AAC Global Analysis

AAC Global AnalysisAAC Global Analysis

Shunzo KumanoShunzo Kumano

High Energy Accelerator Research Organization (KEK) High Energy Accelerator Research Organization (KEK)

Graduate University for Advanced Studies (GUAS)Graduate University for Advanced Studies (GUAS)

June 16, 2008June 16, 2008

[email protected]@kek.jp

http://research.kek.jp/people/kumanos/http://research.kek.jp/people/kumanos/

Illinois-MIT-RBRC Workshop on Gluon Polarization in the NucleonIllinois-MIT-RBRC Workshop on Gluon Polarization in the NucleonJune 16-17, 2008, Urbana, Illinois, U.S.A.June 16-17, 2008, Urbana, Illinois, U.S.A.http://npl.uiuc.edu/phenix/conferences/Gluon_Spin_jun_2008/http://npl.uiuc.edu/phenix/conferences/Gluon_Spin_jun_2008/

AAC: AAC: http://spin.riken.bnl.gov/aachttp://spin.riken.bnl.gov/aac//

ContentsContents

Introduction to polarized PDFs Global analysis of longitudinally polarized PDFs

Polarized PDFs of AACAAC (Asymmetry Analysis Collaboration)

Papers on polarized PDFsPapers on polarized PDFsT. Gehrmann and W. J. Stirling, Z. Phys. C65 (1995) 461; Phys. Rev. D53 (1996) 6100.

D. de Florian, L. N. Epele, H. Fanchiotti, C. A. Garcia Canal, and R. Sassot (+G. A. Navarro), Phys. Rev. D51 (1995) 37; D57 (1998) 5803; D62 (2000) 094025; D71 (2005) 094018.

M. Glück, E. Reya, M. Stratmann, and W. Vogelsang, Phys. Lett. B359 (1995) 201; Phys. Rev. D53 (1996) 4775; D63 (2001) 094005.

D. de Florian, R. Sassot, M. Stratmann, and W. Vogelsang, arXiv:0804.0422 [hep-ph].

G. Altarelli, R. D. Ball, S. Forte, and G. Ridolfi, Nucl. Phys. B496 (1997) 337; Acta Phys. Pol. B29 (1998) 1145.

C. Bourrely, F. Buccella, O. Pisanti, P. Santorelli, and J. Soffer, Prog. Theor. Phys. 99 (1998) 1017; Eur. Phys. J. C23 (2002) 487; C41 (2005) 327; Phys. Lett. B648 (2007) 39.

L. E. Gordon, M. Goshtasbpour, and G. P. Ramsey, Phys. Rev. D58 (1998) 094017.

SMC (B. Adeva et al.), Phys. Rev. D58 (1998) 112002.

E. Leader, A. V. Sidrov, and D. B. Stamenov, Phys. Rev. D58 (1998) 114028; Eur. Phys. J. C23 (2002) 479; PRD67 (2003) 074017; JHEP 0506 (2005) 033; PRD73 (2006) 034023; D75 (2007) 074027.

AAC (Y. Goto et al., M. Hirai et al.), PRD62 (2000) 034017; D69 (2004) 054021; D74 (2006) 014015.

J. Bartelski and S. Tatur, Phys. Rev. D65 (2002) 034002.

J. Blümlein and H. Böttcher, Nucl. Phys. B636 (2002) 225.

It is likely that I miss some papers!(Analyses of experimental groups)

Situation of data for polarized PDFs

Neutrino factory: ~10 years later

Small-x: EIC (eRHIC, ELIC) ?

Charm: EIC (eRHIC, ELIC) ?

RHIC

pp: RHIC

RHIC-Spin program should play an important role in determining polarized PDFs.

J-PARC GSI-FAIR

(MRST, hep/ph-9803445)

(from H1 and ZEUS, hep-ex/0502008)

F2 datafor the proton

0.01

0.1

1

10

0.7 1 10 100 200

Q2[GeV2]

E130

E143

E155

EMC

SMC

HERMES

x = 0.75

x = 0.66

x = 0.55

x = 0.50

x = 0.35

x = 0.25

x = 0.175

x = 0.125

x = 0.08

x = 0.025

x = 0.007

x = 0.05

x = 0.45

[AAC, PRD74 (2006) 014015]

It may be possible to remove small QIt may be possible to remove small Q22 data datain an analysis of unpolarized PDFs, whereasin an analysis of unpolarized PDFs, whereasit is difficult to remove them in git is difficult to remove them in g11 (or A (or A11). ).

