Possible studies of structure functions at JLabPossible studies of structure functions at JLabShunzo 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)

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

November 5, 2009November 5, 2009

Workshop on Workshop on the Jefferson Laboratory Upgrade to 12 GeVSept. 14 - Nov. 20, 2009, INT, Seattle, USASept. 14 - Nov. 20, 2009, INT, Seattle, USA

http://www.int.washington.edu/PROGRAMS/09-3.html

Our codes are available forOur codes are available for Nuclear PDFs:Nuclear PDFs: http://research.kek.jp/people/kumanos/nuclp.html http://research.kek.jp/people/kumanos/nuclp.html Polarized PDFs:Polarized PDFs: http://spin.riken.bnl.gov/aac/ http://spin.riken.bnl.gov/aac/ Fragmentation functions:Fragmentation functions: http://research.kek.jp/people/kumanos/ffs.html http://research.kek.jp/people/kumanos/ffs.html QQ22 evolutions: evolutions: http://research.kek.jp/people/kumanos/program.html http://research.kek.jp/people/kumanos/program.html

OutlineOutline

1. Nuclear modifications of 1. Nuclear modifications of R R == F FL L / F/ FTT at large at large xx

We (M. Ericson and SK) insist thatWe (M. Ericson and SK) insist that nuclear modifications of nuclear modifications of R R == F FL L / F/ FTT should exist at large should exist at large x.x.

2. From nucleon-spin crisis to tensor-structure crisis (?)2. From nucleon-spin crisis to tensor-structure crisis (?) Tensor structure functions of spin-1 hadrons (Tensor structure functions of spin-1 hadrons (bb11, , bb22, …)., …).

3. ∆3. ∆ gg((xx) determination by accurate ) determination by accurate gg11 measurements measurements

Accurate Accurate gg11 by JLab E07-011 by JLab E07-011

NLO gluon term in NLO gluon term in gg11 could be determined. could be determined.

Three different topics. Three different topics. I will stop when time runs out.I will stop when time runs out.

Nuclear modifications Nuclear modifications of of R R == F FL L / F/ FTT at large at large xx

Ref. M. Ericson and SK, Phys. Rev. C 67 (2003) 022201.Ref. M. Ericson and SK, Phys. Rev. C 67 (2003) 022201.

p

X 'L, T

Nuclear effect on Nuclear effect on RR = = FFLL / / FFTT by HERMES by HERMES HERMES, K. Ackerstaff el al., PL B 475 (2000) 386;

Erratum, PL B567 (2003) 339 [hep-ex/0210067; hep-ex/0210068]. Longitudinal and transverse components W = * W,

WT = 12 (W = + 1 + W= – 1) = W1

WL = W = 0 = (1 + 2

Q2) W2 – W1

(2000) (2003)Q2 (GeV2)

RA /RD

Nuclear effects on R by CCFR/NuTeV

U.-K. Yang et al., PRL 87 (2001) 251802.

CCFR HERMESSLAC

No significant deviation is measuredfrom the nucleon case ( ).

No large nuclear modificationof R is observed in +Fe !(note: CCF/NuTeV target is Fe)

note

M. Ericson and SKM. Ericson and SK, Phys. Rev. C 67 (2003) 022201 , Phys. Rev. C 67 (2003) 022201

Submitted (Nov. 30, 2002) just after the HERMES correction paper (Oct. 31, 2002).Submitted (Nov. 30, 2002) just after the HERMES correction paper (Oct. 31, 2002).

Nuclear modifications of transverse-longitudinal ratioNuclear modifications of transverse-longitudinal ratio do exist in medium and large-do exist in medium and large-xx regions regions, , although the modifications do not seem to exist at small although the modifications do not seem to exist at small xx within experimental errors according to the revised within experimental errors according to the revised HERMES paper.HERMES paper.

MechanismsMechanisms

(1)(1) Transverse nucleon motionTransverse nucleon motion T-L admixtureT-L admixture of nucleon structure functions.of nucleon structure functions.

(2)(2) Binding and Fermi-motion effectsBinding and Fermi-motion effects in the spectral function.in the spectral function.

