1/8 constraint on g(x) from 0 production at rhic masanori hirai tokyo tech (asymmetry analysis...
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Constraint on g(x) from 0 production at RHIC
Masanori Hirai
Tokyo Tech
(Asymmetry Analysis collaboration)With S. Kumano and N. Saito
Phys.Rev.D74, 014015 (2006); hep-ph/0603217
2006, Oct 05 @Kyoto
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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 +Lq: Generalized PDF from DVCS
• 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
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Spin asymmetry of production
• Cross section
– gggg, ggqq,qgqg– qqqq, qq’qq’– qqqq, qqgg, ggqq
• Consistent with unpolarized data– Fragmentation functions (FFs)
• Determined by e+e- data• Ambiguity of Dg
(z)
,
ˆ( )
pp X abA Ba b
a bT T
d ddx dx f x f x D z
dp d dp d
1 2
1 1
1 2 1 2
PRL91, 241803 (2003)
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Initial distributions of polarized PDFs
• Initial distribution at Q02
– – Chose of the functional form is arbitrary– Source of model dependence
• Constraint condition:– Positivity condition:
• Constraint of f(x) at large x• Avoiding unphysical behavior for the asymmetry: A1(x) >1 (x1)
– Antiquark SUF(3) symmetry:• 0 asymmetry in low pT: gg process dominates
– Insensitive to flavor dependence of f(x)• Fixed 1st moments: uv=0.926, dv= 0.341• Fixed q=1.0: undetermined small-x behavior
( , ) ( , ), , , ,i i ii ii v vif x Q x x x f x Q i u d q g
2 20 0
( ) ( )f x f x
( ) ( ) ( ) ( ) ( )u x d x s x s x q x
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AAC global analysis
• Added new data – DIS A1[=g1*2x(1+R)/F2]
• COMPASS(d), HERMES(p,d), J-Lab(n) – 0 data
• PHENIX RUN05 preliminary data
• Total # of data: 421– DIS: 413 (Q2 1GeV2)– 0 : 8 (1<pT<10 GeV, R,F =pT)
• NLO analysis– DIS:MS scheme– 0: K factor:<Kpol>=1, <Kunopl>=1.6
• B. Jager, et al, PRD67,054005 (2000)
– 2(/d.o.f.) = 370.47 (0.90)• DIS:359.29• 0 : 11.18
• Q2 dependence of pol-PDFs– DGLAP eq– Q0
2 = 1GeV2
• Minimizing 2
– Scaling error of 0 data is not included
• Error estimation– Hessian method
– 2 (N=11) = 12.64
exp theo, ,
exp
exp
( , ) ( , ),
i i
i
sta sys
A x Q A x Q
22 2
1 122
2 2 2
2 2 1
,
( ) ( ) ( ) ij
i j i j
f x f xf x H
a a
2
0( , ) 0.683 (1 )K N s ds
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g from DIS and 0 data
• 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)
-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)
RUN05
DIS + 0 (g < 0)
DIS + 0 (g > 0)
40% scaling error is not include
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Small-x behavior of g(x)
• 1st moment– g>0: 0.31 0.32 – g<0: 0.56 2.16
• Consistent results– 1st moment (0.1<xBj<1)
• g>0: 0.30 0.30 • g<0: 0.32 0.42
– DIS + 0 data covered
• Huge uncertainty of g<0– Ambiguity of small-x behavior – No constraint on the behavior
• g(x) is positive at large x
-1
-0.5
0
0.5
1
xg(x)
DIS + 0 (g < 0)
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)
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Summary
• Gluon spin component g– DIS only: g = 0.47 1.08
• Small contribution through Q2 evolution (1<Q2<80 GeV2) and higher order correction
– DIS+0: g = 0.31 0.32• Direct contribution to 0 cross section in low and medium pT
• Significant reduction of its uncertainty• Assuming g > 0
• Sign problem:positive or negative g ?– g = 0.56 2.16 (DIS+0)
• gg process dominates in low pT: g(x)
• Ambiguity of the small-x behavior of g(x)• Need constraint on the behavior
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Large-x behavior of g(x)
• Positive g(x)/g(x) at large-x– HERMES A1
d
• 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) asymmetry
• 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
-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) ( ) ( )
( )
g
gx
C x x g x
dz xC z x g
z z
1
.
( ) : . . ,
: . .
g
x
C z z
g x z x z
0 05
0 05 0 2
0 25 1
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Polarized PDFs by AAC analysis
• Improvements– dv(x): J-Lab(n) data– q(x): COMPASS and HERMES data– g(x): PHENIX RUN05 data
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 = 0.45-0.1
0
0.1
0.2
0.3
0.001 0.01 0.1 1
AAC06
GRSV
BB
LSS
-0.2
0
0.2
0.4
0.6
0.8
0.001 0.01 0.1 1
x
xg(x)
Q2 = 1 GeV2
x(x)
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 + 0 (g > 0)
-1
0
1
2
0.001 0.01 0.1 1
xg(x)
DIS (AAC03)
DIS + 0 (g > 0)
-0.04
-0.03
-0.02
-0.01
0
0.01
0.001 0.01 0.1 1
x
xq(x)