1. Review of Polarized lepton-nucleon scattering s z =  = J q + J g =   + L q +  G + L g K. Rith, HERA-III, München, 18.12.2002

2. Spin-dependent Deep-Inelastic Lepton-Nucleon Scattering  Quarks Nucleon  1/2 ~ q + Quarks Nucleon       3/2 ~ q - Polarised:  q f (x):=q f + (x) - q f - (x)  q f =  q f (x) dx  1/2 -  3/2 g 1 Asymmetry: A 1 =  g 1 (x) :=  f z f 2  q f (x)  1/2 +  3/2 F 1 Unpolarised: q f (x):=q f + (x) + q f - (x) F 1 (x) :=  f z f 2 q f (x)

3. SU(3): 2 relations   q 3 =  u -  d = g A /g V = F + D = 1,2573 Neutron-decay   q 8 =  u +  d - 2  s = 3F - D = 0,579 ,  -decay   q 0 =  =  u +  d +  s = + 9 I 1 p,(n) (Q 2 )= [   q 3 +   q 8 ]  C NS (Q 2 ) +   C S (Q 2 ) + 2n f  G  C G (Q 2 ) - Integrals and Sum Rules I 1 := g 1 (x)dx; 18 I 1 p,(n) = 4(1)  u +1(4)  d +  s ? QCDQCD Axial Anomaly Ellis-Jaffe S.R.:  s = 0   q 8 =  I 1 p =(1/12)[  q 3 + (5/3)  q 8 ]  C(Q 2 )  0,175 (at Q 2  10 GeV 2 ) Bjorken Sum Rule: 6(I 1 p - I 1 n )   q 3 = g A /g V

4. A 1  g 1 /F 1 - Proton  g 1 p /F 1 p well known for x  10 -3  Excellent agreement between all experiments  g 1 p /F 1 p (within errors) independent of Q 2 ; Q 2 dependence of g 1 and F 1 very similar  = f(x)  Extrapolation to x  0 for Q 2 = Q 0 2 ?

5. g 1 (x)/F 1 (x) - Deuteron 

6. g 1 (x) - Proton, Deuteron

7. A 1 (x), g 1 (x) - Neutron from 3 He 3 He: good approximation for polarized n-Target, = 0 QPM 18 g 1 n (x) ~  u(x) +4  d(x) < 0 Expt.  d(x)    u(x)  p p n 3 He

8. Gluons  G Rest ? Orbital angular momenta L q, g xg 1 (x) - world data  Integrals at Q 0 2 = 2,5 GeV 2, QCD analysis of Q 2 dependence and SU(3):  =  u+  d+  s  0,20  0,04 .. ? ?

9. Q 2 - dependence of g 1 (x,Q 2 )  Q 2 - dependence in agreement with NLO QCD parameterisation  Data still insufficient for reliable QCD analysis and determination of spin-dependent gluon distribution G(x)

10. NLO QCD (MS) fit Assumptions: - Flavour symmetric spin dependent sea -  u v and  d v constraint by F and D (SU(3) symmetry) Results for Q 0 2 = 4 GeV 2 :  u v  0.73.....0.86 (  0.10)  d v  -0.40...-0.46 (  0.10)  q s  -0.04...-0.09   0.14...0.20  G  0.68...1.26 BB: Blümlein, Böttcher hep/ph 0203155 LSS: Leader et al., hep/ph 0111267 GRSV: Glück et al., hep/ph 0011215 AAC: Goto et. Al., hep/ph 0001046

11. g 2 (x) g 2 (x,Q 2 ) = - g 1 (x,Q 2 ) + g 1 (z,Q 2 ) dz/z + g 2 (x,Q 2 ) = g 2 WW (x,Q 2 ) + g 2 (x,Q 2 ) ~ ~ Quark-Gluon Correlation (Twist-3 Operator) E155x, hep-ex/0204028 Further improvement by HERMES and COMPASS very unlikely x n g 2 (x)dx =  n/(n+1) (-a n +d n ) x n g 1 (x)dx =  a n