FormalismFormalismW

A, N W1A, N g

qqq2

W2

A, N 1MN

2 pA, N p

A, N

F1 MNW1 , F2 W2 , FL Q2

WL 1

Q2

2

F2 2xF1

Projection operators of W1A and W2

A

P̂1

12

g pA pA

p2

, P̂2

pA2

2 pA2 g

3 pA pA

p2

P̂1,2W

A W1,2A

p p

pqq2 q

Convolution: WA (pA , q) d 4 p S(p) W

N (pN ,q)

W1,2A (pA ,q) d 4 p S(p) P̂1,2

WN (pN ,q)

Longitudinal and transverse components WA, N

*W

A, N

WTA, N

12

(W1A, N W 1

A, N )W1A, N WL

A, N W0A, N 1

A, N2

Q2

W2

A, N W1A, N

A2 2

( pN q)2

pN2

Formalism Formalism (continued)(continued)

pN

pN

q

Scaling variables: xA Q2

2 pA q

MN

MA

x, xN Q2

2 pN q

xz

, x Q2

2MA, z

pN qMA

Longitudinal structure functions F1 and F2 : FLA, N 1

Q2

A, N2

F2

A, N 2xA, N F1A, N

Transverse-longitudinal ratio: RA,N FL

A, N

2xA, N F1A, N

Calculating W1,2A = P1,2

WA = P1,2

d4pN S(pN) WN ,

2 xA F1A = d 4pN S(pN) z M N

pN2 [ (1 + pN

2

2 pN2) 2 xN F1

N(xN, Q2) + pN2

2 pN2 FL

N(xN, Q2)]FL

A = d4pN S(pN) z MN

pN2 [ (1 + pN

2

pN2 ) FL

N(xN, Q 2) + pN2

pN2 2 xN F1

N(xN, Q 2) ]

ResultsResults

0

0.1

0.2

0.3

0.4

0 0.2 0.4 0.6 0.8 1

x

R 14N R

RN 10 GeV2

Q2 = 1 GeV2

100 GeV2

0.95

1

1.05

1.1

0 0.2 0.4 0.6 0.8 1

x

without L-T mixing

10 GeV2

Q2 = 1 GeV2

100 GeV2

admixture effects

Spectral function (M A – i = M A – MN – i)

S(p N) = (p N) 2i

(p N0 – M A + M A – i

2 + pN2) for 14N

Transverse–longitudinal ratio: R1990

F2N (PDFs): MRST98–LO

In the kinematical region ofour prediction, data does notexist.Need future experimentalinvestigations at JLab, EIC, factory, …

After the HERMES (CCFR/NuTeV)re-analysis, people tend to lose

interestin the nuclear effect on R. However, we claim that nuclearmodification should exist in mediumand large-x regions.

Physical origins transverse-longitudinal admixture due to the transverse Fermi motion binding and Fermi motion effects in the spectral function

JLab measurements in 2007JLab measurements in 2007 • V. Tvaskis et al., PRL 98 (2007) 142301.• Lingyan ZhuLingyan Zhu (Hampton Univ), (Hampton Univ), personal communications (2009).personal communications (2009).

Ee 2.301, 3.419, 5.648 GeV 0.007 x 0.55, 0.06 Q2 2.8 GeV2

proton, deuteron

Badelek, Kwiecinski, Stasto (1997)Badelek, Kwiecinski, Stasto (1997)E99-118E99-118MRST-2004MRST-2004GRV-1995GRV-1995

Almost same for Almost same for pp an an dd, but at 0.04 < , but at 0.04 < x x < 0.32.< 0.32.

In any case, nuclear modificationsIn any case, nuclear modifications should be small for the deuteron.should be small for the deuteron. Importance of future JLab measurementsImportance of future JLab measurements for heavier nuclei, for heavier nuclei, especially at large especially at large x x (>0.4)(>0.4)..

x 0.32x 0.07

From nucleon-spin crisis From nucleon-spin crisis to tensor-structure crisis (?)to tensor-structure crisis (?)

Refs. Refs. F. E. Close and SK, Phys. Rev. D 42 (1990) 2377, M. Hino and SK, Phys. Rev. D 59 (1999) 094026; D 60 (1999) 054018, SK and M. Miyama, Phys. Lett. B 497 (2000) 149, T.-Y. Kimura and SK, Phys. Rev. D 78 (2008) 117505.

