1/9

Constraint on g(x) at large-xBj

Masanori Hirai

Titech

(Asymmetry Analysis collaboration)With S. Kumano and N. Saito

hep-ph/06032132006 4 22,TUKUBA

2/9

Contents

• Introduction

• AAC analysis with DIS and 0 production– Global analysis and PDF uncertainty estimation– Spin contents : , g ?– Comparison with experimental data and other PDFs set

• Large-x behavior from HERMES and COMPASS data– Positive g(x) at large-xBj

• Summary

3/9

Introduction

• Origin of the nucleon spin 1/2– 1/2 = 1/2 + g + Lq,g

– Quark spin component from polarize DIS: 0.1-0.3

• Orbital angular momentum Lq,g ?– Jq=q+Lq: Generalized PDF from DVCS

– SSA: Sivers function ?

• g is an important piece of the spin puzzle !– Undetermined g = 0.49 1.27 (AAC03)– Experimental data from RHIC-Spin

• Prompt photon, Jet, heavy quark production, et al.– 0 production

• PRL93, 202002 (2004)• RUN05

4/9

AAC analysis and uncertainty estimation

• Initial distribution of polarized PDF

• Constraint condition– Positivity condition:

• Constraint on the large-x behavior of f(x)

– Antiquark SU(3)f symmetry:• Fixed 1st moments: uv=0.926, dv= 0.341

• Fixed q=1.0: undetermined small-x behavior

• PDF uncertainty by Hessian method

– N=11, 2 = 12.64: 　　　　　　　　　　　　　　 [K(N,s): 2 distribution ]

2 2 1

,

( ) ( ) ( ) ij

i j i j

f x f xf x H

a a

( , ) ( , ),

, , ,

i i iii i

v v

f x Q x x x f x Q

i u d q g

2 20 0

( ) ( ) ( ) ( ) ( )u x d x s x s x q x

( ) ( )f x f x

• Unpol PDF:GRV98 • Q0

2 = 1 GeV2

QCDNf=3 = 299 MeV

2

0( , ) 0.683K N s ds

5/9

g from DIS

• Added new data A1(=g1/F1)– HERMES(p,d), J-Lab(n)

COMPASS(d)– Total # of data: 413 (Q2

1GeV2)

• NLO analysis– MS scheme– 2(/d.o.f.) = 358.05 (0.89)

• = 0.25 0.10 – Well determined quark and antiq

uark distributions– J-Lab: dv(x) at large-x– HERMES,COMPASS: q(x)

• g = 0.47 1.08– Undetermined by only DIS

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

xuv(x)

xdv(x)

Q2 = 1 GeV2

DIS (AAC03)

DIS (AAC06)

-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

xg(x)

xq(x)

DIS (AAC03)

DIS (AAC06)

6/9

Spin content , g

– AAC06 (DIS only) – BB02 (ISET4) : Nucl. Phys. B636 (2002) 225– GRSV01(Sta) : Phys. Rev. D63 (2001) 094005– LSS05 (MS) : Phys. Rev. D73 (2006) 034023

-0.1

0

0.1

0.2

0.3

0.001 0.01 0.1 1

AAC06

GRSV

BB

LSS

-0.6-0.4-0.2

00.20.40.60.8

11.21.4

0.001 0.01 0.1 1

x

xg(x)

Q2 = 1 GeV2

x(x)

-0.1 0.1 0.3 0.5

0.171± 0.074

0.254± 0.101

0.165± 0.048

0.204

0.150± 0.061

-1 0 1

Ave.

AAC06

GRSV01

LSS05

BB02

0.289± 0.754

0.473± 1.083

0.179± 0.267

0.420

0.931± 0.679

g

7/9

g from 0 production (RUN05)• 1st moment g

– 0.31 0.32 (DIS+0)– 0.47 1.08 (DIS only)

• Significant reduction of the g uncertainty

• Sign problem – gg process dominates

• g(x)

• Positive or negative g?• 2

0 : 11.18(g>0) vs. 11.05 (g<0)

(8 data points)

-0.6-0.4-0.2

00.20.40.60.8

11.21.4

0.001 0.01 0.1 1

x

xg(x)

DIS (DIS only)

DIS + 0 (g > 0)

-1.2

-0.8

-0.4

0

0.4

0.8

1.2

0.001 0.01 0.1 1

x

HERMES

SMC

COMPASS Q2<1 GeV2

DIS + 0 (g < 0)

DIS + 0 (g > 0)

• Consistent results– 1st moment (0.1<xBj<1)

• g>0: 0.30 0.30 • g<0: 0.32 0.42

– DIS + 0 data covered– Large-x is positive

8/9

Constraint on large-x behavior of g(x)• Positive g(x)/g(x) at large-x

– HERMES A1d

• 0.03 < xBj < 0.07, 1.2 < Q2 < 1.7 • COMPASS-d: 4.5 < Q2 < 8.6

– NLO gluon term• Positive contribution• Relative increasing for g1

D

– euv2 : 4/9(P) → 2.5/9(D)

• Positive g(x) at large-x

• Other DOF for HERMES-d ?– Higher Twist effects

• LSS, PRD73(2006)034023– Antiquark SUf(3) aymmetry

• D. de Florian, et al., PRD71(2005)094018

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.01 0.1 0.3

x0.01 0.1 0.3

x

HERMES COMPASS

( ) ( )

( )gx

C x x g x

dz xC z x g

z z

1

-0.2

-0.1

0

0.1

0.2

0.3

0.001 0.01 0.1 1

z

x=0.001

x=0.05

x=0.3

Cg(z)/10

x/zg(x/z)

9/9

Summary

• Polarized PDF from polarized DIS data– Ave= 0.170.07 (Q2= 1 GeV2 )– g(x) could not be determined

• gAve=0.29 0.75

– Positive g(x) at large-x• HERMES-d (0.03 < xBj < 0.07, 1.2 < Q2 < 1.7 )• Positive NLO gluon term

• 0 production at RHIC-Spin– RUN05 0: g = 0.31 0.32 (AAC06, Q2= 1 GeV2 )– positive or negative g ?– g <0

• Ambiguity of small-x behavior of g(x)• Need constraint on the behavior