12. A T, b 1 and b 2 - deuteron  Deuteron is spin-1 target V = P z = p + - p -,  P z   1 T = P zz = p + + p - - 2p 0, -2  P z z  +1  More structure functions Proton Deuteron F 1   z q 2 [q + + q - ]   z q 2 [q + + q - + q 0 ] F 2 2xF 1 2xF 1 g 1   z q 2 [q + - q - ]   z q 2 [q + - q - ] b 1   z q 2 [2q 0 - (q + + q - )] b 2 2xb 1  meas =  u [1 + P b VA  +  T A T ] A   g 1 /F 1 [ 1 +  T A T ] A T   b 1 /F 1

13. The HERMES polarised internal gas target

14. A T, b 1 and b 2 - deuteron  First measurement, only possible with atomic gas target Model: K. Bora, R.L. Jaffe, PRD 57 (1998) 6906

15. A T, b 1 and b 2 - deuteron  Deuteron is spin-1 target  A T  10 -2 little impact on det. of g1  b 1 d is sizeable ! and interesting by itself  related to - nuclear binding - D-state admixture - diffractive nuclear shadowing - nuclear excess pions in D - VMD + double scattering - See e.g.: - P. Hoodboy et al., N.P. B312 (89) 571 - R.L. Jaffe & A. Manohar N.P. B321 (89) 343 - X. Artru & M. Mekhfi, Z. Phys. C45 (90) 669 - N.N. Nikolaec & W. Schäfer, P.L. B398 (97) 245 - J. Edelmann et al., Z. Phys. A357 (97) 129, P.R. C57 (98) 3392 - K. Bora & R.L. Jaffe, P.R. D57 (98) 6906 -

16. Spin-dependent quark distributions from semi-inclusive asymmetries Leading hadron originates with large probability from struck quark D(z):= Fragmentation function = E - E‘ z = E h /

17. Semi-inclusive asymmetries-1 z q 2  q(x) D q h (z) A 1 h (x,z) = z q 2 q(x) D q h (z) z q 2 q(x) D q h (z)  q(x) = z q‘ 2 q‘(x) D q‘ h (z) q(x) Quark-‘Purity‘ P h q Different targets and hadrons h : Solve linear system for Q with A = (A 1,p, A 1,d, A 1,p  , A 1,d  , A 1,p K  ) A = P Q P.L. B464 (1999) 123 In leading order:

18. Semi-inclusive asymmetries from Deuteron  ,K, p asymmetries identified with RICH Hadrons Pions Kaons  Statistics sufficient for 5-parameter-fit Q = (  u(x)/u(x),  d(x)/d(x),  u(x)/u(x),  d(x)/d(x),  s(x)/s(x) )

19. Purities  Shaded bands: systematic uncertainties  Adequate degree of orthogonality : - u versus d from h + - valence versus sea from hadron charge - u versus d from h -  Kaons have about 10% sensitivity to the strange sea (Probability that observed hadron originates from quark of type f)

20. Extracted quark-polarisations  Polarisation of sea-quarks small and compatible with 0  No direct evidence for a negative polarisation of strange- quarks  Results for NLO analysis very similar !

21. Extracted spin-dependent quark distributions  u >  d ?  s < 0 ?  The HERMES data are consistent with flavour symmetry of spin-dependent sea  Data with much higher statistical accuracy urgently needed

22. Prospects for spin-dependent quark distributions  COMPASS data will extend to lower x-values  Need high statistics data from both LiD and NH 3

23. The gluon polarisation  G/G Method: Photon-Gluon-Fusion  t  h/2m q qqqq Charm-production Pairs of hadrons h + h - with high transverse momenta c c c J/  e +,  + e -,  - ptpt g ** c c c D D ** g ** ( ) g h1h1 h2h2 (Hard scale: mass of c-quark) (Hard scale: p t )

24. Gluon polarisation  G/G 3 main contributions to  *p  h + h - X : p q q q q q q V      h2h2 h1h1 h1h1 h1h1 h2h2 h2h2 ** ** ** g g QCDCVMDPGF A VDM  0.5  q/qA VDM = 0 A PGF  -  G/G ? Relative contributions: Monte Carlo simulation - PYTHIA but: applicable at HERMES energies ? 

