005

7. The extended GDH sum rule
K: equivalent photon energy (n...)
At large Q2
n0, x0: pion threshold (no elastic)
IGDH depends on definition of K
For Q2  0
H.P. Blok, Duality workshop, June 6, 2005

8. H.P. Blok, Duality workshop, June 6, 2005
Global behaviour for the proton
Illustratie
Gip geplot, niet Igdh
Globaal gedrag
Later op terug
H.P. Blok, Duality workshop, June 6, 2005

9. Experiments and results
SLAC
Abe et al., PRL 78 (1997) 815
Ee = 9.7 GeV; 4.50 and 70
NH3 and ND3 targets, A//
W2 < 5 GeV2, Q2 = 0.5 and 1.2 GeV2
Abe et al., PR D58 (1998)
Ee = 16.2, 29.1 GeV (high Q2), A// and A, g2
H.P. Blok, Duality workshop, June 6, 2005

10. H.P. Blok, Duality workshop, June 6, 2005
SLAC results
0.5 GeV2
1.2 GeV2 p n d p
H.P. Blok, Duality workshop, June 6, 2005

11. H.P. Blok, Duality workshop, June 6, 2005
Hermes
Airapetian et al., PRL 90 (2003)
HERA positron beam, Ee+ = 27.6 GeV, Pe  0.55
gas cell fed by ABS (P  0.88)
Hermes spectrometer (20 – 110)
A//  A1 (using SLAC estimate for A2)
1 < W2 < 4 GeV2, Q2 = 1.2 – 12 GeV2
H.P. Blok, Duality workshop, June 6, 2005

12. H.P. Blok, Duality workshop, June 6, 2005

13. H.P. Blok, Duality workshop, June 6, 2005
Comparison of G1res/ G1DIS in same x (or ) range
 =2x / [1+(1+g2)1/2]
What to use for DIS
at low Q2?
Assume A1 for DIS independent of Q2, take F1 from exp.
Higher twist etc. included in F2 (F1)
H.P. Blok, Duality workshop, June 6, 2005

14. H.P. Blok, Duality workshop, June 6, 2005
Comparison of G1res/ G1DIS in same x range
Use PDF
Other choice: use PDF with various ‘corrections’
Bianchi, Fantoni & Liuti, PR D69 (2004)
H.P. Blok, Duality workshop, June 6, 2005

15. H.P. Blok, Duality workshop, June 6, 2005
JLab (CLAS)
Fatemi et al., PRL 91 (2003)
Ee = 2.6 and 4.3 GeV, Pe  0.70
NH3 target (P  0.70  0.40)
A//  A1 (with model for A2)
1 < W2 < 6 GeV2, Q2 = 0.15 – 1.64 GeV2
Yun et al., PR C67 (2003)
Ee = 2.5 GeV, Pe  0.72
ND3 target (P  0.10 – 0.25)
1 < W2 < 4 GeV2, Q2 = 0.27 – 1.3 GeV2
H.P. Blok, Duality workshop, June 6, 2005

16. H.P. Blok, Duality workshop, June 6, 2005
proton data
H.P. Blok, Duality workshop, June 6, 2005

17. H.P. Blok, Duality workshop, June 6, 2005
proton data
H.P. Blok, Duality workshop, June 6, 2005

18. H.P. Blok, Duality workshop, June 6, 2005
deuteron data
H.P. Blok, Duality workshop, June 6, 2005

19. H.P. Blok, Duality workshop, June 6, 2005
JLAB Hall A
Amarian et al., PRL 92 (2004)
Ee = 0.86 – 5.06 GeV; 15.50
3He target, A// and A
Q2 = 0.10 – 0.90 GeV2
Wandzura-Wilczek holds globally
Burkhardt-Cottingham (incl. elastic!) holds
 x
H.P. Blok, Duality workshop, June 6, 2005

20. H.P. Blok, Duality workshop, June 6, 2005
SLAC
Anthony et al., PhL 553B (2003) 18
g2p and g2n
mainly high Q2: 0.7 < Q2 < 20 GeV2
Wandzura-Wilczek appr. ok
Burkhardt-Cottingham for proton violated?
(low x behaviour)
H.P. Blok, Duality workshop, June 6, 2005

21. Conclusions and outlook
Duality in g1?
globally: for Q2  1.5 GeV2 ?
locally: for W  1.6 GeV ? (not D and S11)
(consequences for high x measurement?)
Better fulfilled for A1?
Look in more detail into ‘bumpology’ :
contribution resonance vs. background
W-dependence (especially D and S11 region)
(compare also with e.g. MAID)
(Much/many) more accurate data
H.P. Blok, Duality workshop, June 6, 2005

22. Outlook: more data (JLab)
Hall A (Patricia Solvignon)
Ee = 3.0 , 4.0, 5.0 GeV
1.0 < W < 2.1 GeV, Q2  1.0 – 4.0 GeV2
3He target, A// and A  A1n and g1n
Hall B (Yelena Prok)
Ee = 1.6, 2.5, 4.2, 5.7 GeV
0.8 < W < 3.0 GeV, Q2  0.05 – 4.5 GeV2
NH3 and ND3 target, A//p,d
Hall C (Mark Jones)
Ee = 5.75 GeV, 0.8 < W < 2 GeV, Q2  1.3 GeV2
NH3 and ND3 target, A//p,d and Ap,d, g1p,n and g2p,n
H.P. Blok, Duality workshop, June 6, 2005

23. H.P. Blok, Duality workshop, June 6, 2005
proton data
H.P. Blok, Duality workshop, June 6, 2005

24. The extended GDH sum rule
H.P. Blok, Duality workshop, June 6, 2005

25. H.P. Blok, Duality workshop, June 6, 2005
SLAC: Q2 dependence for different x values
H.P. Blok, Duality workshop, June 6, 2005