1/10

Global analysis and the impact of eRHIC data

Masanori Hirai

TiTech

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

2006 7 19, BNL

2/10

Contents

• Introduction

• AAC analysis with DIS and 0 production– Global analysis and PDF uncertainty estimation– Spin contents : , g ?

• Issues in the global analysis of polarized PDFs– Undetermined large-x and small-x behavior

• Summary

3/10

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= 1/2 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

4/10

AAC analysis and uncertainty estimation

• Initial distribution of polarized PDF

• Constraint condition– Positivity condition:

• Constraint on the large-x behavior of f(x)• Avoiding unphysical behavior of the asymmetry: A1(x) >1 (x1)

– 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

– 2 (N=11) = 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 ii ii

v v

if 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

5/10

Polarized PDFs from DIS data

• Added new data A1

– COMPASS(d), HERMES(p,d), J-Lab(n)

• 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 antiquark di

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

• g = 0.47 1.08– Undetermined by current DIS 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

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)

6/10

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

7/10

g from DIS and 0 data

• 1st moment g– 0.31 0.32 (DIS+0)– 0.47 1.08 (DIS only)

• Significant reduction of g uncertainty• Sign problem

– gg process dominates• g(x)

– Positive or negative g?• g= 0.56 2.16• 2

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

-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)

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

• g>0: 0.30 0.30 • g<0: 0.32 0.42

– Covered by DIS + 0 data• Ambiguity of the small-x behavior

– No experimental data

-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)

8/10

Issues of the global analysis

• Narrow Q2 rage (1<Q2<80 GeV2)– Extract g(x) via Q2 evolution– Need data covering wide rage of Q2

• eRHIC : Q2<104 GeV2

• Large uncertainty of asymmetry A1(x) at large x– Undetermined large-x behavior– Need precise measurements

• eRHIC: High luminosity

• Undetermined q(x) at small x– Fixing one parameter: q=1.0– No data in the small-x region

• eRHIC : x>10-4 (Q2>1 GeV2)

9/10

Small-x behavior of q(x)

• Small-x behavior of q(x) affects value of – Quark spin component : = uv+ dv+6q

– Well determined uv(x) and dv(x)– depends on extrapolated behavior of q(x) to the small-x region – Undetermined q(x) in the small-x region

• No experimental data (x<0.004)

min

( , )x

x Q dx 1 2

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

1E-6 1E-5 1E-4 1E-3 1E-2 1E-1 1E+0

xmin

SMC

LSS

eRHICFixed target DIS

AAC00

q

q

q

10/10

Summary

• Polarized PDF from polarized DIS and 0 data– = 0.270.07 (Q2= 1 GeV2 )

• Assuming flavor SU(3) symmetry for the antiquark distributions

– g = 0.31 0.32 (Q2= 1 GeV2 )• Uncertainty reduction due to 0 data• Sign problem: positive or negative g?• Ambiguity of the small-x behavior

• Issues of current global analysis– Narrow Q2 range (1<Q2<80 GeV2)

• eRHIC: Q2<104 GeV2

– Large uncertainty at large x• High luminosity, precise measurements

– Undetermined small-x behavior of q(x)• eRHIC : x>10-4 (Q2>1 GeV2)