25. Gluon polarisation  G/G Asymmetry is negative From this:  G/G = 0.41  0.18  0.08 (  G/G) G(x) dx  0,6 ..... small, COMPASS RHIC = 0.17  2006 P.R.L. 84 (2000) 2584

26. Gluon polarisation  G/G COMPASS :  N  D 0 X (  h + h - X)  A 0.04 SLAC-E161:  p  D X  A cc 0.006

27. Orbital angular momentum contributions L q,g to nucleon spin ?  =   + L z q +  G + L z g 0,10 > 0,6 ‘No one knows how to measure it‘ (R. Jaffe) one hope: Exclusive processes, Generalised parton distributions (GPDs)     pp p p ? **  ** DVCS , K,  , ,  X.Ji: J q =   + L z q = lim  dx x [H(x, ,t) + E(x, ,t)] t  0

28. Orbital angular momentum contributions L q,g ? Example: DVCS (Interference of DVCS and Bethe-Heitler) Azimuthal asymmetries: beam polarisation, beam charge, target polarisation P.R.L. 87 (2001) 182001 P.R.L. 87 (2001) 182002 Hermes CLAS

29. DVCS HERMES Recoil-Detector Expected accuracies for 2 years of data taking

30.  g 1 = - longitudinal quark spin, ,  q    5 q Transverse quark polarisation, ‘Transversity‘ h 1 Complete description of nucleon in leading order QCD: 3 distribution functions f 1 = Quark momenta,  q   q h 1 = - transverse quark spin, ,  q    5 q     Importance of h 1 measurement: coupling to gluons smaller than in longitudinal case  Q 2 evolution is weaker  QCD test  Redistribution of ang. moment. between quarks and gluons is smaller:  <  < 1  Lattice QCD:  = 0,18(10) and  = 0,56(9) h 1 is chiral odd, can only be measured in conjunction with other chiral odd distribution (pol. Drell-Yan) or fragmentation function (SIDIS)

31. P.R. D64 (2001) 097101 Transverse quark polarisation, ‘Transversity‘ h 1

32. ‘Transversity‘ h 1 - Model calculations A UL sin   S L (M/Q)  z a 2 x [h L a (x) H 1  a (z) - x h 1L  a (x) H a (z)/z +....] - S T  z a 2 x h 1 a (x) H 1  a (z) S L >> S T Collins fragmentation function  0.33 z Example:  Quark Soliton Model Efremov et al., Eur. Phys. J. C24 (2002) 407 Need measurements with transverse target polarisation

33. Azimuthal asymmetries: Collins vs Sivers effect 2 different possible sources for azimuthal asymmetry: product of chiral-odd transversity distribution h 1 (x) and chiral-odd fragmentation function H 1  (z) (Collins) product of T-odd distribution function f 1T  and familiar unpolarised fragmentation function D 1 (z) (Sivers) Longitudinally polarised target: Collins and Sivers effect indistinguishable Transversely polarised target: Collins andSivers distinguishable Lepton Targetspin Hadron lsls lhlh moment; moment

34. Prospects for h 1 measurements, HERMES & COMPASS Deuteron (LiD) COMPASS: Projection for 12 days LiD, (h 1 = g 1 ) SMC magnet L = 4.3 10 37 cm -2 per day E  = 160 GeV x x  e a 2 h 1 a (x) HERMES: Expected accuray for 2 years of data taking with transversely polarised proton target V.A. Korotkov et al., Eur. Phys. J. C18 (01) 639

35. Prospects HERMES (2002-2006): Transversaly polarised target - h 1, g 2 unpolarised high density target: DVCS - L q COMPASS (2002 - ? ): Full polarisation program, especially  G RHIC (2002 - ?) [p p  W  X, jets]:  u(x),  d(x),  u(x),  d(x),  G SLAC-E161 (2003 - ?) [  p  D X]:  G Detailed investigation of h 1 and GPDs via exclusive processes requires a new generation of polarised lepton nucleon scattering experiments with high luminosity and high resolution like ELFE, TESLA-N, EVELIN, JLAB-12GeV