x =0.65

x =0.013

x =0.0005

Comments on the previous figureComments on the previous figure

g lack of small-x data → makesthedeterminationoflimx→ 0

Δq(x)difficult

→ quarkspincontentcannotbewelldetermined

g lack of data in a wide range of Q2 at small x

→ makesthedeterminationofΔg(x)difficult

→ gluoncontributiontotheprotonspincannotbedetermined

g lack of data in a wide range of Q2

→ difficulttoremovethesmallQ2 (<4GeV2 )data,whichmaycontainhigher-twisteffects,fromtheanlysisdataset

Three publications:Three publications:(AAC00) Y. Goto (AAC00) Y. Goto et al.et al., Phys. Rev. D62 (2000) 034017., Phys. Rev. D62 (2000) 034017.(AAC03) M. Hirai, S. Kumano, N. Saito, Phys. Rev. D69 (2004) 05402(AAC03) M. Hirai, S. Kumano, N. Saito, Phys. Rev. D69 (2004) 054021;1;(AAC06) D74 (2006(AAC06) D74 (2006) 014015.) 014015.

Original Members:Original Members: Y. Goto, N. Hayashi, Y. Goto, N. Hayashi, M. Hirai,M. Hirai, H. Horikawa,H. Horikawa, S. Kumano, M. Miyama, T. Morii,S. Kumano, M. Miyama, T. Morii, N. Saito, N. Saito, T.-A. Shibata, E. Taniguchi, T.-A. Shibata, E. Taniguchi, T. YamanishiT. Yamanishi

(Theorist, Experimentalist)

http://spin.riken.bnl.gov/aachttp://spin.riken.bnl.gov/aac//

Asymmetry Analysis Collaboration (AAC) Asymmetry Analysis Collaboration (AAC)

Active members nowActive members now

2000 version (AAC00) - Q2 dependence of A1, positivity - Δq at small and large x Δ issue2004 version (AAC03) - uncertainty estimation (very large Δg uncertainty, impact of accurate g1

p (E155)) - error correlation between Δg and Δq2006 version (AAC06) - include RHIC-Spin 0 (Δg uncertainty is significantly reduced) - Δg at large x ? (Q2 difference between HERMES and COMPASS) - Δg < 0 solution at x < 0.12008 ? - effects of future JLab data (g1

d) on Δg

σ λ+λN∝ ε λ

μ∗ε λνWμν (λ N ) : photoabsorption cross section

A1 ≡

σ1 2 −σ 3 2

σ1 2 +σ 3 2

=MνG1 −Q2G2

M 3W1

;g1

F1

=g1

2x 1+ R( )F2

νM 2

G1 = g1

ν 2

M 2G2 = g2

MW1 =F1

R ≡FL

2xF1

=F2 −2xF1

2xF1

General strategies for determining polarized PDFsGeneral strategies for determining polarized PDFs

g1(x,Q2 ) =12

eq2

q∑ dy

yx

1

∫ Δq(x / y,Q2 ) + Δq(x / y,Q2 )⎡⎣ ⎤⎦ δ(1−y) +αs(Q

2 )2

ΔCq(y) +⋅⋅⋅⎡

⎣⎢

⎤

⎦⎥

+12

eq2 dy

yx

1

∫ Δg(x / y,Q2 ) nf

αs(Q2 )

2ΔCg(y) +⋅⋅⋅

⎡

⎣⎢

⎤

⎦⎥ eq

2 =1nf

eq2

q∑

Leading Order (LO) Next to Leading Order (NLO)

ΔCq (ΔCg ) = quark (gluon) coefficient function

F2 (x,Q2 ) =x eq2

q∑ dy

yx

1

∫ q(x / y,Q2 ) +q(x / y,Q2 )⎡⎣ ⎤⎦ δ(1−y) +αs(Q

2 )2

Cq(2)(y) +⋅⋅⋅

⎡

⎣⎢

⎤

⎦⎥

+ x eq2 dy

y

x

1

∫ g(x / y,Q2 ) nf

αs(Q2 )

2Cg

(2)(y) +⋅⋅⋅⎡

⎣⎢

⎤

⎦⎥

Unpolarized PDFsR(x,Q2 ) : taken from experimental measurements

Initial distributionsInitial distributions Δfi(x,Q0

2) =A i xα i (1 + γi xλ i) fi(x,Q02)

i =uv, dv, q, g A i , α i , γ i , λ i : parameters

χ2 fit to the data [p, n (3He), d]

A 1 ∼

g1

F1=g1

2x (1+R)F2

R =

FL

2xF1=

F2 – 2xF1

2xF1

χ2 =Σ

i

(A 1 idata– A 1 i

calc)2

(σA 1i

data)2

We analyzed the data with the following conditions.