References on tensor structure function References on tensor structure function bb11

Theoretical formalism for polarized electron-deuteron Theoretical formalism for polarized electron-deuteron deep inelastic scatteringdeep inelastic scattering P. Hoodbhoy, R. L. Jaffe, and A. Manohar, NP B312 (1989) 571. [ L. L. Frankfurt and M. I. Strikman, NP A405 (1983) 557. ]

HERMES experimental resultHERMES experimental result A. Airapetian et al., Phys. Rev. Lett. 95 (2005) 242001.

Our worksOur works

Sum rule for Sum rule for bb11

F. E. Close and SK, Phys. Rev. D 42 (1990) 2377.

Projections to Projections to FF11, , FF22, , gg11, , gg22, , bb11, …, , …, bb44 from from WW

T.-Y. Kimura and SK, Phys. Rev. D 78 (2008) 117505.

MotivationMotivation

Spin structure of the spin-1/2 nucleonSpin structure of the spin-1/2 nucleon Nucleon spin puzzle:Nucleon spin puzzle: This issue is not solved yet, This issue is not solved yet, but it is rather well studied theoretically and experimentally.but it is rather well studied theoretically and experimentally.

Spin-1 hadrons (e.g. deuteron) Spin-1 hadrons (e.g. deuteron) Tensor-structure puzzle (???)Tensor-structure puzzle (???) There are some theoretical studies especially on tensor structure There are some theoretical studies especially on tensor structure in electron-deuteron deep inelastic scattering.in electron-deuteron deep inelastic scattering.

HERMES experimental resultsHERMES experimental results

A few investigations have been done for polarizedA few investigations have been done for polarized proton-deuteron processes. proton-deuteron processes.

J-PARC, COMPASS, U70, GSI-FAIR, RHIC … experiment ?J-PARC, COMPASS, U70, GSI-FAIR, RHIC … experiment ?

Structure function Structure function bb11 in a simple example in a simple example

Spin-1 particles (deuteron, mesons)Spin-1 particles (deuteron, mesons)

only in S-waveonly in S-wave

bb11 == 00

The The bb11 probes a dynamical aspect of hadron structure probes a dynamical aspect of hadron structure beyond simple expectations of a naive quark model.beyond simple expectations of a naive quark model. Description of tensor structure Description of tensor structure by quark-gluon degrees of freedomby quark-gluon degrees of freedom

bb11 0: New field of high-energy spin physics 0: New field of high-energy spin physics with orbital angular momenta.with orbital angular momenta.

Electron scattering from a spin-1 hadron Electron scattering from a spin-1 hadron

W F1g F2

p p

g1iqs g2

i 2 q pqs s qp

b1r 16

b2 s t u 12

b3 s u 12

b4 s t

r 1 2 qEqE

13 2

g , s 2 2 qEqE

13 2

p p

t 1

2 2 qE p E qE p E qEp E qEp E

43 p p

u 1

E E E

E 23

M 2 g 23

p p

pq, 1 M 2 Q2 2 , E2 M 2 , s iM 2

E E p

P. Hoodbhoy, R. L. Jaffe, and A. Manohar, NP B312 (1989) 571.[ L. L. Frankfurt and M. I. Strikman, NP A405 (1983) 557. ]

Note: Obvious factors from qW qW 0 are not explicitly written.

spin-1/2, spin-1

spin-1 only

2xb1 b2 in the scaling limit ~ O(1)

b3 , b4 twist-4 ~ M 2

Q2

E polarization vector

b1 ,, b4 tems are defined so that they vanish by spin average.

b1 , b2 tems are defined to satisfy2xb1 b2 in the Bjorken scaling limit.

Projections to Projections to FF11, , FF22, …, , …, bb44 from W from W Calculate W in hadron models need to extract structure functions b1 , b2 , Projection operators are needed to extract them from the calculated W .For F1 and F2 , they are well known:

F1 12

g 1

p p

M 2

W , F2 x

g 1

3p p

M 2

W , 1Q2 2

QuickTimeý Dz êLí£ÉvÉçÉOÉâÉÄ

ǙDZÇÃÉsÉNÉ`ÉÉǾå©ÇÈǞǽDžÇÕïKóvÇ ÇÅB

Try to obtain projectionsin a spin-1 hadron by combinations of

g , p p

M 2 , qs , ...

