1. The Role of Higher Twists in Determining Polarized Parton Densities E. Leader (London), A. Sidorov (Dubna), D. Stamenov (Sofia) 10th International Workshop on HIGH ENERGY SPIN PHYSICS Dubna, September 16-20, 2003

2. OUTLINE Peculiarity of the polarized DIS To separate  q and  q SIDIS, W production Axial (gluon) anomaly _ Conclusions HT effects

3. one of the best tools to study the structure of nucleon Inclusive DIS Q 2 = -q 2 = 4EE`sin 2  l` l k` k N x = Q 2 /(2M )  P q = E – E` F i (x, Q 2 ) g i (x, Q 2 ) unpolarized SF polarized SF DIS regime ==> Q 2 >> M 2, >> M

4. DIS Cross Section Asymmetries Measured quantities where A 1, A 2 are the virtual photon-nucleon asymmetries. At present, A || is much better measured than A  If A || and A  are measured If only A || is measured - kinematic factor NB.  cannot be neglected in the SLAC, HERMES and JLab kinematic regions

5. As in the unpolarized case the main goal is: to test QCD to extract from the DIS data the polarized PD where "+" and "-" denote the helicity of the parton, along or opposite to the helicity of the parent nucleon, respectively.

6. The knowledge of the polarized PD will help us: to make predictions for other processes like polarized hadron-hadron reactions, etc. more generally, to answer the question how the helicity of the nucleon is divided up among its constituents: S z = 1/2 = 1/2  (Q 2 ) +  G (Q 2 ) + L z (Q 2 )  = the parton polarizations  q a and  G are the first moments of the helicity densities:

7. _ DIFFICULTIES, specific for the polarized case neutrino In order to extract  q (  q V ) and  q Semi-inclusive DIS data (SMC, HERMES)

8. e f 2  q f (x,Q 2 ) D f h (z,Q 2 ) e f 2 q f (x,Q 2 ) D f h (z,Q 2 ) Semi-inclusive Asymmetries Fragmentation functions In LO QCD

9. Extra uncertainty in SIDIS D h q (z,Q 2 ) Progress in determining D h q (Kretzer, Leader, Christova) well constrained now (in LO QCD) is undetermined within a factor 2 ! N.B. In the unpolarized case we have never used SIDIS in order to determined PD ! In order to extract correctly the polarized PD from SIDIS data, well determined FF are needed. Although this research is in progress, this is still NOT done at present for all FF.

10. HT corrections should be important ! An important difference between the kinematic regions of the unpolarized and polarized data sets While in the determination of the PD in the unpolarized case we can cut the low Q 2 and W 2 data in order to eliminate the less known non-perturbative HT effects, it is impossible to perform such a procedure for the present data on the spin-dependent structure functions without loosing too much information.

11. DATA CERN EMC -SMC - DESY HERMES - SLAC E142, E154 -E143, E155 - 185 exp. p. The data onare really the experimental values of the quantity very well approximated with even when  can not been neglected

12. Theory In QCD target mass corrections which are calculable J. Blumlein, A.Tkabladze In NLO pQCD dynamical HT power corrections => non-perturbative effects (model dependent) polarized PD evolve in Q 2 according to NLO DGLAP eqs.

13. Factorization scheme dependence Beyond the LO approximation the PD are scheme depended ! In the unpolarized case In the polarized case because of the gluon anomaly n=1 the bigger the difference The larger  G

14. On theoretical grounds we prefer to use the JET scheme (all hard effects are absorbed in the Wilson coefficient functions). Carlitz, Collins, Mueller (1988) Efremov, Teryaev (1989); Muller, Teryaev (1997) Anselmino, Efremov, Leader (1995) In the JET scheme (as well as in AB scheme) it is meaningful to directly interpret  as the contribution of the quark spins to the nucleon spin and to compare its value obtained from DIS region with the predictions of the different (constituent, chiral, etc.) quark models at low.