• unpolarized PDF GRV98• initial Q2 Q0

2 = 1 GeV 2

• number of flavor Nf = 3

• positivity Δf(x) ≤f(x) (tobeprecise, Δσ ≤σ)• antiquarkflavor: Δu=Δd=Δs

(1) Δq(x,Q02 ), Δq(x,Q0

2 ), Δg(x,Q02 ) : expressedintermsofparameters

→ evolvethemtoexperimentalQ2points

→ calculateg1

(2) q(x,Q2 ), q(x,Q2 ), g(x,Q2 ) : calculated by a library code of typical unpolarized PDFs

→ calculateF2

(3) R(x,Q2 ) : typical parametrization for explaining experimental data

(e.g. SLAC parametrization)

(4) calculate A1theo =g1

2x 1+ R( )F2

, thenχ 2 =(A1i

exp −A1itheo)2

σ A1i

2i∑

(5) parameters are determined so as to minimize χ 2

Analysis procedureAnalysis procedure

AAC00AAC00

(Some Highlights)(Some Highlights)

Actual fit to AActual fit to A1 1 datadata

(AAC00)(AAC00)

-0.4

-0.2

0

0.2

0.4

0.6

0.8

0.001 0.01 0.1 1

x

LO

NLO

E142

E154

HERMES

Q2

= 5 GeV2

-0.4

-0.2

0

0.2

0.4

0.6

0.8

0.001 0.01 0.1 1

A1

d

x

LO

NLO

E143

E155

SMC

Q2

= 5 GeV2

-0.2

0

0.2

0.4

0.6

0.8

0.001 0.01 0.1 1

A1p

x

LO

NLO

E130

E143

EMC

SMC

HERMES

Q2 = 5 GeV

2

““neutron”neutron”

protonproton

deuterondeuteron

QQ22 dependence of A dependence of A11 Q2 independence assumption was sometimes used for getting g1 from A1 data.

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.5 1 10 100

A1

p

Q2(GeV2)

LO

NLO

E143

SMC

HERMESx = 0.117

A1 is Q2 dependent especially at small Q2 (< 2 GeV2).

The lack of accurate Q2 dependent data at small x makes the determination of Δg very difficult.

Figure from AAC00 analysis

““Spin content” Spin content” ΔΔ

∫ Δ=Δ1

minmin

)()(x

dxxx

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.000001 0.00001 0.0001 0.001 0.01 0.1 1

xmin

SMC

LSS

αq16

αq10

αq05

AAC (αq : free)

Δqq

∝ xα

q (x → 0)

(from AAC00)

AAC03AAC03

(Some Highlights) (Some Highlights)

Error estimationError estimation Hessian method

χ2() is expanded around its minimum 0 ( =parameter)

where the Hessian matrix is defined by

€

χ 2(ξ0 + δξ ) = χ 2(ξ0) +∂χ 2(ξ0)

∂ξ i

δξ ii

∑ +12

∂ 2χ 2 (ξ0 )∂ξ i∂ξ j

δξ iδξ ji, j∑ + ⋅⋅⋅

In the χ2 analysis, 1σ standard error is

The error of a distribution F(x) is given by

Hij =1

2∂2 χ2(a0)∂ ξi ∂ ξ j

Δ χ2 = χ2(ξ0+δ ξ) − χ2(ξ0) = δ ξi Hij δ ξ j∑i, j

δ F( x)

2=Δ χ2 ∂ F( x)

∂ ξiΗ ij

– 1∂ F( x)∂ ξ j

∑i, j

P(s)N: χ2(=s) distributionwithN degreesof freedom

ds0

Δχ2

P(s)N=11 =0.6826→ Δχ2=12.64 (N =1case, Δχ2=1)

χ 2 =(A1i

exp − A1itheo )2

σ A1i

2i

∑

Polarized PDFs (AAC03)• PDF uncertainties are reduced by

including precise (E155-p) data

• Valence-quark distributions are well determined

– Small uncertainties of Δuv, Δdv

• Antiquark uncertainty is significantly reduced– g1

p 4Δuv+ Δdv+12Δq

• Δg(x) is not determined– Large uncertainty– Indirect contribution to g1

p – Correlation with antiquark

0

0.1

0.2

0.3

0.4

0.5

0.001 0.01 0.1 1

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.001 0.01 0.1 1

x

xΔuv(x)

xΔdv(x)