Results on a spin-1 hadron

Bjorken scaling limit

F1 1

2xF2

12

g 13 f i

W f i

g1 i

2 qs f 1i 1W

f i

b1 1

2xb2

12

g f 1i 1 f 0i 0 W f i T.-Y. Kimura and SK,

PRD 78 (2008) 117505.

StructureStructureFunctionsFunctions

PartonPartonModelModel

F1 d

g1 d ,1 d , 1

b1 d 0 d 1 d 1 2

qH x,Q2

F1 12

ei2

i qi qi qi

13

qi1 qi

0 qi 1

g1 12

ei2 qi qi

i qi qi

1 qi1

b1 12

ei2 qi qi

i qi qi

0 qi1 qi

1

2

note: (0) (1) ( 1)

23

32

(1) ( 1)

dx b1(x)dimensionless : QM 2 ???

M hadron mass Q quadrupole moment

dx b1D (x) dx

49uD uD 1

9dD d D sD sD

59

dx uv (x)uv (x) 19Q Q sea

H , H p, H J0 (0) p, H ei dx qiH qi

H qiH qi

H i

120,0

121,1 1, 1

ei dx qD qD

i

13

dx uv (x)dv (x)

Sum rule for Sum rule for bb11

dx

q 0

Q Q sea

dx 5 u u dD d D 2 sD sD

sea

Elastic amplitude in a parton modelElastic amplitude in a parton model

F.E.Close and SK, PRD42, 2377 (1990).

dx b1D (x)

560,0

121,1 1, 1

19Q Q sea

0,0 limt 0

Fc (t) t

3M 2 FQ(t)

1,1 1, 1 limt 0

Fc (t) t

6M 2 FQ(t)

dx b1D (x)lim

t 0

512

tM 2 FQ(t)

19Q Q sea

limt 0

5

12t

M 2 FQ (t)

dxx

F2p (x) F2

n(x) 13

dx uv dv 23

dx u d

MacroscopicallyMacroscopically t 0

If the sum-rule violationis shown by experiment,it suggests antiquark tensor polarization.

Note: FQ (t) in the unit of 1M 2

HERMES results on HERMES results on bb11

deuteronpositron

27.6 GeV/c , 0

b1 measurement in the kinematical region0.01 x 0.45, 0.5 GeV2 Q2 5 GeV2

b1 sum rule

dx0.002

0.85

b1(x) 1.05 0.34(stat)0.35(sys) 10 2

at Q2 5 GeV2

In the restricted Q2 range Q2 1 GeV2

dx0.02

0.85

b1(x) 0.35 0.10(stat)0.18(sys) 10 2

at Q2 5 GeV2

dx b1D (x)lim

t 0

512

tM 2 FQ (t) 1

9QQ sea

0 ?

dxx

F2p (x) F2

n (x) 13

dx uv dv 23

dx u d 1 / 3

A. Airapetian et al. (HERMES), PRL 95 (2005) 242001.

Drell-Yan experiments probethese antiquark distributions.

E866

E906

J-PARCDrell-Yan: p p X, p d X

DY (pd )2 DY (pp)

12

1d (x2 )u(x2 )

Actual experimental proposals at J-PARC: P04, P24Actual experimental proposals at J-PARC: P04, P24

E866: existing measurements by the Fermilab-E866E906: expected measurements by the Fermilab-E906 (from 2010)J-PARC: proposal stage

It should be possible to use polarized proton-deuteron Drell-Yan processesIt should be possible to use polarized proton-deuteron Drell-Yan processes to measure the tensor polarized distributions.to measure the tensor polarized distributions.

+

–

q

qAntiquarkAntiquarkdistributionsdistributions

References for tensor structure in Drell-YanReferences for tensor structure in Drell-Yan• • General formalism for polarized Drell-Yan processesGeneral formalism for polarized Drell-Yan processes with spin-1/2 and spin-1 hadronswith spin-1/2 and spin-1 hadrons M. Hino and SK, Phys. Rev. D59 (1999) 094026.