15. Connection between Theory and Experiment GRSV, LSS E.Leader, A.Sidorov, D.Stamenov [hep-ph/0212085] Eur. Phys. J. C23, 479 (2002)

16. significant improvement of the precision of the data -LSS 2001 (Q 2 = 5 GeV 2 ) [21] Leader,Sidorov,Stamenov, Euro Phys. J. C23, 479 (2002) JLab: nucl-ex/0308011

17. Very recent (unpublished) results from the fit to the world data including the JLab and HERMES/d data  a very good description of the HERMES/d data  2 =11.0 for 18 points  PD( g 1 NLO + HT) practically do NOT change !! Ch. Weiskopf 02-043 Thesis (2002)

18. SMC; Blumlein, Bottcher (GRSV)

19. METHOD of ANALYSIS Input parton densities 8-2(SR) = 6 par. associated with PD R 1998 (SLAC) NMC HT to g 1 included in model independent way

20. The sum rule (1) reflects the isospin SU(2) symmetry, whereas the relation (2) is a consequence of the SU(3) flavour symmetry treatment of the hyperon  -decays. While isospin symmetry is not in doubt, there is some question about the accuracy of assuming SU(3) f symmetry in analyzing hyperon  -decays. The results of the recent KTeV experiment at Fermilab on the  -decay of  ,  however, are all consistent with exact SU(3) f symmetry. Taking into account the experimental uncertainties one finds that SU(3) f breaking is at most of order 20%. SR for n=1 moments of PD (1) (2)

21. KTeV experiment Fermilab  -decay SU(3) f prediction for the form factor ratio g 1 /f 1 Experimental result A good agreement with the exact SU(3) f symmetry ! From exp. uncertainties SU(3) breaking is at most of order 20%

22. RESULTS OF ANALYSIS Kinematic region - 185 exp. p. Quality of the fits LSS, Phys. Rev. D67 (2003) 074017 NLO JET

23. Higher twist effects Fit LO HT=0 NLO HT=0 LO+HTNLO+HT 244.5218.8150.7145.0 DF 185-6 185-16 1.361.220.8920.858

24. HT corrections to g 1 are better determined now, especially for the neutron target LSS, hep-ph/0309048

26. NLO polarized PD NLO(JET)

27. N.B. In JET scheme  as well as, do NOT depend on Q 2. n=1 moments of PD, JET scheme, Q 2 =1 GeV 2 the correlations between the parameters are taken into account 1/2 = ½  +  + L z = 0.96 + L z L z is negative Spin sum rule: ~ 0.6 at Q 2 ~ 0 in relativistic CQM

28. Non-negative  s would imply a total breaking of SU f (3) flavor symmetry in hyperon  -decays, which contradicts to the present data. New HERMES data on (hep-ex/0307064) Extra uncertainty in SIDIS D h q (z,Q 2 ) Progress in determining D h q (Kretzer, Leader, Christova) well constrained now (in LO QCD) is undetermined within a factor 2 ! LO QCD: = 2.5 GeV 2 In all analyses of inclusive DIS data, it is found that  s is negative. LO QCD:at Q 2 = 4 GeV 2 ( Blumlein, Bottcher) Also, if

29. CONCLUSIONS The fit to the present data on g1 is essentially improved, especially in the LO case, when the higher twist terms are included in the analysis. The size of HT corrections have been extracted from the data in model independent way well consistent with To extract correctly the polarized PD from the g 1 data, the HT corrections to g 1 have to be taken into account in the analysis.

30. Inclusive DIS measurements are sensitive only to thus a new probe is needed to separate quark and anti-quark polarized PD from SIDIS, W production (HERMES, COMPASS, RHIC) Given the limited range and precision of present g 1 (x,Q 2 ) measurements, one would like a direct measurement of  G (COMPASS, RHIC) MORE GENERALLY Data at larger Q 2 and smaller x would be very important for our understanding of the spin properties of the nucleon.