Q2=1GeV2

-2

-1

0

1

2

3

0.001 0.01 0.1 1

-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.001 0.01 0.1 1

x

xΔ (g x)

Q2=1GeV2

xΔ (q x)

AAC03 uncertainties

AAC00 uncertainties

AAC00 AAC03 (with E155-p)

E155 data

(A(A11expexp-A-A11

theotheo)/A)/A11theo theo at the same Qat the same Q22 point point

Correlation betweenCorrelation between ΔΔq(x) andq(x) and ΔΔg(x)g(x)

• analysis with Δg(x)=0 at Q2=1 GeV2

χ2/d.o.f. = 0.915

• Δqv(x) uncertainties are

not affected

• antiquark uncertainties are reduced

Strong correlation with Δg(x) Note: correlation with Δg(x) is almost terminated in the Δg=0 analysis

-2

-1

0

1

2

3

0.001 0.01 0.1 1

-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.001 0.01 0.1 1

x

xΔ (g x)

Q2=1GeV2

xΔ (q x)

0

0.1

0.2

0.3

0.4

0.5

0.001 0.01 0.1 1

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.001 0.01 0.1 1

x

xΔuv(x)

xΔdv(x)

Q2=1GeV2

The error band shrinks due to the correlation with Δg(x).

Δg=0 uncertainties

AAC03 uncertainties

AAC06AAC06

Gluon polarization at large Gluon polarization at large xx

AAC, PRD74 (2006) 014015: Analysis without higher-twist effects

QHERMES2 ~ 1 GeV2 QCOMPASS

2 ~ 6 GeV2

NLOΔCG=0

g1(x,Q2 ) =12

eq2

q∑ dz

zx

1

∫ Δq(x / z,Q2 ) + Δq(x / z,Q2 )⎡⎣ ⎤⎦

× δ(1−z) +αs(Q

2 )2

ΔCq(z) +⋅⋅⋅⎡

⎣⎢

⎤

⎦⎥

+12

eq2 dz

zx

1

∫ Δg(x / z,Q2 ) nf

αs(Q2 )

2ΔCg(z) +⋅⋅⋅

⎡

⎣⎢

⎤

⎦⎥

This term is terminated.

x=0.001 x=0.05 x=0.3

Positive contribution to A1 comesfrom ΔCG ⊗Δgatx~0.05.

Note: ΔCG ⊗Δg> 0ifΔg(0.05 / 0.2 =0.25) > 0Gluonpolarizationispositiveatlargex.

However, it may be a higher-twist effect.However, it may be a higher-twist effect.

LSS, PRD73 (2006) 034023.

LT fit

LT+HT fit

Leading Twist (LT)Higher Twist (HT)

LT+HT fit, only LT term is shown

At this stage, we cannot conclude that the difference betweenthe HERMES and COMPASS data should be 100% HT orHT+ΔG(large x)>0, or 100% ΔG(large x)>0 effects.

A1(x,Q2 ) =g1(x,Q

2 )LT +h(x) /Q2

F2 (x,Q2 )exp

2x 1+ R(x,Q2 )exp⎡⎣ ⎤⎦

dΔσdpT

= dηηmin

ηmax

∫ dxaxamin

1

∫a,b,c∑ Δfa(xa) dxbxb

min

1

∫ Δfb(xb)∂(t̂,zc)∂(pT ,η)

dΔσ̂dpT

Dc (zc)

xamin =

x11−x2

, xbmin =

xax2

xa −x1, zc =

x1xa

+x2

xb

, x1 =xT

2e+η , x2 =

xT

2e−η , xT =

2pT

s, η =−ln tan

θ

2⎛⎝⎜

⎞⎠⎟

⎡

⎣⎢

⎤

⎦⎥

Δσ : Δfa(xa,Q

2 )⊗ Δfb(xb,Q2 )⊗ Δσ̂ (ab→ cX)⊗ Dc

(z,Q2 )a,b,c∑

Parton distribution functions

Parton interactions Fragmentation functions

Description of Description of 00 production production

( ) , ( ) , ,

( , ) , ,

gg q g X qg q g X qq qX

qq q g q X qq qX qq qX

→ → →′ ′ ′→ → →

SubprocessesSubprocesses

g + g→ q(g) + XprocessesaredominantatsmallpT q+ g→ q(g) + XatlargepT

The 0 production process is suitable for findingthe gluon polarization Δg.