• • Parton-model analysis of polarized Drell-Yan processesParton-model analysis of polarized Drell-Yan processes with spin-1/2 and spin-1 hadronswith spin-1/2 and spin-1 hadrons M. Hino and SK, Phys. Rev. D60 (1999) 054018.

• • An application: Possible extraction of polarized An application: Possible extraction of polarized light-antiquark distributions from Drell-Yanlight-antiquark distributions from Drell-Yan SK and M. Miyama, Phys. Lett. B497 (2000) 149.

Comments on the situationComments on the situation• There was a feasibility study for polarized deuteron beam at RHIC: E. D. Courant, BNL-report (1998).• No actual experimental progress with hadron facilities.• Future: J-PARC, COMPASS, U70, GSI-FAIR, RHIC, …

p d X

( p d X is

enough for tensor structure)

Spin asymmetries in the parton modelSpin asymmetries in the parton modelunpolarized: qa , longitudinally polarized: qa ,transversely polarized: T qa , tensor polarized: qa

ddxAdxBd

2

4Q2 1 cos2 13

ea2 qa xA qa xB qa xA qa xB

a

Unpolarized cross section

Spin asymmetries

ALL ea

2 qa xA qa xB qa xA qa xB aea

2 qa xA qa xB qa xA qa xB a

ATT sin2 cos 2

1 cos2

ea2 T qa xA T qa xB T qa xA T qa xB a

ea2 qa xA qa xB qa xA qa xB a

AUQ0

ea2 qa xA qa xB qa xA qa xB aea

2 qa xA qa xB qa xA qa xB aALT ATL AUT ATU ATQ0

AUQ1

ALQ1ATQ1

AUQ2ALQ2

ATQ20

Advantage of the hadron reaction (q measurement)

AUQ0large xF

ea2qa xA qa xB

aea

2qa xA qa xB a

Note: transversity in my notation

Possible JLab measurementsPossible JLab measurements

HERMES (2005)

Possible JLab measurementsPossible JLab measurementsin this in this xx region. region.• • HERMES data have large errorsHERMES data have large errors Important contribution from JLab.Important contribution from JLab.

"Rough" order of magnitude estimate in a conventional model for the deuteron

b1

F1

~ Op2

M 2

(D state admixture)

xF1 ~12

F2

xb1 ~12

F2 Op2

M 2

(D state admixture)

12(0.3)

110

120

0.001 at medium x

expected to be a small quantity! (suitable for JLab experiment)

See P. Hoodbhoy et al., NP B312 (1989) 571.

F2

x 0.18x 0.35

Q2

Possibly, opening of tensor-structure crisis at JLab!?Possibly, opening of tensor-structure crisis at JLab!?

See also a theoretical model by G. A. Miller,See also a theoretical model by G. A. Miller, in Topical Conference on Electronuclear physicsin Topical Conference on Electronuclear physicswith Internal Targets, edited by R. G. Arnoldwith Internal Targets, edited by R. G. Arnold(World Scientific, 1990).(World Scientific, 1990).

Determination of gluon polarizationDetermination of gluon polarizationby accurate by accurate gg11 measurements measurements

Refs. AAC (Asymmetry Analysis Collaboration),Refs. AAC (Asymmetry Analysis Collaboration), Y. Goto et al., Phys. Rev. D 62 (2000) 034017; M. Hirai, SK, N. Saito, Phys. Rev. D 69 (2004) 054021; 74 (2006) 014015; M. Hirai, SK, Nucl. Phys. B 813 (2009) 106.

12

12uv dv qsea

G Lq Lg

Nucleon SpinNucleon Spin

Naïve Quark Model

uv dv 1

0.3Almost none of nucleon spinis carried by quarks!

Nucleon Spin:

QCD

Sea-quarks and gluons?

Gluon: GSea-quarks: qsea

Recent data indicate G is small at x ~ 0.1.

Orbital angular momenta ?

