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A.Nagaytsev Joint Institute for Nuclear Research, Dubna

The Q 2 Dependence of the Generalized GDH Integrals for the Deuteron, Proton and Neutron and Evidence for Quark-Hadron Duality in the Proton Spin Asymmetry A 1. A.Nagaytsev Joint Institute for Nuclear Research, Dubna for the collaboration

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A.Nagaytsev Joint Institute for Nuclear Research, Dubna

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  1. The Q2 Dependence of the Generalized GDH Integrals for the Deuteron, Proton and Neutron and Evidence for Quark-Hadron Duality in the Proton Spin Asymmetry A1 A.Nagaytsev Joint Institute for Nuclear Research, Dubna for the collaboration 1. Motivation: The GDH Sum Rule 2. Extraction of Spin Asymmetry and GDH Integrals 3. The Results on Q2 dependence of the GDH Integrals for proton, deuteron and neutron 4. Motivation: Quark-Hadron Duality in Spin Asymmetry A1 5. The Results on Quark-Hadron Duality 6. Conclusions

  2. Motivation: The GDH Sum Rule The GDH Sum Rule: The generalization of the GDH Integral In leading twist Examining the generalized GDH integrals provides a way to study the transition from real-photon absorption (Q2=0) on the nucleon to polarized DIS

  3. Extraction of Spin Asymmetry and GDH Integrals • Data taken in 1997-2000 with hydrogen (1.5 M) and deuterium (8.3 M) targets, <PB >=0.55 <PT >=0.85 • Three regions on W2 : • The Spin Asymmetry

  4. Extraction of Spin Asymmetry and GDH Integrals The GDH Integral with extracted spin asymmetry DIS region : F2 - NMC P15 fit, R - SLAC fit (R1990), Resonance region: F2 – modified Bodek fit, R=0.18 (PR D8 (1973) 2332), The unmeasured region (W2 > 45 GeV2 ) : N.Bianchi, E.Thomas, PL B450 (1999), 439 The GDH Integral for neutron: C.Ciofi degli Atti et al., nucl-th/9602026

  5. Q2 Dependence of the GDH Integral for Proton, Deuteron and Neutron The generalized GDH Integrals for proton, deuteron and neutron as function of Q2 : resonance region(triangles), DIS region (squares) and full W2 region (circles). J.Soffer and O.Teryaev PR D51 (1995) 25; PRL 70 (1993) 3373. ---- I.G.Aznauryan Phys. of At. Nucl. 58 (1995) 1014 and private commun.

  6. The comparison with Soffer-Teryaev model and data from other experiments • Data are in well agreement a prediction of Soffer-Teryaev model. • The data agree with the first moments of SF g1 measured in SLAC and TJNAF experiments

  7. The generalized GDH integrals after the leading twist • The Q2 – dependence of the generalized GDH integrals after the leading twist dependence , has been divided out. • The data consistent with the expectation that the 1/ Q2 is a good approximation down to Q2 ~ 2 GeV2 .

  8. The generalized GDH Integral for the proton-neutron difference • The dashed curve: 1/ Q2 fit to the data. The dotted curve: Soffer-Teryaev prediction. The open square: E143 data The open circle : E155 data • The data fall out as 1/ Q2 indicating that leading twist dominates. • From fit is in agreement with Bjorken Sum Rule prediction • The data on are in agreement with results from E143 and E155 on

  9. Motivation: Quark-Hadron Duality in Spin Asymmetry A1 • Duality is the relation between DIS and Resonance region E.D. Bloom and F.J. Gilman PRL 25 (1970) 1140 ; PR D4 (1971) 2901 • Duality in unpolarized DIS: Q2 dependence of the ratio of the F2(Reson)/F2(DIS) • Dualityfor the spin asymmetry A1 : spin structure of nucleon at large x

  10. Duality in Spin Asymmetry A1 • Asymmetry A1 measured in Resonance region is in agreement with DIS data on A1 Fit done by A1=x0.7 taken from A.P.Nagaitsev et al., JINR Rapid Commun. N3(71)-1995, 59 • A1 is increasing at large x and does not exceed the SU(6) prediction of 5/9

  11. Ratio of R=G1(Res)/G1(DIS) • Data were divided into three bins in Q2 : 1.2 – 2.4 – 4.0 – 12.0 GeV2 • Ratio of the first moments of g1 = A1 F1 in DIS and resonance regions • R is independent of Q2 for measured Q2 range

  12. Conclusions • The generalized GDH integrals for proton, deuteron and neutron are measured for the first time in both the resonance and DIS regions for the Q2 range from 1.2 to 12 GeV2 . • Above Q2 = 3 GeV2 the DIS contributions to the generalized GDH integrals are dominant for all targets. • Data show no indication for large non-leading twist effects. • Data on GDH proton-neutron difference yields good agreement with Bjorken sum rule prediction • The duality in polarized DIS was measured for the first time by HERMES. • Spin asymmetry A1 in resonance region is in agreement with DIS data at higher Q2 and W2 and same x. A1 is increasing at large x and does not exceed the SU(6) prediction of 5/9. • The duality ratio R=G1(Res)/ G1(DIS) is independent of Q2 in measured range.

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