(from Torii’s talk at Pacific-Spin05)

-0.5

0

0.5

1

1.5

-0.5

0

0.5

1

1.5

-0.5

0

0.5

1

1.5

-0.5

0

0.5

1

1.5

0 0.2 0.4 0.6 0.8 1z

-0.5

0

0.5

1

1.5

0 0.2 0.4 0.6 0.8 1z

gluon

u quark

c quark b quark

Q2=2GeV2

Q2=2GeV2 Q2=2GeV2

Q2=10GeV2 Q2=100GeV2

KKPAKK Kretzer

HKNS

s quark

DSS

Comparison of fragmentation functions in pionComparison of fragmentation functions in pion

• Gluon and light-quark fragmentation functions have large uncertainties, but they are within the uncertainty bands. The functions of KKP, Kretzer, AKK, DSS, and HKNS are consistent with each other.

All the parametrizations agreein charm and bottom functions.

(KKP) Kniehl, Kramer, Pötter(AKK) Albino, Kniehl, Kramer(HKNS) Hirai, Kumano, Nagai, Sudoh(DSS) de Florian, Sassot, Stratmann

M. Hirai, SK, T.-H. Nagai, K. Sudoh, M. Hirai, SK, T.-H. Nagai, K. Sudoh, PRD75 (2007) 094009.PRD75 (2007) 094009.A code is available atA code is available athttp://research.kek.jp/people/kumanos/ffs.http://research.kek.jp/people/kumanos/ffs.htmlhtml

Analysis with RHIC pion data Analysis with RHIC pion data

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

1 2 3 4 5 6 7 8 9 10p

T (GeV)

RUN05ALL0(AAC06)

AAC03

AAC06(with PHENIX π0)

Possibility of negative gluon polarization Possibility of negative gluon polarization ΔΔgg << 0 0

-0.01

0

0.01

0.02

1 2 3 4 5pT (GeV)

RUN05

DIS + π0 (Type 3)

DIS only (Type 2)DIS + π0 (Type 1)ALLπ0

-0.4

-0.2

0

0.2

0.4

0.6

0.001 0.01 0.1 1

x

DIS + π0 (Type 3)

DIS only (Type 2)

DIS + π0 (Type 1)

00 production data do not distinguish between production data do not distinguish between ΔΔg < 0 and g < 0 and ΔΔg > 0 g > 0

Possibility of a node-type g(∆Possibility of a node-type g(∆ xx) for explaining p) for explaining pTT=2.38 GeV (Type 3).=2.38 GeV (Type 3).

Roles of RHIC-pion dataRoles of RHIC-pion data

0

0.1

0.2

0.3

0.4

0.5

0.001 0.01 0.1 1

-0.2

-0.1

0

0.001 0.01 0.1 1

x

xΔuv(x)

xΔdv(x)

Q2=1GeV2

( 03)DIS AAC+DIS 0( 1type )

-0.04

-0.03

-0.02

-0.01

0

0.01

0.001 0.01 0.1 1

x

-1

0

1

2

0.001 0.01 0.1 1

xΔ (g x)

xΔ (q x)

( 03)DIS AAC+DIS 0( 1type )

Polarized PDFs, especially Δg, are better determined by the additional RHIC-0 data.

(AAC06)

Gluon polarization from lepton scatteringGluon polarization from lepton scattering

S. Koblitz@DIS07

(AAC06)

Situation of gSituation of g11 measurements measurementsand polarized PDF errors and polarized PDF errors

0.01

0.1

1

10

0.7 1 10 100 200

Q2[GeV2]

E130

E143

E155

EMC

SMC

HERMES

x = 0.75

x = 0.66

x = 0.55

x = 0.50

x = 0.35

x = 0.25

x = 0.175

x = 0.125

x = 0.08

x = 0.025

x = 0.007

x = 0.05

x = 0.45

Comparison with other parameterizationsComparison with other parameterizations

0

0.1

0.2

0.3

0.4

0.5

0.001 0.01 0.1 1

-0.2

-0.1

0

0.001 0.01 0.1 1

x

AAC06

GRSV

BB

LSS

xΔuv(x)

xΔdv(x)

Q2=1GeV2

-0.2

0

0.2

0.4

0.6

0.8

0.001 0.01 0.1 1

AAC06

GRSV

BB

LSS

-0.04

-0.03

-0.02

-0.01

0

0.01

0.001 0.01 0.1 1

x

xΔ (g x)

