1

Resonance Spin Structure

Jefferson Lab RSS Collaboration

Spokespersons: Oscar Rondon (University of Virginia) and Mark Jones (Jefferson Laboratory)

Spokespersons: Oscar Rondon(UVa), Mark Jones(JLab)

Analysis: Paul Mckee, Karl Slifer, S. Tajima, Frank Wesselmann, Hongguo Zhu, (Peter Bosted, Eric Christy)

1

Physics:

! Measure proton and deuteron spin asymmetries A1 (W, Q!) and A

2(W, Q!)

at momentum transfer Q! ! 1.3 GeV! and invariant mass 0.8 " W " 2 GeV.

! Study W dependence, onset of polarized local duality, twist-3 effects.

! Extract asymmetries from inclusive polarized electron scattering on

polarized nuclei.

Precision Measurement of the Nucleon Spin Structure Functions in the

Region of the Nucleon Resonances

U. Basel, Florida International U., Hampton U., U. Massachusetts, U. Maryland,

Mississippi S. U., North Carolina A&T U., U. of N. C. at Wilmington, Norfolk S. U.,

Old Dominion U., S.U. New Orleans, U. of Tel-Aviv, TJNAF, U. of Virginia,

Virginia P. I. & S.U., Yerevan Physics I.

Spokesmen: Oscar A. Rondon (UVA) and Mark K. Jones (JLab)

JLab E-01-006 Resonances Spin Structure (RSS)Shigeyuki Tajima (UVa)

Hall C January Meeting on Jan.25, 2007

2

The physics goals

• Measure proton and deuteron spin asymmetries

A1(W, Q2) and A2(W, Q2) in the nucleon resonance region

(1.1<W<1.9 GeV) at four-momentum transfer squared

Q2 ~1.3 (GeV/c)2. => Study W dependence.

• Extract polarized structure functions g1 and g2 and study:

i. Polarized local dualityii. Twist-3 effects from moments of g1 and g2

• Extract Neutron spin structure functions from the proton

and deuteron data.

• Calculate GDH Sum rules, Quark polarizations

W (GeV)

Q2 (

GeV

2)

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2

3

RSS Experiment in Hall C at JLab

• High Momentum Spectrometer (HMS) detects scattered electrons. Momentum settings: 4.7 , 4.1 GeV/c

• <Q2> =1.3 GeV2 , 0.8<W<2.0 GeV. W: Elastic+Resonance regions.

• I ~ 100nA for NH3 and ND3

• Beam Polarization (PB) by Moller:PB = 65.5 ± 2.6 (%) for B||

PB = 70.9 ± 1.7 (%) for B⊥

• Beam charge asym. < 0.1%

HMS

W(GeV)0.6 2.0

Q2 (G

eV2)

0.8

2.0

•Dynamic Nuclear polarization

driven by microwave

•4He evaporation refrigerator

•5T polarizing field on target.

•NMR system for polarization

measurement

•Polarization can be flipped by

180o. Ran ± for equal times

•Average target polarization

PT =68 % (NH3); 18 % (ND3)

•Relative systematic error ~2.9%

Polarized Targets (15NH3 and 15ND3)

4

5

Proton Elastic Asymmetry

• The product PB!PT extracted from A||

• Ratio of the Proton EM Form Factors, GE/GM at

Q2=1.5(GeV/c)

2, measured from A⊥ (results published)

Ael =K1 cos !! + K2

GE

GMsin !! cos "!

G2

E/G2

M+ #/$

Sensitivity || ⊥

0.02 ~1.0!Ael/Ael

!GE

GM/ GE

GM

!!,"! = polar and azimuthal angles

between !q and target spin

K1,K2 = kinematic factors

RSS

PROTON GE/GM FROM BEAM-TARGET ASYMMETRY PHYSICAL REVIEW C 74, 035201 (2006)

TABLE I. Relative systematic errors on r = GE/GM .

Variable Error !r/r(%)

"e 0.5 mr 0.2"! 0.1" 0.1#! 1.0" 0.45E 0.003 GeV 0.005E# 0.005 GeV 0.01f 1.1% 1.1PT 2.9% 2.8PB 1.3% 1.3Total 3.3

is 1.509 (GeV/c)2. The lab coordinate system is defined bythe incoming and scattered electron’s momentum vectors,k and k#, as positive z direction along k, y = k $ k# andx = y $ z with +# rotation from +x to +y. Because thescattered electron is bent downwards by the target’s magnetfield, the average azimuthal angle, #e, is out-of-plane with avalue of 348.8". The %q points at the angles "q = 50.43" and#q = 168.8". For Eq. (7), one needs the polar and azimuthalangles, "! and #!, between the %q and the proton’s spin vector.Specifically, when the proton’s spin vector is pointing at"s = 90" and #s = 180", "! and #! can be calculated by theformulas:

"! = arccos(sin "q cos #e)

#! = 180 + arctan!

tan #e

& cos "q

".

For the present kinematics, "! = 40.87" and #! = 197.26".With these kinematic factors and the radiatively correctedaverage Ap,µGE/GM = 0.884 ± 0.027. The solution toEq. (2) for GE/GM is double valued. The positive value of thesquare root was chosen, because the negative solution givesan unreasonable value of µGE/GM = &4.05. For this kine-matic point, the systematic error on !(GE/GM )/(GE/GM ) =0.97 $ !Ap/Ap. The total relative systematic error onµGE/GM is 3.3%. A break down of the systematic errorsis given in Table I. The beam and target polarization are thedominant contributions systematic contributions.

IV. CONCLUSION

In Fig. 6, the ratio µGE/GM from this experiment iscompared to previous measurements. A recent global fit ofGE and GM to the world cross section data has been done [3]and the result for µGE/GM is plotted by a dashed line in Fig.6. The solid line is µGE/GM from a fit to all nucleon formfactors by Lomon [30] that uses only proton GE/GM fromthe polarization transfer technique at large Q2. The differencebetween the two curves is 12% at Q2 = 1.509 (GeV/c)2. Thestatistical error and systematic error for this measurement arecomparable to previous µGE/GM values from cross-sectionand recoil polarization experiments. The data point is midwaybetween the two curves so it is about 2$ away from either

1 2 3

Q2 [(GeV/c)2]

0.6

0.8

1.0

µGE/G

M

World xnJLAB05MIT-BatesJLAB00JLAB02JLAB06This experiment

FIG. 6. (Color online) Ratio µGE/GM plotted as a function ofQ2. The ratio µGE/GM from this experiment is plotted as a filledcircle with the error bar being the statistical and systematic errorcombined in quadrature. The solid line is a fit [30] to all form factordata, which only included proton GE/GM from Refs. [11] and [12]for large Q2. Other symbols are same as in Fig. 1.

curve. Unfortunately, the new measurement does not helpto determine whether the discrepancy between µGE/GM

from the Rosenbluth technique and the polarization transfertechnique is due to unknown systematic errors in eithertechnique. At this Q2, inclusion the Coulomb distortion effects[14] in the Rosenbluth technique would reduce µGE/GM

by 0.05, which would make it overlap with the present datapoint and bring measurements from all three techniques intoreasonable agreement.

The inclusion of two-photon exchange mechanisms in theextraction of the Born cross section will reduce µGE/GM

and bring it closer to µGE/GM determined by this mea-surement and previous measurements using the polarizationtransfer technique. A calculation [15] including all two-photonexchange mechanisms would reduce µGE/GM by about0.08 compared to the dashed line in Fig. 6. This beam-asymmetry measurement is at % = 0.963, which minimizesthe contribution from two-photon exchange mechanisms and,from Ref. [15], µGE/GM would be reduced by roughly afactor of 0.995 by accounting for the two-photon amplitudemechanisms.

This experiment is the first to measure GE/GM usingbeam-target asymmetry in elastic ep scattering. To definitivelydistinguish between experimental techniques at this Q2, abeam-target asymmetry experiment needs to reduce both thestatistical and systematic error. The systematic error that ishardest to reduce is the error on the target polarization. Oneapproach would be to simultaneously measure the beam-targetasymmetry at a given Q2 with two separate spectrometersthat are at the same electron scattering angle but oppositesides of the beam. By taking the ratio of the two asymmetrymeasurements, the beam and target polarization will canceland GE/GM can be extracted with no systematic from either

035201-7

µG

E/G

M

Q2

[(GeV/c)2]

M.K. Jones et al Phys. Rev. C 74, 035201 (2006)

1 2 30

3

FIG. 1: Our measured asymmetries A! and A", fully cor-rected (points) and without radiative corrections (curves).

Fig. 1; A! is notably non-zero. The average proton po-larization was 62% (70%), and the beam polarization was71% (66%) during the parallel (perpendicular) running.For the parallel alignment, the product Pb ! Pt was de-rived by normalizing the measured elastic asymmetry [19]to the known value, resulting in better accuracy thanachievable from direct measurements. In the perpendic-ular case, the limited knowledge of the elastic asymme-try made the direct measurement the better choice. Thesystematic errors are summarized in Table I, highlightingthe lack of models and data for perpendicular radiativecorrections.

The dilution factor represents the fraction of eventsthat truly scattered from a polarized proton in the tar-get. It was determined from the ratio of free proton tototal target rates calculated via a Monte Carlo simula-tion which had been matched to calibration data acquiredspecifically for this purpose. The QFS parameterization[20], modified to improve agreement with our data, wasused as input for the Born inelastic cross sections forA " 3 nuclei. Fits to Hall C inelastic e–p data [21] wereused for the H contribution. The uncertainty in thesecross sections was the dominant source of systematic er-ror for the dilution correction.

Convoluting radiative prescriptions with models of theresonance region, the elastic peak, and our target, weobtained radiated cross sections and asymmetries. Theexternal radiative corrections were determined using theprocedure established in [22], while the POLRAD soft-ware [23] was used to determine the internal radiativecorrections. The resonance fit model was iteratively im-proved, until the radiated values matched our experimen-tal data. The model then trivially provided the correc-tions to our measurements, with fRC accounting for theradiative dilution from the elastic tail and ARC for allother influences.

We extract the virtual photon asymmetries A1 and A2,shown in Fig. 2, from the corrected physics asymmetriesA|| and A!, using only R as model dependent input. Thespin structure functions g1 and g2 (Figs. 3 and 4) are thenobtained utilizing F1. The unpolarized quantities F1 and

FIG. 2: Virtual photon asymmetries A1 and A2 from ourdata and corresponding fits. Also shown is the E155 fit toDIS data [24, 25], evaluated at our (x,Q2), and the So!erlimit for A2 [26], based on our A1 fit. The upper error bandindicates the systematic error in A1, the lower one A2.

R (also used in the previously discussed model calcula-tions) were evaluated from recent fits to other Je!ersonLab data [21, 27]; these fits’ uncertainty is included inour total systematic error and in the error bands of ourplots.

FIG. 3: Results for g1 from this experiment (RSS) and otherrelevant data, as well as target mass corrected NLO PDFs.

FIG. 4: Our (RSS) values for g2 and the approximation gWW

2

(Eq. 1) as evaluated from our data.

We have fitted the W dependence of our A1 and A2

data using an approach similar to that applied to un-

6

Proton A1 and A2 versus W3

FIG. 1: Our measured asymmetries A! and A", fully cor-rected (points) and without radiative corrections (curves).

Fig. 1; A! is notably non-zero. The average proton po-larization was 62% (70%), and the beam polarization was71% (66%) during the parallel (perpendicular) running.For the parallel alignment, the product Pb ! Pt was de-rived by normalizing the measured elastic asymmetry [19]to the known value, resulting in better accuracy thanachievable from direct measurements. In the perpendic-ular case, the limited knowledge of the elastic asymme-try made the direct measurement the better choice. Thesystematic errors are summarized in Table I, highlightingthe lack of models and data for perpendicular radiativecorrections.

The dilution factor represents the fraction of eventsthat truly scattered from a polarized proton in the tar-get. It was determined from the ratio of free proton tototal target rates calculated via a Monte Carlo simula-tion which had been matched to calibration data acquiredspecifically for this purpose. The QFS parameterization[20], modified to improve agreement with our data, wasused as input for the Born inelastic cross sections forA " 3 nuclei. Fits to Hall C inelastic e–p data [21] wereused for the H contribution. The uncertainty in thesecross sections was the dominant source of systematic er-ror for the dilution correction.

Convoluting radiative prescriptions with models of theresonance region, the elastic peak, and our target, weobtained radiated cross sections and asymmetries. Theexternal radiative corrections were determined using theprocedure established in [22], while the POLRAD soft-ware [23] was used to determine the internal radiativecorrections. The resonance fit model was iteratively im-proved, until the radiated values matched our experimen-tal data. The model then trivially provided the correc-tions to our measurements, with fRC accounting for theradiative dilution from the elastic tail and ARC for allother influences.