Lq , Lg

Future experiments

Electron / muon scattering

Gluon polarization from lepton scatteringGluon polarization from lepton scattering

F. Kunne (COMPASS), AIP Conf. Proc. 1149 (2009) 321.

Gluon polarization from RHIC πGluon polarization from RHIC π00 production production

Parton distribution functionsParton distribution functions Parton interactionsParton interactions

Fragmentation functionsFragmentation functions

(Torii’s talk at Pacific-Spin05)

Gluonic processes dominate.Determination of ∆ghowever with uncertainties of however with uncertainties of gluon fragmentation functions.gluon fragmentation functions.

-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 10pT (GeV)

RUN05

ALL 0

Uncertainty range ofgluon fragmentation functions in LO.(See the next page.)In the NLO, the range is smaller.

p p 0 X

-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 = 2 GeV2

Q2 = 2 GeV2 Q2 = 2 GeV2

Q2 = 10 GeV2 Q2 = 100 GeV2

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.htmlhttp://research.kek.jp/people/kumanos/ffs.html

NLO

Global analyses of polarized PDFs: Global analyses of polarized PDFs: Asymmetry Analysis Collaboration (AAC)Asymmetry Analysis Collaboration (AAC)

20002000 version (AAC00) version (AAC00) Y. Goto et al., PRD 62 (2000) 034017.

- Q2 dependence of A1, positivity - q at small and large x issue2004 version (AAC03) 2004 version (AAC03) M. Hirai, SK, N. Saito, PRD 69 (2004) 054021.

- uncertainty estimation (very large g uncertainty, impact of accurate g1

p (E155)) - error correlation between g and q2006 version (AAC06) 2006 version (AAC06) M. Hirai, SK, N. Saito, PRD 74 (2006) 014015.

- include RHIC-Spin 0 (g uncertainty is significantly reduced) - g at large x ? (from Q2 difference between HERMES and COMPASS) - g < 0 solution2008 version (AAC08) 2008 version (AAC08) M. Hirai, SK, NPB 813 (2009) 106.

- impact of g by JLab E07-011 ? (g uncertainty could be significantly reduced.)

Today’s talkToday’s talk

AAC codes for polarized PDFs: http://spin.riken.bnl.gov/aac/AAC codes for polarized PDFs: http://spin.riken.bnl.gov/aac/

Spin asymmetry: A1

g1

F1

g12x 1 R

F2

R FL

2xF1

F2 2xF1

2xF1

General method for determining polarized PDFsGeneral method for determining polarized PDFs

g1(x,Q2 )12

eq2

q dy

yx

1

q(x / y,Q2 ) q(x / y,Q2 ) (1 y) s (Q

2 )2

Cq (y)

+12

eq2 dy

yx

1

g(x / y,Q2 ) n f s (Q

2 )2

Cg (y)

eq

2 1n f

eq2

q

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

Cq (Cg )quark (gluon) coefficient function

F2 (x,Q2 )x eq2

q dy

yx

1

q(x / y,Q2 ) q(x / y,Q2 ) (1 y) s (Q

2 )2

Cq(2)(y)

x eq2 dy

y

x

1

g(x / y,Q2 ) n f s (Q

2 )2

Cg(2)(y)

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

Parametrization: fi (x,Q02 )Aix

i (1 ixi ) fi (x,Q0

2 ), i uv , dv , q, g Ai , i , i , i are determined by data

e p e X

Constraint on ∆Constraint on ∆ gg((xx))from current from current gg11 data data

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

NLOCG=0

g1(x,Q2 )12

eq2

q dz

zx

1

q(x / z,Q2 ) q(x / z,Q2 )

(1 z) s (Q

2 )2

Cq (z)

+12

eq2 dz

zx

1

g(x / z,Q2 ) n f s (Q

2 )2

Cg (z)

This term is terminated.

x=0.001 x=0.05 x=0.3

Positive contribution to A1 comesfrom CG g at x ~ 0.05.

Note: CG g 0 if g(0.05 / 0.2 0.25) 0Gluon polarization is positive at large x.

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

LSS, PRD73 (2006) 034023.

LT fitLT+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 betweenAt this stage, we cannot conclude that the difference betweenthe HERMES and COMPASS data should be 100% HT orthe HERMES and COMPASS data should be 100% HT orHT+HT+gg(large (large xx)>0, or 100% )>0, or 100% gg(large (large xx)>0 effects.)>0 effects.