Q2=1GeV2xΔ (q x)

1st 1st momentsmoments

– GRSV01(Sta) [ Phys. Rev. D63 (2001) 094005 ]– LSS01 (MS) [ Eur.Phys.J. C23 (2002) 479 ]– BB02 (SET3) [ Nucl. Phys. B636 (2002) 225 ]– DNS05 (KKP) [ Phys. Rev. D71 (2005) 094018 ] (Q2=10 GeV2 )

Δg ΔAAC06 0.31 0.32 0.27 0.07

AAC03 0.50 1.27 0.21 0.14

GRSV01 0.420 0.204

LSS 0.680 0.210

BB 1.026 0.138

DNS 0.574 0.311

€

Δ =Δuv + Δdv + 6Δq( )

€

Q2 = 1 GeV2

AAC08 ?AAC08 ?

Effects of expected JLab E07-011 data Effects of expected JLab E07-011 data

QuickTime˛ Ç∆ êLí£ÉvÉçÉOÉâÉÄ

Ç™Ç±ÇÃÉsÉNÉ`ÉÉÇ å©ÇÈÇΩÇflÇ…ÇÕïKóvÇ≈Ç∑ÅB

““Expected data” Expected data” from Xiaodong Jiang from Xiaodong Jiang

AAC asymmetries AAC asymmetries

Analyses with / without E07-011 dataAnalyses with / without E07-011 data in comparison with effects of RHIC π in comparison with effects of RHIC π00 data data

Analysis set Current DIS RHIC ÉŒ0 JLab E07-011

1 ÅZ Å[ Å[

2 ÅZ ÅZ Å[

3 ÅZ Å[ ÅZ

Two initial functions Two initial functions for∆g(for∆g(xx) )

““positive” positive”

““node” node”

xx

Effects of expected JLab E07-011 data Effects of expected JLab E07-011 data

-0.04

-0.03

-0.02

-0.01

0

0.01

0.001 0.01 0.1 1

x

-0.5

0

0.5

1

1.5

Q

2

=1GeV

2

Δ ( )g node

+ 07-011Currnt DIS E

Current DIS

-0.04

-0.03

-0.02

-0.01

0

0.01

0.001 0.01 0.1 1

x

-0.5

0

0.5

1

1.5

Q

2

=1GeV

2

Δ ( )g positive

+ 07-011Currnt DIS E

Current DIS

preliminary

Positivity i

s not satisfied

at this stage!

preliminary

∆∆g(g(xx) with PHENIX run-5 or JLab E07-011 data ) with PHENIX run-5 or JLab E07-011 data

-0.5

0

0.5

1

1.5

0.001 0.01 0.1 1x

Postive

Q2 = 1 GeV2

DIS + PHENIX π0

DIS + JLab-E07-011

-0.5

0

0.5

1

1.5

0.001 0.01 0.1 1x

Node

preliminary

É¢g function First moment DIS DIS+RHIC ÉŒDIS+E07-011

positive É¢g 0.53 0.36 0.53

positive δ(É¢g) 0.72 0.26 0.38

positive δ(É¢g)/É¢g 1.36 0.72 0.72

node É¢g 0.87 0.4 0.87

node δ(É¢g) 0.89 0.31 0.47

node δ(É¢g)/É¢g 1.02 0.72 0.54

Significant improvementsSignificant improvements

Note: πNote: π00 data are from run-5 data are from run-5 although it may not be a good although it may not be a good idea to compare future data idea to compare future data with past ones.with past ones.

JLab-E07-011 is comparableJLab-E07-011 is comparableto RHIC run-5 πto RHIC run-5 π00 in determining g(x).∆in determining g(x).∆

preliminary

Positivity i

s not satisfied.

Summary of the AAC global analysis for polarized PDFs – Δuv(x), Δdv(x) are determined well– Δ= 0.27 0.07 (Q2= 1 GeV2 )– Δg(x) could not be well constrained

AAC-polarized-pdfs code could be obtained fromhttp://spin.riken.bnl.gov/aac/

• Uncertainties of polarized PDFs • Effects of E155-proton data • Global analysis also with Δg=0• Error correlation between Δg and Δq • Better Δg determination by RHIC-pion• Δg determination at large x by scaling violation (HERMES, COMPASS)• Possibility of a node-type Δg (Δg>0 at x>0.1, Δg<0 at x<0.1)

AAC03

AAC06

AAC08 ? in progress

The End

The End

Documents

AAC Global Analysis