We extract the virtual photon asymmetries A1 and A2,shown in Fig. 2, from the corrected physics asymmetriesA|| and A!, using only R as model dependent input. Thespin structure functions g1 and g2 (Figs. 3 and 4) are thenobtained utilizing F1. The unpolarized quantities F1 and

FIG. 2: Virtual photon asymmetries A1 and A2 from ourdata and corresponding fits. Also shown is the E155 fit toDIS data [24, 25], evaluated at our (x,Q2), and the So!erlimit for A2 [26], based on our A1 fit. The upper error bandindicates the systematic error in A1, the lower one A2.

R (also used in the previously discussed model calcula-tions) were evaluated from recent fits to other Je!ersonLab data [21, 27]; these fits’ uncertainty is included inour total systematic error and in the error bands of ourplots.

FIG. 3: Results for g1 from this experiment (RSS) and otherrelevant data, as well as target mass corrected NLO PDFs.

FIG. 4: Our (RSS) values for g2 and the approximation gWW

2

(Eq. 1) as evaluated from our data.

We have fitted the W dependence of our A1 and A2

data using an approach similar to that applied to un-

3

FIG. 1: Our measured asymmetries A! and A", fully cor-rected (points) and without radiative corrections (curves).

Fig. 1; A! is notably non-zero. The average proton po-larization was 62% (70%), and the beam polarization was71% (66%) during the parallel (perpendicular) running.For the parallel alignment, the product Pb ! Pt was de-rived by normalizing the measured elastic asymmetry [19]to the known value, resulting in better accuracy thanachievable from direct measurements. In the perpendic-ular case, the limited knowledge of the elastic asymme-try made the direct measurement the better choice. Thesystematic errors are summarized in Table I, highlightingthe lack of models and data for perpendicular radiativecorrections.

The dilution factor represents the fraction of eventsthat truly scattered from a polarized proton in the tar-get. It was determined from the ratio of free proton tototal target rates calculated via a Monte Carlo simula-tion which had been matched to calibration data acquiredspecifically for this purpose. The QFS parameterization[20], modified to improve agreement with our data, wasused as input for the Born inelastic cross sections forA " 3 nuclei. Fits to Hall C inelastic e–p data [21] wereused for the H contribution. The uncertainty in thesecross sections was the dominant source of systematic er-ror for the dilution correction.

Convoluting radiative prescriptions with models of theresonance region, the elastic peak, and our target, weobtained radiated cross sections and asymmetries. Theexternal radiative corrections were determined using theprocedure established in [22], while the POLRAD soft-ware [23] was used to determine the internal radiativecorrections. The resonance fit model was iteratively im-proved, until the radiated values matched our experimen-tal data. The model then trivially provided the correc-tions to our measurements, with fRC accounting for theradiative dilution from the elastic tail and ARC for allother influences.

We extract the virtual photon asymmetries A1 and A2,shown in Fig. 2, from the corrected physics asymmetriesA|| and A!, using only R as model dependent input. Thespin structure functions g1 and g2 (Figs. 3 and 4) are thenobtained utilizing F1. The unpolarized quantities F1 and

FIG. 2: Virtual photon asymmetries A1 and A2 from ourdata and corresponding fits. Also shown is the E155 fit toDIS data [24, 25], evaluated at our (x,Q2), and the So!erlimit for A2 [26], based on our A1 fit. The upper error bandindicates the systematic error in A1, the lower one A2.

R (also used in the previously discussed model calcula-tions) were evaluated from recent fits to other Je!ersonLab data [21, 27]; these fits’ uncertainty is included inour total systematic error and in the error bands of ourplots.

FIG. 3: Results for g1 from this experiment (RSS) and otherrelevant data, as well as target mass corrected NLO PDFs.

FIG. 4: Our (RSS) values for g2 and the approximation gWW

2

(Eq. 1) as evaluated from our data.

We have fitted the W dependence of our A1 and A2

data using an approach similar to that applied to un-

3

FIG. 1: Our measured asymmetries A! and A", fully cor-rected (points) and without radiative corrections (curves).

Fig. 1; A! is notably non-zero. The average proton po-larization was 62% (70%), and the beam polarization was71% (66%) during the parallel (perpendicular) running.For the parallel alignment, the product Pb ! Pt was de-rived by normalizing the measured elastic asymmetry [19]to the known value, resulting in better accuracy thanachievable from direct measurements. In the perpendic-ular case, the limited knowledge of the elastic asymme-try made the direct measurement the better choice. Thesystematic errors are summarized in Table I, highlightingthe lack of models and data for perpendicular radiativecorrections.

The dilution factor represents the fraction of eventsthat truly scattered from a polarized proton in the tar-get. It was determined from the ratio of free proton tototal target rates calculated via a Monte Carlo simula-tion which had been matched to calibration data acquiredspecifically for this purpose. The QFS parameterization[20], modified to improve agreement with our data, wasused as input for the Born inelastic cross sections forA " 3 nuclei. Fits to Hall C inelastic e–p data [21] wereused for the H contribution. The uncertainty in thesecross sections was the dominant source of systematic er-ror for the dilution correction.

Convoluting radiative prescriptions with models of theresonance region, the elastic peak, and our target, weobtained radiated cross sections and asymmetries. Theexternal radiative corrections were determined using theprocedure established in [22], while the POLRAD soft-ware [23] was used to determine the internal radiativecorrections. The resonance fit model was iteratively im-proved, until the radiated values matched our experimen-tal data. The model then trivially provided the correc-tions to our measurements, with fRC accounting for theradiative dilution from the elastic tail and ARC for allother influences.

We extract the virtual photon asymmetries A1 and A2,shown in Fig. 2, from the corrected physics asymmetriesA|| and A!, using only R as model dependent input. Thespin structure functions g1 and g2 (Figs. 3 and 4) are thenobtained utilizing F1. The unpolarized quantities F1 and

FIG. 2: Virtual photon asymmetries A1 and A2 from ourdata and corresponding fits. Also shown is the E155 fit toDIS data [24, 25], evaluated at our (x,Q2), and the So!erlimit for A2 [26], based on our A1 fit. The upper error bandindicates the systematic error in A1, the lower one A2.

R (also used in the previously discussed model calcula-tions) were evaluated from recent fits to other Je!ersonLab data [21, 27]; these fits’ uncertainty is included inour total systematic error and in the error bands of ourplots.

FIG. 3: Results for g1 from this experiment (RSS) and otherrelevant data, as well as target mass corrected NLO PDFs.

FIG. 4: Our (RSS) values for g2 and the approximation gWW

2

(Eq. 1) as evaluated from our data.

We have fitted the W dependence of our A1 and A2

data using an approach similar to that applied to un-

3

FIG. 1: Our measured asymmetries A! and A", fully cor-rected (points) and without radiative corrections (curves).

Fig. 1; A! is notably non-zero. The average proton po-larization was 62% (70%), and the beam polarization was71% (66%) during the parallel (perpendicular) running.For the parallel alignment, the product Pb ! Pt was de-rived by normalizing the measured elastic asymmetry [19]to the known value, resulting in better accuracy thanachievable from direct measurements. In the perpendic-ular case, the limited knowledge of the elastic asymme-try made the direct measurement the better choice. Thesystematic errors are summarized in Table I, highlightingthe lack of models and data for perpendicular radiativecorrections.

The dilution factor represents the fraction of eventsthat truly scattered from a polarized proton in the tar-get. It was determined from the ratio of free proton tototal target rates calculated via a Monte Carlo simula-tion which had been matched to calibration data acquiredspecifically for this purpose. The QFS parameterization[20], modified to improve agreement with our data, wasused as input for the Born inelastic cross sections forA " 3 nuclei. Fits to Hall C inelastic e–p data [21] wereused for the H contribution. The uncertainty in thesecross sections was the dominant source of systematic er-ror for the dilution correction.

Convoluting radiative prescriptions with models of theresonance region, the elastic peak, and our target, weobtained radiated cross sections and asymmetries. Theexternal radiative corrections were determined using theprocedure established in [22], while the POLRAD soft-ware [23] was used to determine the internal radiativecorrections. The resonance fit model was iteratively im-proved, until the radiated values matched our experimen-tal data. The model then trivially provided the correc-tions to our measurements, with fRC accounting for theradiative dilution from the elastic tail and ARC for allother influences.

We extract the virtual photon asymmetries A1 and A2,shown in Fig. 2, from the corrected physics asymmetriesA|| and A!, using only R as model dependent input. Thespin structure functions g1 and g2 (Figs. 3 and 4) are thenobtained utilizing F1. The unpolarized quantities F1 and

FIG. 2: Virtual photon asymmetries A1 and A2 from ourdata and corresponding fits. Also shown is the E155 fit toDIS data [24, 25], evaluated at our (x,Q2), and the So!erlimit for A2 [26], based on our A1 fit. The upper error bandindicates the systematic error in A1, the lower one A2.

R (also used in the previously discussed model calcula-tions) were evaluated from recent fits to other Je!ersonLab data [21, 27]; these fits’ uncertainty is included inour total systematic error and in the error bands of ourplots.

FIG. 3: Results for g1 from this experiment (RSS) and otherrelevant data, as well as target mass corrected NLO PDFs.

FIG. 4: Our (RSS) values for g2 and the approximation gWW

2

(Eq. 1) as evaluated from our data.

We have fitted the W dependence of our A1 and A2

data using an approach similar to that applied to un-

3

FIG. 1: Our measured asymmetries A! and A", fully cor-rected (points) and without radiative corrections (curves).

Fig. 1; A! is notably non-zero. The average proton po-larization was 62% (70%), and the beam polarization was71% (66%) during the parallel (perpendicular) running.For the parallel alignment, the product Pb ! Pt was de-rived by normalizing the measured elastic asymmetry [19]to the known value, resulting in better accuracy thanachievable from direct measurements. In the perpendic-ular case, the limited knowledge of the elastic asymme-try made the direct measurement the better choice. Thesystematic errors are summarized in Table I, highlightingthe lack of models and data for perpendicular radiativecorrections.

The dilution factor represents the fraction of eventsthat truly scattered from a polarized proton in the tar-get. It was determined from the ratio of free proton tototal target rates calculated via a Monte Carlo simula-tion which had been matched to calibration data acquiredspecifically for this purpose. The QFS parameterization[20], modified to improve agreement with our data, wasused as input for the Born inelastic cross sections forA " 3 nuclei. Fits to Hall C inelastic e–p data [21] wereused for the H contribution. The uncertainty in thesecross sections was the dominant source of systematic er-ror for the dilution correction.

Convoluting radiative prescriptions with models of theresonance region, the elastic peak, and our target, weobtained radiated cross sections and asymmetries. Theexternal radiative corrections were determined using theprocedure established in [22], while the POLRAD soft-ware [23] was used to determine the internal radiativecorrections. The resonance fit model was iteratively im-proved, until the radiated values matched our experimen-tal data. The model then trivially provided the correc-tions to our measurements, with fRC accounting for theradiative dilution from the elastic tail and ARC for allother influences.

We extract the virtual photon asymmetries A1 and A2,shown in Fig. 2, from the corrected physics asymmetriesA|| and A!, using only R as model dependent input. Thespin structure functions g1 and g2 (Figs. 3 and 4) are thenobtained utilizing F1. The unpolarized quantities F1 and

FIG. 2: Virtual photon asymmetries A1 and A2 from ourdata and corresponding fits. Also shown is the E155 fit toDIS data [24, 25], evaluated at our (x,Q2), and the So!erlimit for A2 [26], based on our A1 fit. The upper error bandindicates the systematic error in A1, the lower one A2.

R (also used in the previously discussed model calcula-tions) were evaluated from recent fits to other Je!ersonLab data [21, 27]; these fits’ uncertainty is included inour total systematic error and in the error bands of ourplots.

FIG. 3: Results for g1 from this experiment (RSS) and otherrelevant data, as well as target mass corrected NLO PDFs.

FIG. 4: Our (RSS) values for g2 and the approximation gWW

2

(Eq. 1) as evaluated from our data.

We have fitted the W dependence of our A1 and A2

data using an approach similar to that applied to un-

• A1 and A2 are extracted from A|| and A⊥ using Hall C R fit by M.E. Christy

• Quoted errors are for the data only. Phenomenology systematics for the PDFs (±0.06 for the global ratio) needs to be added.

• Local duality is not observed in proton g1 at Q2 =1.3 GeV2

• The global ratio becomes worse (1.42 ±0.10) if large-x resummations for the PDFs (Bianchi et al, PRD 69, 014505 (2004)) are included.

7

Proton g1 and Study of Polarized DualityNLO PDFs (BSB, GRSV, AAC) have

been evolved to Q2 =1.3 GeV2 , and have target mass corrections.

W rangeRatio of Integrals (PDF and data fit)

Delta 1.11--1.30 3.93 ± 0.56

R1 1.30--1.39 1.38 ± 0.10

R2 1.39--1.68 0.78 ± 0.05

R3 1.68--1.79 0.81 ± 0.06

Global 1.09--1.91 1.17 ± 0.08

M-R1 0.94--1.40 0.42 ± 0.06

R2 + 1.40--1.91 0.87 ± 0.06

R1

R2

!