Obtained polarized PDFs by AAC06Obtained polarized PDFs by AAC06

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 1x

AAC06GRSVBBLSS

xuv(x)

xdv(x)

Q2 = 1 GeV2

-0.2

0

0.2

0.4

0.6

0.8

0.001 0.01 0.1 1

AAC06GRSVBBLSS

-0.04

-0.03

-0.02

-0.01

0

0.01

0.001 0.01 0.1 1x

xg(x)

Q2 = 1 GeV2xq(x)

Gluon polarization tends toGluon polarization tends tobe positive at large be positive at large x.x.

Constraint on ∆Constraint on ∆ gg((xx))from future from future gg11 data: data:

Effects of E07-011 at JLab 12 GeVEffects of E07-011 at JLab 12 GeV

3 data sets for global analyses of polarized PDFs3 data sets for global analyses of polarized PDFsData setData set CurrentCurrent

DIS (DIS (gg11))RHICRHIC0 0 (run 5)(run 5)

JLabJLabE07-011 (E07-011 (gg11))

A Included — —

B Included Included —

C Included — Included

Set A: Only DIS data for the determination of polarized PDFs [g(x)]

Set B: Effects of collider data setsSet B: Effects of collider data sets 0 production [Run-5 PHENIX, PRD76, 051106R (2007)]

Set C: Effect of DIS accurate Set C: Effect of DIS accurate gg11 data data by JLab E07-011. by JLab E07-011. g1 measurements [E. Brash, et al., JLab experiment E07-011; X. Jiang, personal communications.]

Expected E07-011 data Expected E07-011 data

A1

d (x,Q2 )E07-011 g1

d (x,Q2 )g1

d (x,Q2 )

E07-011

A1d (x,Q2 )Set-A

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

Q2= 1 GeV2

g (node)

Currnt DIS + E07-011Current DIS

-0.04

-0.03

-0.02

-0.01

0

0.01

0.001 0.01 0.1 1x

-0.5

0

0.5

1

1.5

Q2= 1 GeV2

g (positive)

Currnt DIS + E07-011Current DIS

Two initial functions for∆Two initial functions for∆ gg((xx): positive, node): positive, node ““positive”positive”

““node”node”

xx

GluonGluon

AntiquarkAntiquark

Reduction ofReduction ofuncertaintiesuncertaintiesfor ∆for ∆ gg((xx) ) by E07-011by E07-011

PositivePositive NodeNode

∆∆ gg((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 ¹ 0

DIS + JLab-E07-011

-0.5

0

0.5

1

1.5

0.001 0.01 0.1 1x

Node

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 ∆in determining ∆ gg((xx))if gluon fragmentation errorsif gluon fragmentation errorsare neglected.are neglected.

Δg function First moment DIS DIS+RHIC π DIS+E07-011

positive Δg 0.53 0.36 0.53positive (Δg) 0.72 0.26 0.38positive (Δg)/Δg 1.36 0.71 0.73

node Δg 0.87 0.40 0.87node (Δg) 0.89 0.31 0.47node (Δg)/Δg 1.02 0.77 0.54

Significant improvementsSignificant improvements

In this table, g dxg(x)

0.1

1

.

Why such a large improvement of ∆Why such a large improvement of ∆ gg((xx) by E07-011 data? ) by E07-011 data?

-0.2-0.1

00.10.2

-0.6-0.3

00.30.6

-0.4-0.2

00.20.4

0 0.1 0.2 0.3 0.4 0.5 0.6

x

set C (positive)set C (node)

CLAS proton data

CLAS deuteron data

E07-011 deuteron data

g1(x,Q2 )12

eq2

q dz

zx

1

q(x / z,Q2 ) q(x / z,Q2 )

(1 z) s (Q

2 )2

Cq (z)

+12

eq2 dz

zx

1

g(x / z,Q2 ) n f s (Q

2 )2

Cg (z)

g1g corr

CLAS: g1g corr ~ g1 errors

E07-011: g1g corr g1 errors

NLO gluonic term in g1 could be probed by the E07-011 experiment.

The EndThe End

The EndThe End