1/9 Constraint on g(x) at large-x Bj Masanori Hirai Titech (Asymmetry Analysis collaboration) With...
-
Upload
reid-gravette -
Category
Documents
-
view
216 -
download
0
Transcript of 1/9 Constraint on g(x) at large-x Bj Masanori Hirai Titech (Asymmetry Analysis collaboration) With...
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