R3

3

total target rates calculated via a Monte Carlo simula-tion which had been matched to calibration data acquiredspecifically for this purpose. The QFS parameterization[15], modified to improve agreement with our data, wasused as input for the unradiated (Born) inelastic crosssections for A ! 3 nuclei. Fits to Hall C inelastic e–p

data [16] were used for the H contribution.Convoluting radiative prescriptions with models of the

resonance region, the elastic peak, and our target, weobtained radiated cross sections and asymmetries. Theexternal radiative corrections were determined using theprocedure established in [17], while the POLRAD soft-ware [18] was used to determine the internal radiativecorrections. The resonance fit model was iteratively im-proved, until the radiated values matched our experimen-tal data. The model then trivially provided the correc-tions required to unradiate our measurements, with fRC

accounting for the radiative dilution from the elastic tailand ARC for all other influences.

FIG. 2: Virtual photon asymmetries Ap

1and Ap

2from our

data and corresponding fits, as well as the E155 fit to DISdata [19, 20], evaluated at our (x, Q2). The upper error bandindicates the systematic error in A1, the lower one A2.

From the corrected physics asymmetries A|| and A!,we extracted the virtual photon asymmetries A1 and A2,shown in Fig. 2,

A1 =1

(E+E")D"

!

(E"E"cos !)A|| "E" sin !

cos"A!

"

A2 =

#

Q2

2ED"

!

A|| +E " E" cos !

E" sin ! cos"A!

"

and the spin structure functions g1 and g2 (Figs. 3 and 4):

g1 =F1

1 + #2(#A2 + A1) g2 =

F1

1 + #2

!A2

#" A1

"

We used the standard definitions D" = (1"$)/(1+$R),$#1 = 1+2(1+##2) tan2 !

2 , R = %L/%T , and # =#

Q2/&,with ! and " as the polar and azimuthal electron scatter-ing angles. This extraction (and the previously discussedmodel calculations) utilized the unpolarized quantities F1

and R from recent fits to other Je!erson Lab data [16, 21];

these fits’ uncertainty is included in our total systematicerror and in the error bands of our plots.

FIG. 3: Results for g1 from this experiment (RSS) and otherrelevant data, as well as target mass corrected NLO PDFs.

FIG. 4: Our values for g2 and the approximation gWW

2 [26] asevaluated from our data.

We have fitted the W dependence of our A1 and A2

data using an approach similar to that applied to in-elastic inclusive unpolarized cross sections in Ref. [17].These fits served as input in the iterative procedure toobtain our radiative corrections and to calculate the in-tegral of g1 at constant Q2. For the resonances we usedfour Breit-Wigner shapes with amplitudes, centroids, andwidths as fit parameters. Other parameters used to de-scribe the nucleon resonances were kept at the valuesindicated in [17]. The DIS component of the fit is de-scribed by a form based on previous phenomenologicalparameterizations of the spin structure [19, 20]. Eachspin asymmetry was fitted independently, since they rep-resent di!erent physical quantities. The choice of fourresonances resulted in better fits than using only three,an option also supported by examining the second deriva-tives of the data smoothed with a spline curve.

Global duality can be tested quantitatively by inte-grating in x over the resonance region and comparing theresults obtained from resonance data and DIS extrapola-tions. We have computed the integral of g1 using our fitover the four resonance regions and compared the resultto the integrals over DIS extrapolations calculated from

3

total target rates calculated via a Monte Carlo simula-tion which had been matched to calibration data acquiredspecifically for this purpose. The QFS parameterization[15], modified to improve agreement with our data, wasused as input for the unradiated (Born) inelastic crosssections for A ! 3 nuclei. Fits to Hall C inelastic e–p

data [16] were used for the H contribution.Convoluting radiative prescriptions with models of the

resonance region, the elastic peak, and our target, weobtained radiated cross sections and asymmetries. Theexternal radiative corrections were determined using theprocedure established in [17], while the POLRAD soft-ware [18] was used to determine the internal radiativecorrections. The resonance fit model was iteratively im-proved, until the radiated values matched our experimen-tal data. The model then trivially provided the correc-tions required to unradiate our measurements, with fRC

accounting for the radiative dilution from the elastic tailand ARC for all other influences.

FIG. 2: Virtual photon asymmetries Ap

1and Ap

2from our

data and corresponding fits, as well as the E155 fit to DISdata [19, 20], evaluated at our (x, Q2). The upper error bandindicates the systematic error in A1, the lower one A2.

From the corrected physics asymmetries A|| and A!,we extracted the virtual photon asymmetries A1 and A2,shown in Fig. 2,

A1 =1

(E+E")D"

!

(E"E"cos !)A|| "E" sin !

cos"A!

"

A2 =

#

Q2

2ED"

!

A|| +E " E" cos !

E" sin ! cos"A!

"

and the spin structure functions g1 and g2 (Figs. 3 and 4):

g1 =F1

1 + #2(#A2 + A1) g2 =

F1

1 + #2

!A2

#" A1

"

We used the standard definitions D" = (1"$)/(1+$R),$#1 = 1+2(1+##2) tan2 !

2 , R = %L/%T , and # =#

Q2/&,with ! and " as the polar and azimuthal electron scatter-ing angles. This extraction (and the previously discussedmodel calculations) utilized the unpolarized quantities F1

and R from recent fits to other Je!erson Lab data [16, 21];

these fits’ uncertainty is included in our total systematicerror and in the error bands of our plots.

FIG. 3: Results for g1 from this experiment (RSS) and otherrelevant data, as well as target mass corrected NLO PDFs.

FIG. 4: Our values for g2 and the approximation gWW

2 [26] asevaluated from our data.

We have fitted the W dependence of our A1 and A2

data using an approach similar to that applied to in-elastic inclusive unpolarized cross sections in Ref. [17].These fits served as input in the iterative procedure toobtain our radiative corrections and to calculate the in-tegral of g1 at constant Q2. For the resonances we usedfour Breit-Wigner shapes with amplitudes, centroids, andwidths as fit parameters. Other parameters used to de-scribe the nucleon resonances were kept at the valuesindicated in [17]. The DIS component of the fit is de-scribed by a form based on previous phenomenologicalparameterizations of the spin structure [19, 20]. Eachspin asymmetry was fitted independently, since they rep-resent di!erent physical quantities. The choice of fourresonances resulted in better fits than using only three,an option also supported by examining the second deriva-tives of the data smoothed with a spline curve.

Global duality can be tested quantitatively by inte-grating in x over the resonance region and comparing theresults obtained from resonance data and DIS extrapola-tions. We have computed the integral of g1 using our fitover the four resonance regions and compared the resultto the integrals over DIS extrapolations calculated from

3

total target rates calculated via a Monte Carlo simula-tion which had been matched to calibration data acquiredspecifically for this purpose. The QFS parameterization[15], modified to improve agreement with our data, wasused as input for the unradiated (Born) inelastic crosssections for A ! 3 nuclei. Fits to Hall C inelastic e–p

data [16] were used for the H contribution.Convoluting radiative prescriptions with models of the

resonance region, the elastic peak, and our target, weobtained radiated cross sections and asymmetries. Theexternal radiative corrections were determined using theprocedure established in [17], while the POLRAD soft-ware [18] was used to determine the internal radiativecorrections. The resonance fit model was iteratively im-proved, until the radiated values matched our experimen-tal data. The model then trivially provided the correc-tions required to unradiate our measurements, with fRC

accounting for the radiative dilution from the elastic tailand ARC for all other influences.

FIG. 2: Virtual photon asymmetries Ap

1and Ap

2from our

data and corresponding fits, as well as the E155 fit to DISdata [19, 20], evaluated at our (x, Q2). The upper error bandindicates the systematic error in A1, the lower one A2.

From the corrected physics asymmetries A|| and A!,we extracted the virtual photon asymmetries A1 and A2,shown in Fig. 2,

A1 =1

(E+E")D"

!

(E"E"cos !)A|| "E" sin !

cos"A!

"

A2 =

#

Q2

2ED"

!

A|| +E " E" cos !

E" sin ! cos"A!

"

and the spin structure functions g1 and g2 (Figs. 3 and 4):

g1 =F1

1 + #2(#A2 + A1) g2 =

F1

1 + #2

!A2

#" A1

"

We used the standard definitions D" = (1"$)/(1+$R),$#1 = 1+2(1+##2) tan2 !

2 , R = %L/%T , and # =#

Q2/&,with ! and " as the polar and azimuthal electron scatter-ing angles. This extraction (and the previously discussedmodel calculations) utilized the unpolarized quantities F1

and R from recent fits to other Je!erson Lab data [16, 21];

these fits’ uncertainty is included in our total systematicerror and in the error bands of our plots.

FIG. 3: Results for g1 from this experiment (RSS) and otherrelevant data, as well as target mass corrected NLO PDFs.

FIG. 4: Our values for g2 and the approximation gWW

2 [26] asevaluated from our data.

We have fitted the W dependence of our A1 and A2

data using an approach similar to that applied to in-elastic inclusive unpolarized cross sections in Ref. [17].These fits served as input in the iterative procedure toobtain our radiative corrections and to calculate the in-tegral of g1 at constant Q2. For the resonances we usedfour Breit-Wigner shapes with amplitudes, centroids, andwidths as fit parameters. Other parameters used to de-scribe the nucleon resonances were kept at the valuesindicated in [17]. The DIS component of the fit is de-scribed by a form based on previous phenomenologicalparameterizations of the spin structure [19, 20]. Eachspin asymmetry was fitted independently, since they rep-resent di!erent physical quantities. The choice of fourresonances resulted in better fits than using only three,an option also supported by examining the second deriva-tives of the data smoothed with a spline curve.

Global duality can be tested quantitatively by inte-grating in x over the resonance region and comparing theresults obtained from resonance data and DIS extrapola-tions. We have computed the integral of g1 using our fitover the four resonance regions and compared the resultto the integrals over DIS extrapolations calculated from

3

total target rates calculated via a Monte Carlo simula-tion which had been matched to calibration data acquiredspecifically for this purpose. The QFS parameterization[15], modified to improve agreement with our data, wasused as input for the unradiated (Born) inelastic crosssections for A ! 3 nuclei. Fits to Hall C inelastic e–p

data [16] were used for the H contribution.Convoluting radiative prescriptions with models of the

resonance region, the elastic peak, and our target, weobtained radiated cross sections and asymmetries. Theexternal radiative corrections were determined using theprocedure established in [17], while the POLRAD soft-ware [18] was used to determine the internal radiativecorrections. The resonance fit model was iteratively im-proved, until the radiated values matched our experimen-tal data. The model then trivially provided the correc-tions required to unradiate our measurements, with fRC

accounting for the radiative dilution from the elastic tailand ARC for all other influences.

FIG. 2: Virtual photon asymmetries Ap

1and Ap

2from our

data and corresponding fits, as well as the E155 fit to DISdata [19, 20], evaluated at our (x, Q2). The upper error bandindicates the systematic error in A1, the lower one A2.

From the corrected physics asymmetries A|| and A!,we extracted the virtual photon asymmetries A1 and A2,shown in Fig. 2,

A1 =1

(E+E")D"

!

(E"E"cos !)A|| "E" sin !

cos"A!

"

A2 =

#

Q2

2ED"

!

A|| +E " E" cos !

E" sin ! cos"A!

"

and the spin structure functions g1 and g2 (Figs. 3 and 4):

g1 =F1

1 + #2(#A2 + A1) g2 =

F1

1 + #2

!A2

#" A1

"

We used the standard definitions D" = (1"$)/(1+$R),$#1 = 1+2(1+##2) tan2 !

2 , R = %L/%T , and # =#

Q2/&,with ! and " as the polar and azimuthal electron scatter-ing angles. This extraction (and the previously discussedmodel calculations) utilized the unpolarized quantities F1

and R from recent fits to other Je!erson Lab data [16, 21];

these fits’ uncertainty is included in our total systematicerror and in the error bands of our plots.

FIG. 3: Results for g1 from this experiment (RSS) and otherrelevant data, as well as target mass corrected NLO PDFs.

FIG. 4: Our values for g2 and the approximation gWW

2 [26] asevaluated from our data.

We have fitted the W dependence of our A1 and A2

data using an approach similar to that applied to in-elastic inclusive unpolarized cross sections in Ref. [17].These fits served as input in the iterative procedure toobtain our radiative corrections and to calculate the in-tegral of g1 at constant Q2. For the resonances we usedfour Breit-Wigner shapes with amplitudes, centroids, andwidths as fit parameters. Other parameters used to de-scribe the nucleon resonances were kept at the valuesindicated in [17]. The DIS component of the fit is de-scribed by a form based on previous phenomenologicalparameterizations of the spin structure [19, 20]. Eachspin asymmetry was fitted independently, since they rep-resent di!erent physical quantities. The choice of fourresonances resulted in better fits than using only three,an option also supported by examining the second deriva-tives of the data smoothed with a spline curve.

