1

The QThe Q2 2 Dependence of the Generalized GDH Integrals for the Dependence of the Generalized GDH Integrals for the Deuteron, Proton and Neutron and Evidence for Quark-Hadron Deuteron, Proton and Neutron and Evidence for Quark-Hadron

Duality in the Proton Spin Asymmetry ADuality in the Proton Spin Asymmetry A11

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

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

0

22

1/ 2 3 / 2 22( ) ( )GDH

dI kM

Motivation: The GDH Sum Rule

204 ( 1.79)

233 ( 1.91) 0.65 ( 0.143)

PGDH P

N DGDH N GDH D

I b k

I b k I b k

0 2 2 222 1 2

20

( , ) ( , )8( )

1

x

GDH

g x Q g x Q dxI Q

M x

2

12 22

1 12 20

16 16( ) ( )GDHI Q g x dx

Q Q

3

Extraction of Spin Asymmetry and GDH Integrals

//1 2 //

P P

A N L N LA A A

D N L N L

2 2

2 2

2 2

(1.0 < W < 4.2) GeV - resonance region

(4.2 < W < 45 ) GeV - DIS region

(45 < W ) GeV - extrapolation

Data taken in 1997-2000 with hydrogen (1.5 M)Data taken in 1997-2000 with hydrogen (1.5 M) and deuterium (8.3 M) targets,and deuterium (8.3 M) targets, <P<PB B >=0.55 <P>=0.55 <PT T >=0.85 >=0.85

Three regions on W2 :

The Spin AsymmetryThe 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

022 1 1

20

8( )

1

x

GDH

AF dxI Q

M x

2

1 2(1 ) /(2 (1 ))F F x R

( ) 22 0.5(0.05) /p dA xM Q

( )2 0.06(0.0)p dA

1 1.5

dn pGDHGDH GDH

d

II I

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 gg1 1 measured in SLAC and TJNAFmeasured in SLAC and TJNAF

experimentsexperiments

7

The generalized GDH integrals after the leading twist

The QThe Q2 2 – dependence of the generalized – dependence of the generalized GDH integrals after the leading twistGDH integrals after the leading twist dependence , has been dependence , has been divided out.divided out.

The data consistent with the expectation that the 1/ QQ2 2 is a good approximation is a good approximation down to Qdown to Q2 2 ~ 2 GeV ~ 2 GeV2 2 ..

2 2/(16 )Q

8

The generalized GDH Integral for the proton-neutron difference

The dashed curve: 1/ QThe dashed curve: 1/ Q2 2 fit to the data. fit to the data. The dotted curve: Soffer-TeryaevThe dotted curve: Soffer-Teryaev prediction.prediction. The open square: E143 data The open square: E143 data The open circle : E155 data The open circle : E155 data

The data fall out as 1/ Q1/ Q2 2 indicating thatindicating that leading twist dominates.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

14.3 0.9 1.3 Bp nGDH GDHI I

16.3 0.5 Bp nGDH GDHI I

1 1p n

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)

Duality for the spin asymmetry A1 : spin structure of nucleon at large x

max max

min min

2 Re 22 2( ) ( ) ( ) ( )

x xs DIS

x x

I Q F x dx S Q F x dx

2R=I/S independent of Q Duality test

max max

min min

2 Re 21 1( ) ( ) ( ) ( )

x xs DIS

x x

I Q g x dx S Q g x dx

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

Re1 1/ 1.11 0.16(stat.) 0.18(syst.)s DISA A

11

Ratio of RResDIS)

Data were divided into three bins in QData were divided into three bins in Q22 : : 1.2 – 2.4 – 4.0 – 12.0 GeV1.2 – 2.4 – 4.0 – 12.0 GeV2 2

Ratio of the first moments of gRatio of the first moments of g11 = A = A11 F F11 in in

DIS and resonance regionsDIS and resonance regions

R is independent of QR is independent of Q2 2 for measured Q for measured Q2 2

rangerange

max

min

max

min

Re 2 Re1 1

21 1

( ) ( )

( ) ( )

xs s

x

xDIS DIS

x

Q g x dx

Q g x dx

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=Res)/ DIS) is independent of Q2 in measured range.