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The Role of Higher Twists in Determining Polarized Parton Densities

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

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The Role of Higher Twists in Determining Polarized Parton Densities

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

  2. OUTLINE Peculiarity of the polarizedDIS _ To separate Dqand DqSIDIS, W production HT effects Axial(gluon) anomaly Conclusions

  3. Inclusive DIS one of the best tools to study the structure of nucleon Q2 = -q2 = 4EE`sin2(q/2) l` k` x = Q2/(2Mn) n = E – E` l k q g* DIS regime==>Q2 >> M2, n >> M N P Fi(x, Q2)gi(x, Q2) unpolarized SF polarized SF

  4. DIS Cross Section Asymmetries Measured quantities where A1,A2 are the virtual photon-nucleon asymmetries. At present, A|| is much better measured than A^ If A||and A^are measured Ifonly A||is measured - kinematic factor NB. g cannot be neglected in the SLAC, HERMESandJLab 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 parentnucleon, 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: Sz = 1/2 =1/2 DS(Q2) + DG (Q2) + Lz (Q2) DS = the parton polarizations Dqa and DG arethe first moments of the helicity densities:

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

  8. Semi-inclusive Asymmetries Fragmentation functions ef2Dqf(x,Q2)Dfh (z,Q2) In LO QCD ef2 qf(x,Q2) Dfh (z,Q2)

  9. Extra uncertainty in SIDIS Dhq(z,Q2) Progress in determining Dhq (Kretzer, Leader, Christova) well constrained now (in LO QCD) is undetermined within a factor 2 ! 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. N.B.In the unpolarized case we have never used SIDIS in order to determined PD !

  10. An important difference between the kinematic regionsof theunpolarized and polarized data sets While in the determination of the PD in the unpolarized case wecan cut the low Q2 and W2 data in order to eliminate theless known non-perturbative HT effects, it is impossible toperform such a procedure for the present data on thespin-dependent structure functions without loosing too muchinformation. HT corrections should beimportant !

  11. DATA CERN EMC - SMC - 185 exp.p. DESY HERMES - SLAC E142, E154 - E143, E155 - The data on are really the experimentalvalues of thequantity very well approximated with even wheng(h) cannot been neglected

  12. Theory In QCD target masscorrections which are calculable J. Blumlein, A.Tkabladze dynamical HT power corrections => non-perturbative effects(model dependent) In NLO pQCD polarized PD evolve in Q2 according to NLO DGLAPeqs.

  13. Factorization scheme dependence Beyond the LO approximation the PD are scheme depended! In the unpolarized case In the polarized case because of the gluonanomaly n=1 The larger DG the bigger thedifference

  14. On theoretical grounds we prefer to use the JETscheme (allhard 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 meaningfulto directly interpret DS as the contribution of thequark spins to the nucleon spin and to compare its value obtainedfrom DIS region with the predictions of the different(constituent, chiral, etc.) quark models at low .

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

  16. JLab: nucl-ex/0308011 significantimprovement of the precision of the data • LSS 2001 (Q2 = 5 GeV2) • [21] Leader,Sidorov,Stamenov, Euro Phys. J. C23, 479 (2002)

  17. Very recent (unpublished) results from the fit to the world data including the JLab and HERMES/ddata ia very good description of the HERMES/d data c2=11.0 for 18 points iPD( g1NLO+ HT) practically do NOT change !! Ch. Weiskopf 02-043 Thesis (2002)

  18. SMC;Blumlein, Bottcher (GRSV)

  19. METHOD of ANALYSIS HT to g1 included in modelindependent way R1998 (SLAC) NMC Input parton densities 8-2(SR) = 6 par. associated with PD

  20. SRfor n=1moments of PD (1) (2) The sum rule (1) reflects the isospin SU(2)symmetry, whereas the relation (2)is a consequence ofthe SU(3) flavour symmetry treatment of the hyperonb-decays. While isospin symmetry is not in doubt, there is some question about the accuracy of assuming SU(3)f symmetry in analyzing hyperon b-decays. The results of the recent KTeV experiment at Fermilab on the b-decay of X0, , however, are all consistent with exactSU(3)f symmetry. Taking intoaccount the experimental uncertainties one finds that SU(3)fbreaking is at most of order 20%.

  21. KTeV experiment Fermilab b-decay SU(3)f prediction for the form factor ratio g1/f1 Experimental result A good agreement with theexact SU(3)f symmetry ! SU(3) breaking is at most of order 20% From exp. uncertainties

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

  23. Higher twist effects

  24. LSS, hep-ph/0309048 HT corrections to g1 are better determined now, especially for the neutron target

  25. NLO polarized PD NLO(JET)

  26. n=1 moments of PD, JET scheme, Q2=1GeV2 the correlations between the parametersare takeninto account N.B. In JET schemeDS, as well as , do NOT depend on Q2. ~ 0.6 at Q2 ~ 0 in relativistic CQM Spin sum rule: 1/2 =½ 0.32 + 0.80 + Lz = 0.96 + Lz Lz is negative

  27. Extra uncertainty in SIDIS Dhq(z,Q2) Progress in determining Dhq (Kretzer, Leader, Christova) well constrained now (in LO QCD) is undetermined within a factor 2 ! New HERMES data on (hep-ex/0307064) LO QCD: <Q2 > = 2.5 GeV2 In all analyses of inclusive DIS data, it is found that Ds is negative. LO QCD: at Q2 = 4 GeV2 (Blumlein, Bottcher) Also, if Non-negative Ds would imply a total breaking of SUf(3) flavor symmetry in hyperon b-decays, which contradicts to the present data.

  28. CONCLUSIONS The fit to the present data on g1is essentiallyimproved, 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 g1data, the HT corrections tog1have to be takeninto account in the analysis.

  29. MORE GENERALLY Given the limited range and precision of present g1(x,Q2)measurements, one would like a direct measurement of DG (COMPASS, RHIC) Inclusive DIS measurements are sensitive only to thus a new probe is needed to separate quark and anti-quark polarized PDfrom SIDIS, W production (HERMES, COMPASS, RHIC) Data at largerQ2 and smallerx would be veryimportant for our understanding of the spin properties of thenucleon.

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