Global duality can be tested quantitatively by inte-grating in x over the resonance region and comparing theresults obtained from resonance data and DIS extrapola-tions. We have computed the integral of g1 using our fitover the four resonance regions and compared the resultto the integrals over DIS extrapolations calculated from

3

total target rates calculated via a Monte Carlo simula-tion which had been matched to calibration data acquiredspecifically for this purpose. The QFS parameterization[15], modified to improve agreement with our data, wasused as input for the unradiated (Born) inelastic crosssections for A ! 3 nuclei. Fits to Hall C inelastic e–p

data [16] were used for the H contribution.Convoluting radiative prescriptions with models of the

resonance region, the elastic peak, and our target, weobtained radiated cross sections and asymmetries. Theexternal radiative corrections were determined using theprocedure established in [17], while the POLRAD soft-ware [18] was used to determine the internal radiativecorrections. The resonance fit model was iteratively im-proved, until the radiated values matched our experimen-tal data. The model then trivially provided the correc-tions required to unradiate our measurements, with fRC

accounting for the radiative dilution from the elastic tailand ARC for all other influences.

FIG. 2: Virtual photon asymmetries Ap

1and Ap

2from our

data and corresponding fits, as well as the E155 fit to DISdata [19, 20], evaluated at our (x, Q2). The upper error bandindicates the systematic error in A1, the lower one A2.

From the corrected physics asymmetries A|| and A!,we extracted the virtual photon asymmetries A1 and A2,shown in Fig. 2,

A1 =1

(E+E")D"

!

(E"E"cos !)A|| "E" sin !

cos"A!

"

A2 =

#

Q2

2ED"

!

A|| +E " E" cos !

E" sin ! cos"A!

"

and the spin structure functions g1 and g2 (Figs. 3 and 4):

g1 =F1

1 + #2(#A2 + A1) g2 =

F1

1 + #2

!A2

#" A1

"

We used the standard definitions D" = (1"$)/(1+$R),$#1 = 1+2(1+##2) tan2 !

2 , R = %L/%T , and # =#

Q2/&,with ! and " as the polar and azimuthal electron scatter-ing angles. This extraction (and the previously discussedmodel calculations) utilized the unpolarized quantities F1

and R from recent fits to other Je!erson Lab data [16, 21];

these fits’ uncertainty is included in our total systematicerror and in the error bands of our plots.

FIG. 3: Results for g1 from this experiment (RSS) and otherrelevant data, as well as target mass corrected NLO PDFs.

FIG. 4: Our values for g2 and the approximation gWW

2 [26] asevaluated from our data.

We have fitted the W dependence of our A1 and A2

data using an approach similar to that applied to in-elastic inclusive unpolarized cross sections in Ref. [17].These fits served as input in the iterative procedure toobtain our radiative corrections and to calculate the in-tegral of g1 at constant Q2. For the resonances we usedfour Breit-Wigner shapes with amplitudes, centroids, andwidths as fit parameters. Other parameters used to de-scribe the nucleon resonances were kept at the valuesindicated in [17]. The DIS component of the fit is de-scribed by a form based on previous phenomenologicalparameterizations of the spin structure [19, 20]. Eachspin asymmetry was fitted independently, since they rep-resent di!erent physical quantities. The choice of fourresonances resulted in better fits than using only three,an option also supported by examining the second deriva-tives of the data smoothed with a spline curve.

Global duality can be tested quantitatively by inte-grating in x over the resonance region and comparing theresults obtained from resonance data and DIS extrapola-tions. We have computed the integral of g1 using our fitover the four resonance regions and compared the resultto the integrals over DIS extrapolations calculated from

g1 versus XBJ=Q2/2Mp(E-E’)

XBJ

• Q2 dependence of Q2 <g1> for each W region indicated is shown above. (Taken from Fig.3 of hep-ph/0607283 (P. Bosted et al) and RSS data added)

• Hatched bands show the average ranges calculated from extrapolated NLO DIS fits

8

Comparison of RSS proton g1 to eg1b results

g1 versus XBJ=Q2/2Mp(E-E’) RSS

eg1b

9

Proton g2 and Higher Twist

• Use measured to calculate gWW2g1

g2 = gWW2 + g2; Twist 2 : gWW

2 (x,Q2) = !g1(x,Q2) +

! 1

x

dy

yg1(y,Q2)

3

total target rates calculated via a Monte Carlo simula-tion which had been matched to calibration data acquiredspecifically for this purpose. The QFS parameterization[15], modified to improve agreement with our data, wasused as input for the unradiated (Born) inelastic crosssections for A ! 3 nuclei. Fits to Hall C inelastic e–p

data [16] were used for the H contribution.Convoluting radiative prescriptions with models of the

resonance region, the elastic peak, and our target, weobtained radiated cross sections and asymmetries. Theexternal radiative corrections were determined using theprocedure established in [17], while the POLRAD soft-ware [18] was used to determine the internal radiativecorrections. The resonance fit model was iteratively im-proved, until the radiated values matched our experimen-tal data. The model then trivially provided the correc-tions required to unradiate our measurements, with fRC

accounting for the radiative dilution from the elastic tailand ARC for all other influences.

FIG. 2: Virtual photon asymmetries Ap

1and Ap

2from our

data and corresponding fits, as well as the E155 fit to DISdata [19, 20], evaluated at our (x, Q2). The upper error bandindicates the systematic error in A1, the lower one A2.

From the corrected physics asymmetries A|| and A!,we extracted the virtual photon asymmetries A1 and A2,shown in Fig. 2,

A1 =1

(E+E")D"

!

(E"E"cos !)A|| "E" sin !

cos"A!

"

A2 =

#

Q2

2ED"

!

A|| +E " E" cos !

E" sin ! cos"A!

"

and the spin structure functions g1 and g2 (Figs. 3 and 4):

g1 =F1

1 + #2(#A2 + A1) g2 =

F1

1 + #2

!A2

#" A1

"

We used the standard definitions D" = (1"$)/(1+$R),$#1 = 1+2(1+##2) tan2 !

2 , R = %L/%T , and # =#

Q2/&,with ! and " as the polar and azimuthal electron scatter-ing angles. This extraction (and the previously discussedmodel calculations) utilized the unpolarized quantities F1

and R from recent fits to other Je!erson Lab data [16, 21];

these fits’ uncertainty is included in our total systematicerror and in the error bands of our plots.

FIG. 3: Results for g1 from this experiment (RSS) and otherrelevant data, as well as target mass corrected NLO PDFs.

FIG. 4: Our values for g2 and the approximation gWW

2 [26] asevaluated from our data.

We have fitted the W dependence of our A1 and A2

data using an approach similar to that applied to in-elastic inclusive unpolarized cross sections in Ref. [17].These fits served as input in the iterative procedure toobtain our radiative corrections and to calculate the in-tegral of g1 at constant Q2. For the resonances we usedfour Breit-Wigner shapes with amplitudes, centroids, andwidths as fit parameters. Other parameters used to de-scribe the nucleon resonances were kept at the valuesindicated in [17]. The DIS component of the fit is de-scribed by a form based on previous phenomenologicalparameterizations of the spin structure [19, 20]. Eachspin asymmetry was fitted independently, since they rep-resent di!erent physical quantities. The choice of fourresonances resulted in better fits than using only three,an option also supported by examining the second deriva-tives of the data smoothed with a spline curve.

Global duality can be tested quantitatively by inte-grating in x over the resonance region and comparing theresults obtained from resonance data and DIS extrapola-tions. We have computed the integral of g1 using our fitover the four resonance regions and compared the resultto the integrals over DIS extrapolations calculated from

3

total target rates calculated via a Monte Carlo simula-tion which had been matched to calibration data acquiredspecifically for this purpose. The QFS parameterization[15], modified to improve agreement with our data, wasused as input for the unradiated (Born) inelastic crosssections for A ! 3 nuclei. Fits to Hall C inelastic e–p

data [16] were used for the H contribution.Convoluting radiative prescriptions with models of the

resonance region, the elastic peak, and our target, weobtained radiated cross sections and asymmetries. Theexternal radiative corrections were determined using theprocedure established in [17], while the POLRAD soft-ware [18] was used to determine the internal radiativecorrections. The resonance fit model was iteratively im-proved, until the radiated values matched our experimen-tal data. The model then trivially provided the correc-tions required to unradiate our measurements, with fRC

accounting for the radiative dilution from the elastic tailand ARC for all other influences.

FIG. 2: Virtual photon asymmetries Ap

1and Ap

2from our

data and corresponding fits, as well as the E155 fit to DISdata [19, 20], evaluated at our (x, Q2). The upper error bandindicates the systematic error in A1, the lower one A2.

From the corrected physics asymmetries A|| and A!,we extracted the virtual photon asymmetries A1 and A2,shown in Fig. 2,

A1 =1

(E+E")D"

!

(E"E"cos !)A|| "E" sin !

cos"A!

"

A2 =

#

Q2

2ED"

!

A|| +E " E" cos !

E" sin ! cos"A!

"

and the spin structure functions g1 and g2 (Figs. 3 and 4):

g1 =F1

1 + #2(#A2 + A1) g2 =

F1

1 + #2

!A2

#" A1

"

We used the standard definitions D" = (1"$)/(1+$R),$#1 = 1+2(1+##2) tan2 !

2 , R = %L/%T , and # =#

Q2/&,with ! and " as the polar and azimuthal electron scatter-ing angles. This extraction (and the previously discussedmodel calculations) utilized the unpolarized quantities F1

and R from recent fits to other Je!erson Lab data [16, 21];

these fits’ uncertainty is included in our total systematicerror and in the error bands of our plots.

FIG. 3: Results for g1 from this experiment (RSS) and otherrelevant data, as well as target mass corrected NLO PDFs.

FIG. 4: Our values for g2 and the approximation gWW

2 [26] asevaluated from our data.

We have fitted the W dependence of our A1 and A2

data using an approach similar to that applied to in-elastic inclusive unpolarized cross sections in Ref. [17].These fits served as input in the iterative procedure toobtain our radiative corrections and to calculate the in-tegral of g1 at constant Q2. For the resonances we usedfour Breit-Wigner shapes with amplitudes, centroids, andwidths as fit parameters. Other parameters used to de-scribe the nucleon resonances were kept at the valuesindicated in [17]. The DIS component of the fit is de-scribed by a form based on previous phenomenologicalparameterizations of the spin structure [19, 20]. Eachspin asymmetry was fitted independently, since they rep-resent di!erent physical quantities. The choice of fourresonances resulted in better fits than using only three,an option also supported by examining the second deriva-tives of the data smoothed with a spline curve.

Global duality can be tested quantitatively by inte-grating in x over the resonance region and comparing theresults obtained from resonance data and DIS extrapola-tions. We have computed the integral of g1 using our fitover the four resonance regions and compared the resultto the integrals over DIS extrapolations calculated from

3

total target rates calculated via a Monte Carlo simula-tion which had been matched to calibration data acquiredspecifically for this purpose. The QFS parameterization[15], modified to improve agreement with our data, wasused as input for the unradiated (Born) inelastic crosssections for A ! 3 nuclei. Fits to Hall C inelastic e–p

data [16] were used for the H contribution.Convoluting radiative prescriptions with models of the

resonance region, the elastic peak, and our target, weobtained radiated cross sections and asymmetries. Theexternal radiative corrections were determined using theprocedure established in [17], while the POLRAD soft-ware [18] was used to determine the internal radiativecorrections. The resonance fit model was iteratively im-proved, until the radiated values matched our experimen-tal data. The model then trivially provided the correc-tions required to unradiate our measurements, with fRC

accounting for the radiative dilution from the elastic tailand ARC for all other influences.

FIG. 2: Virtual photon asymmetries Ap

1and Ap

2from our

data and corresponding fits, as well as the E155 fit to DISdata [19, 20], evaluated at our (x, Q2). The upper error bandindicates the systematic error in A1, the lower one A2.

From the corrected physics asymmetries A|| and A!,we extracted the virtual photon asymmetries A1 and A2,shown in Fig. 2,

A1 =1

(E+E")D"

!

(E"E"cos !)A|| "E" sin !

cos"A!

"

A2 =

#

Q2

2ED"

!

A|| +E " E" cos !

E" sin ! cos"A!

"

and the spin structure functions g1 and g2 (Figs. 3 and 4):

g1 =F1

1 + #2(#A2 + A1) g2 =

F1

1 + #2

!A2

#" A1

"

We used the standard definitions D" = (1"$)/(1+$R),$#1 = 1+2(1+##2) tan2 !

2 , R = %L/%T , and # =#

Q2/&,with ! and " as the polar and azimuthal electron scatter-ing angles. This extraction (and the previously discussedmodel calculations) utilized the unpolarized quantities F1

and R from recent fits to other Je!erson Lab data [16, 21];

these fits’ uncertainty is included in our total systematicerror and in the error bands of our plots.

FIG. 3: Results for g1 from this experiment (RSS) and otherrelevant data, as well as target mass corrected NLO PDFs.

FIG. 4: Our values for g2 and the approximation gWW

2 [26] asevaluated from our data.

We have fitted the W dependence of our A1 and A2

data using an approach similar to that applied to in-elastic inclusive unpolarized cross sections in Ref. [17].These fits served as input in the iterative procedure toobtain our radiative corrections and to calculate the in-tegral of g1 at constant Q2. For the resonances we usedfour Breit-Wigner shapes with amplitudes, centroids, andwidths as fit parameters. Other parameters used to de-scribe the nucleon resonances were kept at the valuesindicated in [17]. The DIS component of the fit is de-scribed by a form based on previous phenomenologicalparameterizations of the spin structure [19, 20]. Eachspin asymmetry was fitted independently, since they rep-resent di!erent physical quantities. The choice of fourresonances resulted in better fits than using only three,an option also supported by examining the second deriva-tives of the data smoothed with a spline curve.

Global duality can be tested quantitatively by inte-grating in x over the resonance region and comparing theresults obtained from resonance data and DIS extrapola-tions. We have computed the integral of g1 using our fitover the four resonance regions and compared the resultto the integrals over DIS extrapolations calculated from

3

total target rates calculated via a Monte Carlo simula-tion which had been matched to calibration data acquiredspecifically for this purpose. The QFS parameterization[15], modified to improve agreement with our data, wasused as input for the unradiated (Born) inelastic crosssections for A ! 3 nuclei. Fits to Hall C inelastic e–p

data [16] were used for the H contribution.Convoluting radiative prescriptions with models of the

resonance region, the elastic peak, and our target, weobtained radiated cross sections and asymmetries. Theexternal radiative corrections were determined using theprocedure established in [17], while the POLRAD soft-ware [18] was used to determine the internal radiativecorrections. The resonance fit model was iteratively im-proved, until the radiated values matched our experimen-tal data. The model then trivially provided the correc-tions required to unradiate our measurements, with fRC

accounting for the radiative dilution from the elastic tailand ARC for all other influences.

FIG. 2: Virtual photon asymmetries Ap

1and Ap

2from our

data and corresponding fits, as well as the E155 fit to DISdata [19, 20], evaluated at our (x, Q2). The upper error bandindicates the systematic error in A1, the lower one A2.

From the corrected physics asymmetries A|| and A!,we extracted the virtual photon asymmetries A1 and A2,shown in Fig. 2,

A1 =1

(E+E")D"

!

(E"E"cos !)A|| "E" sin !

cos"A!

"

A2 =

#

Q2

2ED"

!

A|| +E " E" cos !

E" sin ! cos"A!

"

and the spin structure functions g1 and g2 (Figs. 3 and 4):

g1 =F1

1 + #2(#A2 + A1) g2 =

F1

1 + #2

!A2

#" A1

"

We used the standard definitions D" = (1"$)/(1+$R),$#1 = 1+2(1+##2) tan2 !

2 , R = %L/%T , and # =#

Q2/&,with ! and " as the polar and azimuthal electron scatter-ing angles. This extraction (and the previously discussedmodel calculations) utilized the unpolarized quantities F1

and R from recent fits to other Je!erson Lab data [16, 21];

these fits’ uncertainty is included in our total systematicerror and in the error bands of our plots.

FIG. 3: Results for g1 from this experiment (RSS) and otherrelevant data, as well as target mass corrected NLO PDFs.

FIG. 4: Our values for g2 and the approximation gWW

2 [26] asevaluated from our data.

We have fitted the W dependence of our A1 and A2

data using an approach similar to that applied to in-elastic inclusive unpolarized cross sections in Ref. [17].These fits served as input in the iterative procedure toobtain our radiative corrections and to calculate the in-tegral of g1 at constant Q2. For the resonances we usedfour Breit-Wigner shapes with amplitudes, centroids, andwidths as fit parameters. Other parameters used to de-scribe the nucleon resonances were kept at the valuesindicated in [17]. The DIS component of the fit is de-scribed by a form based on previous phenomenologicalparameterizations of the spin structure [19, 20]. Eachspin asymmetry was fitted independently, since they rep-resent di!erent physical quantities. The choice of fourresonances resulted in better fits than using only three,an option also supported by examining the second deriva-tives of the data smoothed with a spline curve.

Global duality can be tested quantitatively by inte-grating in x over the resonance region and comparing theresults obtained from resonance data and DIS extrapola-tions. We have computed the integral of g1 using our fitover the four resonance regions and compared the resultto the integrals over DIS extrapolations calculated from

( X=Q2/2Mp(E-E’) )

10

Twist-3 Matrix Element d2

•The measured

d2 (RSS) is more than 5 sigmas above zero

•pQCD evolution courtesy of A. Deur

d2 =

! 0.84

0.29

x2(2g1 + 3g2)dx = 0.0057 ± 0.0009 ± 0.0007(stat) (syst)

d2 =

! 1

0

x2(2g1 + 3g2)dx = 3

! 1

0

x2(g2 ! gWW2 )dx

__SANE d2 expected statistical errors

SLAC

Lattice QCD - Goeckeler et al.

__ RSS d2

Elastic contribution

d2 = d2(RSS) ! (Q2

RSS / Q2)

SANE combined Q2 3.5 to 6.5 GeV

2

d2 pQCD (NP B201:141)

Q2 [GeV

2]

1 2 3 4 5 6 7

d2

-0.005

0.000

0.005

0.010

0.015

0.020

0.025

0.030

Preliminary RSS inelastic d2

__SANE d2 expected statistical errors

SLAC

Lattice QCD - Goeckeler et al.

__ RSS d2

Elastic contribution

d2 = d2(RSS) ! (Q2

RSS / Q2)

SANE combined Q2 3.5 to 6.5 GeV

2

d2 pQCD (NP B201:141)

Q2 [GeV

2]

1 2 3 4 5 6 7

d2

-0.005

0.000

0.005

0.010

0.015

0.020

0.025

0.030

Preliminary RSS inelastic d2

__SANE d2 expected statistical errors

SLAC

Lattice QCD - Goeckeler et al.

__ RSS d2

Elastic contribution

d2 = d2(RSS) ! (Q2

RSS / Q2)

SANE combined Q2 3.5 to 6.5 GeV

2

d2 pQCD (NP B201:141)

Q2 [GeV

2]

1 2 3 4 5 6 7

d2

-0.005

0.000

0.005

0.010

0.015

0.020

0.025

0.030

Preliminary RSS inelastic d2

[RSS]

-

800 1000 1200 1400 1600 1800 2000W (MeV)

-0.15

-0.1

-0.05

0

0.05

0.1

Aper

p

Measured dataQE model full radData full rad corr

800 1000 1200 1400 1600 1800 2000W ( MeV)

-0.05

0

0.05

0.1

0.15

0.2

0.25

Ap

ara

Measured dataData full rad corrQE model radiated

11

Deuteron A" and A! versus W

• Arenhövel calculated the deuteron QE cross sections, A" and A!

at RSS kinematics. Dipole form factor with Gen=0 was used.

• Arenhövel’s QE asym models agree with data in the QE region

• Radiative corrections have been applied to our data.

Preliminary

A" A!

1 1.2 1.4 1.6 1.8 2

W (GeV)

-0.4

-0.2

0

0.2

0.4

0.6

Deu

tero

n A

1,

A2

Deuteron A2 Soffer LimitRSS A1D (born)

RSS A2D (born)

12

Deuteron A1 and A2 versus W

• Radiative corrections have been applied.

Preliminary

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9Xbj

-0.2

-0.1

0

0.1

0.2

0.3

g1d (born)g2d (born)

13

Deuteron g1 and g2 versus x

Preliminary

• Radiative corrections have been applied.

• P. Bosted’s deuteron fits were used to obtain F1d , F2d

14

Extraction of Neutron Spin Structure

• Extraction of neutron spin structure functions (SSFs) from the RSS proton and deuteron data

• Smeared proton SSFs need to be subtracted from the deuteron SSFs.

• We employ Bodek-Ritchie version of Atwood-West smearing technique: Form the convolution of the momentum distribution and on-shell quantities

• Need to obtain smeared proton g1 and g2

Smear

gp

2

gp

1g

ps

1

gps

2!!ps

!

!!ps

!!!

p

!(gp

1, g

p

2)

!!p

!(gp

1, g

p

2)

gns1 = g

d1 ! g

ps1

gns2 = g

d2 ! g

ps2

F (Q2, !) =

!!

0

| f("p) |2 g(Q2, W ", !")d"p

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9Xbj

-0.1

-0.05

0

0.05

g2n (E97103) Q2=1.1, 1.3

g2n (E99117) Q2=2.7, 3.5, 4.8

g2n (SLAC) Q2=5.0

g2p (RSS, smeared)

g2d (RSS)

g2n (RSS, smeared)

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9Xbj

-0.1

0

0.1

0.2

0.3g1n (E97103) Q

2=1.1, 1.3

g1n (E99117) Q2=2.7, 3.5, 4.8

g1n (SLAC) Q2=5.0

g1p (RSS, smeared)

g1d (RSS)

g1n (RSS, smeared)

15

Smeared Neutron g1 and g2 versus x

• Radiative corrections applied to RSS data.

• Previous measurements ( JLab E97-103, E99-117, SLAC ) were in the Deep Inelastic Scattering (DIS) region

RSS: Preliminary

g1n

g2n

GDH Sum rule from RSS proton data

16

0 1 2 3 4 5

Q2 (GeV

2)

0

10

20

30

40

50

60

I B

(µ

b)

Hermes-B (Sys)

MAID-BHermes-B (Tot)Hermes-B (Res)RSS-B (Res)RSS-B (Tot)

PRELIMIN

ARY

!2=

Q2

"2=

4m2x2

Q2

where

I =16!2"

Q2

IB = I

! xth

0

g1(x) ! !2g2(x)"

1 + !2dx

0.1 1 10

Q2 (GeV

2)

-0.04

-0.02

0

0.02

0.04

Elastic Maid E155xRSS (Res)

RSS (Res + DIS)

RSS (Res + DIS + Elastic)

VER

Y P

RELIM

INA

RY

The Burkhardt-Cottingham Sum Rule

from RSS proton data

17

!"

!2 =

! 1

0

g2(x)dx

0 0.2 0.4 0.6 0.8 1X

-1

-0.5

0

0.5

!d

/d

0

0.25

0.5

0.75

1

1.25

!u

/u

HALL ARSS CLASHERMES

stat. erro

r only

PRELIMINARY

• Phys. Lett. B641, 11 (2006) (K.V. Dharmawardane et al.) [CLAS]

• CLAS, RSS: used data for W>1.77 GeV and Q2 1 GeV2

• RSS data agrees with world data

18

Quark Polarizations#u/u and#d/d

0

0.25

0.5

0.75

1

!u

/u

This work

HERMES

JLab/HallA

x

!d

/d

GRV

AAC

GS

LSS

-1

-0.5

0

0.5

0 0.2 0.4 0.6 0.8 1

!u/u !d/dW = 1.77

Q2 = 1 2

d/u!d/d

x

3

!u/u !d/dg1

F p1 F d

1

!u

u!

5gp1 " 2gd

1/(1 " 1.5wD)

5F p1 " 2F d

1

;

!d

d!

8gd1/(1 " 1.5wD) " 5gp

1

8F d1 " 5F p

1

.

!d/d Ap1 Ad

1

!d/d Wx

Q2 > 3 2

W

3

x ! 0.6!u/u

!u/u = 1 x!u/u !d/d

A1 g1/F1

xx Q2

W < 2

u x

d

x

x x ! 0.8

#

RSS: Prel

iminary

Stat e

rror o

nly

19

Summary

• Precise measurement of the proton and deuteron spin asymmetries A1, A2 and spin structure functions g1, g2 in the resonance region.

• Studied polarized duality in the resonance region, twist-3 effect, and extracted d2 matrix element

• Deuteron, neutron and sum rule results are preliminary.

• Proton elastic paper has been published: M.K. Jones et al, PRC 74, 035201 (2006)

• Proton SSFs paper has been submitted to PRL F.R. Wesselmann et al. Preprint: nucl-ex/0608003

• New papers on proton and neutron sum rules (K.Slifer) and Deuteron/Neutron SSFs (S. Tajima) will be written.

20

NH3

Helium

Helium

Packing Fraction

Packing Fraction (PF) for

the proton target is the ratio

of NH3 to (NH3 +He).

Similarly for the deuteron

target (ND3)

• PF for each target cell was

determined by comparing the

simulated W spectrum with

data.

• Measured NH3 PFs: 53-60%,

Measured ND3 PFs: 52-58%,

Systematic error in PFs: <2%

21

0

2

4

6

8

10

12

14

16

0.8 1 1.2 1.4 1.6 1.8 2 2.2

W (Scaled)

COMMON /PAWC/ in memoryCOMMON /PAWC/ in memoryCOMMON /PAWC/ in memoryCOMMON /PAWC/ in memoryCOMMON /PAWC/ in memory

DataMC(ALL)MC(Proton) ! Eric 7/22MC(No Proton) ! QFSData-MC(No Proton)

43724 (hi), 43740 (low)nh3 , para , top

PF (low W)=53.2% PF (high W)=53.2%

W

COMMON /PAWC/ in memory

Ratio: /(Data-MC(no P)) MC(P)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0.8 1 1.2 1.4 1.6 1.8 2 2.2

1200 1400 1600 1800

W (GeV)

0

0.1

0.2

Dil

uti

on

fa

cto

r

Parallel field, Bottom cup

Parallel field, Top cup

Perpendicular field, Bottom cup

Perpendicular field, Top cup

Dilution Factor

800 1000 1200 1400 1600 1800 2000W (MeV)

0

0.1

0.2

0.3

0.4

0.5

Dil

uti

on

Fac

tor

Para Field, TOP cupPara Field, Bottom cupPerp Field, Bottom cup

Q.E.

"Dilu

tion F

acto

r

"

• Dilution Factor: f(W)

f(W)= Rate(proton) ! Rate(total)

• Hall C fits for F2 and R by

M.E. Christy); QFS for A>2

• f(w) ~ 0.1-0.2 (resonance region)

Proton Deuteron

• Dilution Factor: f(W)

f(W)= Rate(deuteron)!Rate(total)

• Fit to the deuteron cross section obtained by I. Niculescu; • QFS for A>2

• f(w) ~ 0.2-0.3 (resonance region)

W(MeV)22

23

Beam-Target asymmetries

• Counts are normalized by the charge and deadtime

• f = dilution factor; PB, PT = beam and target polarizations

• CN = corrections for 15N asymmetry

• frc , Arc = radiative corrections. POLRAD (Akusevich et al.) modified to include a fit to our data.

A!," =1

CNfrc

Araw

fPBPT

+ Arc

Araw =N!"

! N#"

N!" + N#"or

N!$! N#$

N!$ + N#$

PT: (parallel) (perpendicular)Target polarization: (longitudinal) (perpendicular)

24

Proton A" and A! versus W

• Points: Fully-corrected asymmetries Curves: Without radiative corrections

2

providing a clean test of the theory. Quark-gluon in-teractions reflected in the twist-3 terms are also visiblein the related A2 asymmetry in the form of a 1/Q evo-lution. Each higher order of twist, interpretable as in-creased correlation between partons, adds another 1/Qterm, so their contribution should be more prominent atlow Q2.

Experiment E01-006 was conducted over six weeks inHall C of the Thomas Je!erson National Accelerator Fa-cility. Utilizing established procedures and equipment,we have measured the asymmetries A! and A" in thescattering of polarized electrons o! a polarized protontarget at Q2 ! 1.3 GeV2. These asymmetries are definedas the dimensionless, relative di!erence between the crosssections with parallel and anti-parallel (or perpendicularand anti-perpendicular) alignment of the proton and theelectron spins:

A|| =d!#$ " d!$$

d!#$ + d!$$A" =

d!#% " d!$%

d!#% + d!$%

The experiment used Je!erson Lab’s continuous, po-larized electron beam with energy of 5.755 GeV and anominal current of 100 nA. The beam polarization wasmeasured by a Møller polarimeter [11] installed upstreamof the target. The beam helicity was flipped at 30 Hzon a pseudo-random basis. False asymmetries or biaswere further minimized by actively correcting for anybeam charge asymmetry, and accounting for the mea-sured residual of < 0.1% (absolute).

Frozen 15NH3, in 1" 2 mm fragments, was used asthe proton target in the University of Virginia appara-tus [12] in which a 4He evaporation refrigerator at 1 Kcoupled with a 5 T polarizing magnet created a stablepolarization environment. The polarization populationenhancement was achieved via a dynamic nuclear polar-ization technique and measured by an NMR system usingpickup coils embedded in the target material. For the A"

measurement, the entire target apparatus was rotated by90&. To reduce systematic e!ects, about equal amountsof data were taken with each polarization directions byflipping the nuclear spin. To maintain uniform polariza-tion in the bulk target material, the beam was continuallymoved across the face of the target in a 1 cm maximumradius spiral raster pattern around the beam axis. Thisextra degree of freedom required a dedicated beam posi-tion monitor [13] for accurate event reconstruction.

Scattered electrons were detected using the High Mo-mentum Spectrometer (HMS), positioned at a scatteringangle of 13.15&. Two di!erent HMS momentum settingswere used, 4.078 and 4.703 GeV, to cover the desired widekinematic range. A detector package consisting of ho-doscope planes, wire chambers, a gas Cerenkov counter,and a lead glass calorimeter allowed for particle identifi-cation and measurement of the event kinematics.

Approximately 160 million scattering events wererecorded on the proton target, resulting in highly precise

determinations of the parallel and perpendicular asym-metries. These are obtained from observed raw eventcounting asymmetries which are scaled to 100% polar-ization and corrected for contamination from radiativeand dilution processes:

A =1

fCNPbPtfRC#

N' " N+

N' + N++ ARC

Here, N± is the charge corrected observed count ratefor the parallel (perpendicular) and anti-parallel (anti-perpendicular) spin alignment, respectively. Pb and Pt

are the beam and target polarizations, f is the dilutionfactor, CN is a small 15N nuclear correction, and fRC

and ARC are radiative corrections.

FIG. 1: Our measured beam–target asymmetries A! andA", fully corrected (points) and without radiative corrections(curves).

The corrected asymmetries A! and A" are shown inFig. 1. The average proton polarization was 62% (70%),and the beam polarization was around 71% (66%) dur-ing the parallel (perpendicular) running. A summary ofthe average systematic errors is shown in Table I, high-lighting the lack of models and data for perpendicularradiative corrections.

A! A"

Target Polarization 2.9 %Beam Polarization

!

1.1 %1.3 %

Dilution Factor 4.9 % 4.9 %Radiative Corrections 2.7 % 12.9 %Kinematic Reconstruction 0.4 % 0.4 %

TABLE I: Averaged Systematic Errors in the Asymmetries.

For the parallel alignment, the product Pb # Pt wasderived by normalizing the measured elastic asymmetry[14] to the known value, resulting in better accuracy thanachievable from direct measurements. In the perpendic-ular case, the limited knowledge of the elastic asymmetrymade the direct measurement the better choice.

The dilution factor represents the fraction of eventsthat truly scattered from a polarized proton in the tar-get. It was determined from the ratio of free proton to

2

providing a clean test of the theory. Quark-gluon in-teractions reflected in the twist-3 terms are also visiblein the related A2 asymmetry in the form of a 1/Q evo-lution. Each higher order of twist, interpretable as in-creased correlation between partons, adds another 1/Qterm, so their contribution should be more prominent atlow Q2.

Experiment E01-006 was conducted over six weeks inHall C of the Thomas Je!erson National Accelerator Fa-cility. Utilizing established procedures and equipment,we have measured the asymmetries A! and A" in thescattering of polarized electrons o! a polarized protontarget at Q2 ! 1.3 GeV2. These asymmetries are definedas the dimensionless, relative di!erence between the crosssections with parallel and anti-parallel (or perpendicularand anti-perpendicular) alignment of the proton and theelectron spins:

A|| =d!#$ " d!$$

d!#$ + d!$$A" =

d!#% " d!$%

d!#% + d!$%

The experiment used Je!erson Lab’s continuous, po-larized electron beam with energy of 5.755 GeV and anominal current of 100 nA. The beam polarization wasmeasured by a Møller polarimeter [11] installed upstreamof the target. The beam helicity was flipped at 30 Hzon a pseudo-random basis. False asymmetries or biaswere further minimized by actively correcting for anybeam charge asymmetry, and accounting for the mea-sured residual of < 0.1% (absolute).

Frozen 15NH3, in 1" 2 mm fragments, was used asthe proton target in the University of Virginia appara-tus [12] in which a 4He evaporation refrigerator at 1 Kcoupled with a 5 T polarizing magnet created a stablepolarization environment. The polarization populationenhancement was achieved via a dynamic nuclear polar-ization technique and measured by an NMR system usingpickup coils embedded in the target material. For the A"

measurement, the entire target apparatus was rotated by90&. To reduce systematic e!ects, about equal amountsof data were taken with each polarization directions byflipping the nuclear spin. To maintain uniform polariza-tion in the bulk target material, the beam was continuallymoved across the face of the target in a 1 cm maximumradius spiral raster pattern around the beam axis. Thisextra degree of freedom required a dedicated beam posi-tion monitor [13] for accurate event reconstruction.

Scattered electrons were detected using the High Mo-mentum Spectrometer (HMS), positioned at a scatteringangle of 13.15&. Two di!erent HMS momentum settingswere used, 4.078 and 4.703 GeV, to cover the desired widekinematic range. A detector package consisting of ho-doscope planes, wire chambers, a gas Cerenkov counter,and a lead glass calorimeter allowed for particle identifi-cation and measurement of the event kinematics.

Approximately 160 million scattering events wererecorded on the proton target, resulting in highly precise

determinations of the parallel and perpendicular asym-metries. These are obtained from observed raw eventcounting asymmetries which are scaled to 100% polar-ization and corrected for contamination from radiativeand dilution processes:

A =1

fCNPbPtfRC#

N' " N+

N' + N++ ARC

Here, N± is the charge corrected observed count ratefor the parallel (perpendicular) and anti-parallel (anti-perpendicular) spin alignment, respectively. Pb and Pt

are the beam and target polarizations, f is the dilutionfactor, CN is a small 15N nuclear correction, and fRC

and ARC are radiative corrections.

FIG. 1: Our measured beam–target asymmetries A! andA", fully corrected (points) and without radiative corrections(curves).

The corrected asymmetries A! and A" are shown inFig. 1. The average proton polarization was 62% (70%),and the beam polarization was around 71% (66%) dur-ing the parallel (perpendicular) running. A summary ofthe average systematic errors is shown in Table I, high-lighting the lack of models and data for perpendicularradiative corrections.

A! A"

Target Polarization 2.9 %Beam Polarization

!

1.1 %1.3 %

Dilution Factor 4.9 % 4.9 %Radiative Corrections 2.7 % 12.9 %Kinematic Reconstruction 0.4 % 0.4 %

TABLE I: Averaged Systematic Errors in the Asymmetries.

For the parallel alignment, the product Pb # Pt wasderived by normalizing the measured elastic asymmetry[14] to the known value, resulting in better accuracy thanachievable from direct measurements. In the perpendic-ular case, the limited knowledge of the elastic asymmetrymade the direct measurement the better choice.

The dilution factor represents the fraction of eventsthat truly scattered from a polarized proton in the tar-get. It was determined from the ratio of free proton to

2

providing a clean test of the theory. Quark-gluon in-teractions reflected in the twist-3 terms are also visiblein the related A2 asymmetry in the form of a 1/Q evo-lution. Each higher order of twist, interpretable as in-creased correlation between partons, adds another 1/Qterm, so their contribution should be more prominent atlow Q2.

Experiment E01-006 was conducted over six weeks inHall C of the Thomas Je!erson National Accelerator Fa-cility. Utilizing established procedures and equipment,we have measured the asymmetries A! and A" in thescattering of polarized electrons o! a polarized protontarget at Q2 ! 1.3 GeV2. These asymmetries are definedas the dimensionless, relative di!erence between the crosssections with parallel and anti-parallel (or perpendicularand anti-perpendicular) alignment of the proton and theelectron spins:

A|| =d!#$ " d!$$

d!#$ + d!$$A" =

d!#% " d!$%

d!#% + d!$%

The experiment used Je!erson Lab’s continuous, po-larized electron beam with energy of 5.755 GeV and anominal current of 100 nA. The beam polarization wasmeasured by a Møller polarimeter [11] installed upstreamof the target. The beam helicity was flipped at 30 Hzon a pseudo-random basis. False asymmetries or biaswere further minimized by actively correcting for anybeam charge asymmetry, and accounting for the mea-sured residual of < 0.1% (absolute).

Frozen 15NH3, in 1" 2 mm fragments, was used asthe proton target in the University of Virginia appara-tus [12] in which a 4He evaporation refrigerator at 1 Kcoupled with a 5 T polarizing magnet created a stablepolarization environment. The polarization populationenhancement was achieved via a dynamic nuclear polar-ization technique and measured by an NMR system usingpickup coils embedded in the target material. For the A"

measurement, the entire target apparatus was rotated by90&. To reduce systematic e!ects, about equal amountsof data were taken with each polarization directions byflipping the nuclear spin. To maintain uniform polariza-tion in the bulk target material, the beam was continuallymoved across the face of the target in a 1 cm maximumradius spiral raster pattern around the beam axis. Thisextra degree of freedom required a dedicated beam posi-tion monitor [13] for accurate event reconstruction.

Scattered electrons were detected using the High Mo-mentum Spectrometer (HMS), positioned at a scatteringangle of 13.15&. Two di!erent HMS momentum settingswere used, 4.078 and 4.703 GeV, to cover the desired widekinematic range. A detector package consisting of ho-doscope planes, wire chambers, a gas Cerenkov counter,and a lead glass calorimeter allowed for particle identifi-cation and measurement of the event kinematics.

Approximately 160 million scattering events wererecorded on the proton target, resulting in highly precise

determinations of the parallel and perpendicular asym-metries. These are obtained from observed raw eventcounting asymmetries which are scaled to 100% polar-ization and corrected for contamination from radiativeand dilution processes:

A =1

fCNPbPtfRC#

N' " N+

N' + N++ ARC

Here, N± is the charge corrected observed count ratefor the parallel (perpendicular) and anti-parallel (anti-perpendicular) spin alignment, respectively. Pb and Pt

are the beam and target polarizations, f is the dilutionfactor, CN is a small 15N nuclear correction, and fRC

and ARC are radiative corrections.

FIG. 1: Our measured beam–target asymmetries A! andA", fully corrected (points) and without radiative corrections(curves).

The corrected asymmetries A! and A" are shown inFig. 1. The average proton polarization was 62% (70%),and the beam polarization was around 71% (66%) dur-ing the parallel (perpendicular) running. A summary ofthe average systematic errors is shown in Table I, high-lighting the lack of models and data for perpendicularradiative corrections.

A! A"

Target Polarization 2.9 %Beam Polarization

!

1.1 %1.3 %

Dilution Factor 4.9 % 4.9 %Radiative Corrections 2.7 % 12.9 %Kinematic Reconstruction 0.4 % 0.4 %

TABLE I: Averaged Systematic Errors in the Asymmetries.

For the parallel alignment, the product Pb # Pt wasderived by normalizing the measured elastic asymmetry[14] to the known value, resulting in better accuracy thanachievable from direct measurements. In the perpendic-ular case, the limited knowledge of the elastic asymmetrymade the direct measurement the better choice.

The dilution factor represents the fraction of eventsthat truly scattered from a polarized proton in the tar-get. It was determined from the ratio of free proton to

2

providing a clean test of the theory. Quark-gluon in-teractions reflected in the twist-3 terms are also visiblein the related A2 asymmetry in the form of a 1/Q evo-lution. Each higher order of twist, interpretable as in-creased correlation between partons, adds another 1/Qterm, so their contribution should be more prominent atlow Q2.

Experiment E01-006 was conducted over six weeks inHall C of the Thomas Je!erson National Accelerator Fa-cility. Utilizing established procedures and equipment,we have measured the asymmetries A! and A" in thescattering of polarized electrons o! a polarized protontarget at Q2 ! 1.3 GeV2. These asymmetries are definedas the dimensionless, relative di!erence between the crosssections with parallel and anti-parallel (or perpendicularand anti-perpendicular) alignment of the proton and theelectron spins:

A|| =d!#$ " d!$$

d!#$ + d!$$A" =

d!#% " d!$%

d!#% + d!$%

The experiment used Je!erson Lab’s continuous, po-larized electron beam with energy of 5.755 GeV and anominal current of 100 nA. The beam polarization wasmeasured by a Møller polarimeter [11] installed upstreamof the target. The beam helicity was flipped at 30 Hzon a pseudo-random basis. False asymmetries or biaswere further minimized by actively correcting for anybeam charge asymmetry, and accounting for the mea-sured residual of < 0.1% (absolute).

Frozen 15NH3, in 1" 2 mm fragments, was used asthe proton target in the University of Virginia appara-tus [12] in which a 4He evaporation refrigerator at 1 Kcoupled with a 5 T polarizing magnet created a stablepolarization environment. The polarization populationenhancement was achieved via a dynamic nuclear polar-ization technique and measured by an NMR system usingpickup coils embedded in the target material. For the A"

measurement, the entire target apparatus was rotated by90&. To reduce systematic e!ects, about equal amountsof data were taken with each polarization directions byflipping the nuclear spin. To maintain uniform polariza-tion in the bulk target material, the beam was continuallymoved across the face of the target in a 1 cm maximumradius spiral raster pattern around the beam axis. Thisextra degree of freedom required a dedicated beam posi-tion monitor [13] for accurate event reconstruction.

Scattered electrons were detected using the High Mo-mentum Spectrometer (HMS), positioned at a scatteringangle of 13.15&. Two di!erent HMS momentum settingswere used, 4.078 and 4.703 GeV, to cover the desired widekinematic range. A detector package consisting of ho-doscope planes, wire chambers, a gas Cerenkov counter,and a lead glass calorimeter allowed for particle identifi-cation and measurement of the event kinematics.

Approximately 160 million scattering events wererecorded on the proton target, resulting in highly precise

determinations of the parallel and perpendicular asym-metries. These are obtained from observed raw eventcounting asymmetries which are scaled to 100% polar-ization and corrected for contamination from radiativeand dilution processes:

A =1

fCNPbPtfRC#

N' " N+

N' + N++ ARC

Here, N± is the charge corrected observed count ratefor the parallel (perpendicular) and anti-parallel (anti-perpendicular) spin alignment, respectively. Pb and Pt

are the beam and target polarizations, f is the dilutionfactor, CN is a small 15N nuclear correction, and fRC

and ARC are radiative corrections.

FIG. 1: Our measured beam–target asymmetries A! andA", fully corrected (points) and without radiative corrections(curves).

The corrected asymmetries A! and A" are shown inFig. 1. The average proton polarization was 62% (70%),and the beam polarization was around 71% (66%) dur-ing the parallel (perpendicular) running. A summary ofthe average systematic errors is shown in Table I, high-lighting the lack of models and data for perpendicularradiative corrections.

A! A"

Target Polarization 2.9 %Beam Polarization

!

1.1 %1.3 %

Dilution Factor 4.9 % 4.9 %Radiative Corrections 2.7 % 12.9 %Kinematic Reconstruction 0.4 % 0.4 %

TABLE I: Averaged Systematic Errors in the Asymmetries.

For the parallel alignment, the product Pb # Pt wasderived by normalizing the measured elastic asymmetry[14] to the known value, resulting in better accuracy thanachievable from direct measurements. In the perpendic-ular case, the limited knowledge of the elastic asymmetrymade the direct measurement the better choice.

The dilution factor represents the fraction of eventsthat truly scattered from a polarized proton in the tar-get. It was determined from the ratio of free proton to

2

providing a clean test of the theory. Quark-gluon in-teractions reflected in the twist-3 terms are also visiblein the related A2 asymmetry in the form of a 1/Q evo-lution. Each higher order of twist, interpretable as in-creased correlation between partons, adds another 1/Qterm, so their contribution should be more prominent atlow Q2.

Experiment E01-006 was conducted over six weeks inHall C of the Thomas Je!erson National Accelerator Fa-cility. Utilizing established procedures and equipment,we have measured the asymmetries A! and A" in thescattering of polarized electrons o! a polarized protontarget at Q2 ! 1.3 GeV2. These asymmetries are definedas the dimensionless, relative di!erence between the crosssections with parallel and anti-parallel (or perpendicularand anti-perpendicular) alignment of the proton and theelectron spins:

A|| =d!#$ " d!$$

d!#$ + d!$$A" =

d!#% " d!$%

d!#% + d!$%

The experiment used Je!erson Lab’s continuous, po-larized electron beam with energy of 5.755 GeV and anominal current of 100 nA. The beam polarization wasmeasured by a Møller polarimeter [11] installed upstreamof the target. The beam helicity was flipped at 30 Hzon a pseudo-random basis. False asymmetries or biaswere further minimized by actively correcting for anybeam charge asymmetry, and accounting for the mea-sured residual of < 0.1% (absolute).

Frozen 15NH3, in 1" 2 mm fragments, was used asthe proton target in the University of Virginia appara-tus [12] in which a 4He evaporation refrigerator at 1 Kcoupled with a 5 T polarizing magnet created a stablepolarization environment. The polarization populationenhancement was achieved via a dynamic nuclear polar-ization technique and measured by an NMR system usingpickup coils embedded in the target material. For the A"

measurement, the entire target apparatus was rotated by90&. To reduce systematic e!ects, about equal amountsof data were taken with each polarization directions byflipping the nuclear spin. To maintain uniform polariza-tion in the bulk target material, the beam was continuallymoved across the face of the target in a 1 cm maximumradius spiral raster pattern around the beam axis. Thisextra degree of freedom required a dedicated beam posi-tion monitor [13] for accurate event reconstruction.

Scattered electrons were detected using the High Mo-mentum Spectrometer (HMS), positioned at a scatteringangle of 13.15&. Two di!erent HMS momentum settingswere used, 4.078 and 4.703 GeV, to cover the desired widekinematic range. A detector package consisting of ho-doscope planes, wire chambers, a gas Cerenkov counter,and a lead glass calorimeter allowed for particle identifi-cation and measurement of the event kinematics.

Approximately 160 million scattering events wererecorded on the proton target, resulting in highly precise

determinations of the parallel and perpendicular asym-metries. These are obtained from observed raw eventcounting asymmetries which are scaled to 100% polar-ization and corrected for contamination from radiativeand dilution processes:

A =1

fCNPbPtfRC#

N' " N+

N' + N++ ARC

Here, N± is the charge corrected observed count ratefor the parallel (perpendicular) and anti-parallel (anti-perpendicular) spin alignment, respectively. Pb and Pt

are the beam and target polarizations, f is the dilutionfactor, CN is a small 15N nuclear correction, and fRC

and ARC are radiative corrections.

FIG. 1: Our measured beam–target asymmetries A! andA", fully corrected (points) and without radiative corrections(curves).

The corrected asymmetries A! and A" are shown inFig. 1. The average proton polarization was 62% (70%),and the beam polarization was around 71% (66%) dur-ing the parallel (perpendicular) running. A summary ofthe average systematic errors is shown in Table I, high-lighting the lack of models and data for perpendicularradiative corrections.

A! A"

Target Polarization 2.9 %Beam Polarization

!

1.1 %1.3 %

Dilution Factor 4.9 % 4.9 %Radiative Corrections 2.7 % 12.9 %Kinematic Reconstruction 0.4 % 0.4 %

TABLE I: Averaged Systematic Errors in the Asymmetries.

For the parallel alignment, the product Pb # Pt wasderived by normalizing the measured elastic asymmetry[14] to the known value, resulting in better accuracy thanachievable from direct measurements. In the perpendic-ular case, the limited knowledge of the elastic asymmetrymade the direct measurement the better choice.

The dilution factor represents the fraction of eventsthat truly scattered from a polarized proton in the tar-get. It was determined from the ratio of free proton to

2

providing a clean test of the theory. Quark-gluon in-teractions reflected in the twist-3 terms are also visiblein the related A2 asymmetry in the form of a 1/Q evo-lution. Each higher order of twist, interpretable as in-creased correlation between partons, adds another 1/Qterm, so their contribution should be more prominent atlow Q2.

Experiment E01-006 was conducted over six weeks inHall C of the Thomas Je!erson National Accelerator Fa-cility. Utilizing established procedures and equipment,we have measured the asymmetries A! and A" in thescattering of polarized electrons o! a polarized protontarget at Q2 ! 1.3 GeV2. These asymmetries are definedas the dimensionless, relative di!erence between the crosssections with parallel and anti-parallel (or perpendicularand anti-perpendicular) alignment of the proton and theelectron spins:

A|| =d!#$ " d!$$

d!#$ + d!$$A" =

d!#% " d!$%

d!#% + d!$%

The experiment used Je!erson Lab’s continuous, po-larized electron beam with energy of 5.755 GeV and anominal current of 100 nA. The beam polarization wasmeasured by a Møller polarimeter [11] installed upstreamof the target. The beam helicity was flipped at 30 Hzon a pseudo-random basis. False asymmetries or biaswere further minimized by actively correcting for anybeam charge asymmetry, and accounting for the mea-sured residual of < 0.1% (absolute).

Frozen 15NH3, in 1" 2 mm fragments, was used asthe proton target in the University of Virginia appara-tus [12] in which a 4He evaporation refrigerator at 1 Kcoupled with a 5 T polarizing magnet created a stablepolarization environment. The polarization populationenhancement was achieved via a dynamic nuclear polar-ization technique and measured by an NMR system usingpickup coils embedded in the target material. For the A"

measurement, the entire target apparatus was rotated by90&. To reduce systematic e!ects, about equal amountsof data were taken with each polarization directions byflipping the nuclear spin. To maintain uniform polariza-tion in the bulk target material, the beam was continuallymoved across the face of the target in a 1 cm maximumradius spiral raster pattern around the beam axis. Thisextra degree of freedom required a dedicated beam posi-tion monitor [13] for accurate event reconstruction.

Scattered electrons were detected using the High Mo-mentum Spectrometer (HMS), positioned at a scatteringangle of 13.15&. Two di!erent HMS momentum settingswere used, 4.078 and 4.703 GeV, to cover the desired widekinematic range. A detector package consisting of ho-doscope planes, wire chambers, a gas Cerenkov counter,and a lead glass calorimeter allowed for particle identifi-cation and measurement of the event kinematics.

Approximately 160 million scattering events wererecorded on the proton target, resulting in highly precise

determinations of the parallel and perpendicular asym-metries. These are obtained from observed raw eventcounting asymmetries which are scaled to 100% polar-ization and corrected for contamination from radiativeand dilution processes:

A =1

fCNPbPtfRC#

N' " N+

N' + N++ ARC

Here, N± is the charge corrected observed count ratefor the parallel (perpendicular) and anti-parallel (anti-perpendicular) spin alignment, respectively. Pb and Pt

are the beam and target polarizations, f is the dilutionfactor, CN is a small 15N nuclear correction, and fRC

and ARC are radiative corrections.

FIG. 1: Our measured beam–target asymmetries A! andA", fully corrected (points) and without radiative corrections(curves).

The corrected asymmetries A! and A" are shown inFig. 1. The average proton polarization was 62% (70%),and the beam polarization was around 71% (66%) dur-ing the parallel (perpendicular) running. A summary ofthe average systematic errors is shown in Table I, high-lighting the lack of models and data for perpendicularradiative corrections.

A! A"

Target Polarization 2.9 %Beam Polarization

!

1.1 %1.3 %

Dilution Factor 4.9 % 4.9 %Radiative Corrections 2.7 % 12.9 %Kinematic Reconstruction 0.4 % 0.4 %

TABLE I: Averaged Systematic Errors in the Asymmetries.

For the parallel alignment, the product Pb # Pt wasderived by normalizing the measured elastic asymmetry[14] to the known value, resulting in better accuracy thanachievable from direct measurements. In the perpendic-ular case, the limited knowledge of the elastic asymmetrymade the direct measurement the better choice.

The dilution factor represents the fraction of eventsthat truly scattered from a polarized proton in the tar-get. It was determined from the ratio of free proton to

2

providing a clean test of the theory. Quark-gluon in-teractions reflected in the twist-3 terms are also visiblein the related A2 asymmetry in the form of a 1/Q evo-lution. Each higher order of twist, interpretable as in-creased correlation between partons, adds another 1/Qterm, so their contribution should be more prominent atlow Q2.

Experiment E01-006 was conducted over six weeks inHall C of the Thomas Je!erson National Accelerator Fa-cility. Utilizing established procedures and equipment,we have measured the asymmetries A! and A" in thescattering of polarized electrons o! a polarized protontarget at Q2 ! 1.3 GeV2. These asymmetries are definedas the dimensionless, relative di!erence between the crosssections with parallel and anti-parallel (or perpendicularand anti-perpendicular) alignment of the proton and theelectron spins:

A|| =d!#$ " d!$$

d!#$ + d!$$A" =

d!#% " d!$%

d!#% + d!$%

The experiment used Je!erson Lab’s continuous, po-larized electron beam with energy of 5.755 GeV and anominal current of 100 nA. The beam polarization wasmeasured by a Møller polarimeter [11] installed upstreamof the target. The beam helicity was flipped at 30 Hzon a pseudo-random basis. False asymmetries or biaswere further minimized by actively correcting for anybeam charge asymmetry, and accounting for the mea-sured residual of < 0.1% (absolute).

Frozen 15NH3, in 1" 2 mm fragments, was used asthe proton target in the University of Virginia appara-tus [12] in which a 4He evaporation refrigerator at 1 Kcoupled with a 5 T polarizing magnet created a stablepolarization environment. The polarization populationenhancement was achieved via a dynamic nuclear polar-ization technique and measured by an NMR system usingpickup coils embedded in the target material. For the A"

measurement, the entire target apparatus was rotated by90&. To reduce systematic e!ects, about equal amountsof data were taken with each polarization directions byflipping the nuclear spin. To maintain uniform polariza-tion in the bulk target material, the beam was continuallymoved across the face of the target in a 1 cm maximumradius spiral raster pattern around the beam axis. Thisextra degree of freedom required a dedicated beam posi-tion monitor [13] for accurate event reconstruction.

Scattered electrons were detected using the High Mo-mentum Spectrometer (HMS), positioned at a scatteringangle of 13.15&. Two di!erent HMS momentum settingswere used, 4.078 and 4.703 GeV, to cover the desired widekinematic range. A detector package consisting of ho-doscope planes, wire chambers, a gas Cerenkov counter,and a lead glass calorimeter allowed for particle identifi-cation and measurement of the event kinematics.

Approximately 160 million scattering events wererecorded on the proton target, resulting in highly precise

determinations of the parallel and perpendicular asym-metries. These are obtained from observed raw eventcounting asymmetries which are scaled to 100% polar-ization and corrected for contamination from radiativeand dilution processes:

A =1

fCNPbPtfRC#

N' " N+

N' + N++ ARC

Here, N± is the charge corrected observed count ratefor the parallel (perpendicular) and anti-parallel (anti-perpendicular) spin alignment, respectively. Pb and Pt

are the beam and target polarizations, f is the dilutionfactor, CN is a small 15N nuclear correction, and fRC

and ARC are radiative corrections.

FIG. 1: Our measured beam–target asymmetries A! andA", fully corrected (points) and without radiative corrections(curves).

The corrected asymmetries A! and A" are shown inFig. 1. The average proton polarization was 62% (70%),and the beam polarization was around 71% (66%) dur-ing the parallel (perpendicular) running. A summary ofthe average systematic errors is shown in Table I, high-lighting the lack of models and data for perpendicularradiative corrections.

A! A"

Target Polarization 2.9 %Beam Polarization

!

1.1 %1.3 %

Dilution Factor 4.9 % 4.9 %Radiative Corrections 2.7 % 12.9 %Kinematic Reconstruction 0.4 % 0.4 %

TABLE I: Averaged Systematic Errors in the Asymmetries.

For the parallel alignment, the product Pb # Pt wasderived by normalizing the measured elastic asymmetry[14] to the known value, resulting in better accuracy thanachievable from direct measurements. In the perpendic-ular case, the limited knowledge of the elastic asymmetrymade the direct measurement the better choice.

The dilution factor represents the fraction of eventsthat truly scattered from a polarized proton in the tar-get. It was determined from the ratio of free proton to

• D’(E, E’, $,R) are functions of kinematic variables and

• A1 and A2 are extracted from the measured A|| , A⊥ and the fit of R (obtained from JLab data) by M.E. Christy

• Determination of A1 and A2 in a model independent way (RSS is the only experiment which measured both A|| and

A⊥ on protons and deuterons in the resonance region)

25

How to get Spin Asymmetries A1 and A2

3

total target rates calculated via a Monte Carlo simula-tion which had been matched to calibration data acquiredspecifically for this purpose. The QFS parameterization[15], modified to improve agreement with our data, wasused as input for the unradiated (Born) inelastic crosssections for A ! 3 nuclei. Fits to Hall C inelastic e–p

data [16] were used for the H contribution.Convoluting radiative prescriptions with models of the

resonance region, the elastic peak, and our target, weobtained radiated cross sections and asymmetries. Theexternal radiative corrections were determined using theprocedure established in [17], while the POLRAD soft-ware [18] was used to determine the internal radiativecorrections. The resonance fit model was iteratively im-proved, until the radiated values matched our experimen-tal data. The model then trivially provided the correc-tions required to unradiate our measurements, with fRC

accounting for the radiative dilution from the elastic tailand ARC for all other influences.

FIG. 2: Virtual photon asymmetries Ap

1and Ap

2from our

data and corresponding fits, as well as the E155 fit to DISdata [19, 20], evaluated at our (x, Q2). The upper error bandindicates the systematic error in A1, the lower one A2.

From the corrected physics asymmetries A|| and A!,we extracted the virtual photon asymmetries A1 and A2,shown in Fig. 2,

A1 =1

(E+E")D"

!

(E"E"cos !)A|| "E" sin !

cos"A!

"

A2 =

#

Q2

2ED"

!

A|| +E " E" cos !

E" sin ! cos"A!

"

and the spin structure functions g1 and g2 (Figs. 3 and 4):

g1 =F1

1 + #2(#A2 + A1) g2 =

F1

1 + #2

!A2

#" A1

"

We used the standard definitions D" = (1"$)/(1+$R),$#1 = 1+2(1+##2) tan2 !

2 , R = %L/%T , and # =#

Q2/&,with ! and " as the polar and azimuthal electron scatter-ing angles. This extraction (and the previously discussedmodel calculations) utilized the unpolarized quantities F1

and R from recent fits to other Je!erson Lab data [16, 21];

these fits’ uncertainty is included in our total systematicerror and in the error bands of our plots.

FIG. 3: Results for g1 from this experiment (RSS) and otherrelevant data, as well as target mass corrected NLO PDFs.

FIG. 4: Our values for g2 and the approximation gWW

2 [26] asevaluated from our data.

We have fitted the W dependence of our A1 and A2

data using an approach similar to that applied to in-elastic inclusive unpolarized cross sections in Ref. [17].These fits served as input in the iterative procedure toobtain our radiative corrections and to calculate the in-tegral of g1 at constant Q2. For the resonances we usedfour Breit-Wigner shapes with amplitudes, centroids, andwidths as fit parameters. Other parameters used to de-scribe the nucleon resonances were kept at the valuesindicated in [17]. The DIS component of the fit is de-scribed by a form based on previous phenomenologicalparameterizations of the spin structure [19, 20]. Eachspin asymmetry was fitted independently, since they rep-resent di!erent physical quantities. The choice of fourresonances resulted in better fits than using only three,an option also supported by examining the second deriva-tives of the data smoothed with a spline curve.

Global duality can be tested quantitatively by inte-grating in x over the resonance region and comparing theresults obtained from resonance data and DIS extrapola-tions. We have computed the integral of g1 using our fitover the four resonance regions and compared the resultto the integrals over DIS extrapolations calculated from

R = !L/!T

26

!"#$#%$#&'$()%#%*$+,-.

! !%/)$0)'"#12"3*')$)'.%*4*5'$.&46'.$67/.$89+$:45;3)%/*<$

! !"#$,=$4*<$,

>$"*<'6'*<'*#7?

! @'</5'<$">$A$=BC$1$=BD$$E%)$=>$<B%BEB

!"#$#%$#&'$()%#%*$+,-.

! !%/)$0)'"#12"3*')$)'.%*4*5'$.&46'.$67/.$89+$:45;3)%/*<$

! !"#$,=$4*<$,

>$"*<'6'*<'*#7?

! @'</5'<$">$A$=BC$1$=BD$$E%)$=>$<B%BEB

!"#$#%$#&'$()%#%*$+,-.

! !%/)$0)'"#12"3*')$)'.%*4*5'$.&46'.$67/.$89+$:45;3)%/*<$

! !"#$,=$4*<$,

>$"*<'6'*<'*#7?

! @'</5'<$">$A$=BC$1$=BD$$E%)$=>$<B%BEB

!"#$#%$#&'$()%#%*$+,-.

! !%/)$0)'"#12"3*')$)'.%*4*5'$.&46'.$67/.$89+$:45;3)%/*<$

! !"#$,=$4*<$,

>$"*<'6'*<'*#7?

! @'</5'<$">$A$=BC$1$=BD$$E%)$=>$<B%BEB

!"#$#%$#&'$()%#%*$+,-.

! !%/)$0)'"#12"3*')$)'.%*4*5'$.&46'.$67/.$89+$:45;3)%/*<$

! !"#$,=$4*<$,

>$"*<'6'*<'*#7?

! @'</5'<$">$A$=BC$1$=BD$$E%)$=>$<B%BEB

!"#$#%$#&'$()%#%*$+,-.

! !%/)$0)'"#12"3*')$)'.%*4*5'$.&46'.$67/.$89+$:45;3)%/*<$

! !"#$,=$4*<$,

>$"*<'6'*<'*#7?

! @'</5'<$">$A$=BC$1$=BD$$E%)$=>$<B%BEB

27

How to get spin structure functions

g1 and g2

• g1 and g2 are extracted from the measured

A1 and A2 using the JLab F2 and R fits by M.E. Christy (to be published)

g2 =F1

1 + !2(A2/! ! A1)

g1 =F1

1 + !2(A1 + !A2)

! =

!

Q2

"2

F1 = F2(1 + !2 )/2x/(1 + R)

Q2 Dependence of Global Duality

28

Q2 (GeV

2)

0.50 1.00 1.50 2.00 2.50 3.00

I (

Re

s/D

IS)

of

g1

0.00

0.50

1.00

1.50

2.00

2.50

RSS M<W <1.91 GeV

RSS 1.08<W <1.91 GeV

eg1a M<W <2 GeV (from M.E.K.)

eg1b resonances

eg1b resonances + elastic

}Res. only

}Res.+ elastic

29

Systematic Uncertainties

Proton A|| Proton A⊥

Target Polarization

} 1.1%

2.9 %

Beam Polarization 1.3 %

Dilution Factor 4.9 % 4.9 %

Radiative Corrections 2.7 % 12.9 %

Kinematic Reconstruction 0.4 % 0.4%

Total 5.7% 14.2%

30

Effect of Smearing (I)

• Proton data fit and Paris W.F. for the deuteron were used to smear the proton cross sections.

1 1.2 1.4 1.6 1.8 2W (GeV)

-0.02

0

0.02

0.04

0.06

0.08

dsigma para & perp SMEARED (15MeV bin)FILE: psmear_all_dw15.dat (May31)

W(GeV)

!!p

!

!!ps

!

!!ps

!

!!p

!

Preliminary

0.3 0.4 0.5 0.6 0.7 0.8Xbj

-0.1

0

0.1

0.2 g1p (data)g1p (smeared)g2p (data)g2p (smeared)

31

Effect of Smearing (II)

• g1p and g2p before and after smearing

Preliminary