Recent results of the AAC analysis
description
Transcript of Recent results of the AAC analysis
Recent results of the AAC analysis
Masanori HiraiTUS, Noda
(Asymmetry Analysis collaboration)Collaborators: S. Kumano and N. Saito
arXiv:0808.0413 [hep-ph]
2009 1 10,KEK
1/15
Contents
• Introduction
• AAC08 analysis– Global analysis of the polarized PDFs– Data sets
– Assumptions: positivity condition, antiquark SU(3)f symmetry
• Impact of RHIC 0 data – Discussion about a functional form of g(x)
• Impact of E07-011 data– Relative errors G/G ?
• Summary
2/15
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
– Unknown orbital angular moments Lq,g
• Quantitative value from sum rule of GPDFs• Qualitative understanding ?
– G is an important piece of the spin puzzle !• Undetermined G = 0.49 1.27 (AAC03)
– Experimental data from RHIC-Spin• 0 production [RUN05, PRD76, 051106 (2007)]
• AAC analysis– AAC00 [PRD62, 0304017 (2000)]: DIS– AAC04 [PRD69, 054021 (2004)]: DIS, uncertainty estimation– AAC06 [PRD74, 014015 (2006)]:DIS+0, uncertainty, G– AAC08 [arXiv:0808.0413 [hep-ph]]: DIS+0, uncertainty, E07-011(J-Lab)
3/15
4/15
• Cross section
• Hadron tensor (asymmetric part)
• Structure function g1
Polarized deeply inelastic scattering
2 2
2
,
, 0 12
P qQ q
M
Qx x
M
2 2
4' 2
d EL
d dE MW
Q E
1 2
( )A
q s q PW s x s
Mg g x
21
1
1
2( ) ( )
f
i i
n
i q gi
C x C xg x q x q x g xe
( ) ( ) ( ), ( ) ( ) (
, coefficient func: t on
)
iq g
q x q x q x q x q x
C C
q x
1
x
dy x dyf g f g y
y y y
5/15
Spin asymmetry A1(x,Q2)
• Polarized DIS experiments– Proton : E130, E143, EMC, SMC, HERMES, E155,CLAS– Deuteron: E143, E155, SMC, HERMES, COMPASS, CLAS– Neutron : E142, E154, HERMES, J-Lab (Hall-A)
• Q2 dependence is obtained by the DGLAP equation
12
1
1
( ) ( )
( ) ( )
2 (1 )
d dA
d d
g
F
xg
R
F
2, T
L
R x Q
• L. W. Whitlow et al., Phys. Lett. B 250
(1990) 193
Total data 441 points
(Q2>1GeV2)
6/15
Spin asymmetry of production
• Cross section
– gggg, ggqq,qgqg– qqqq, qq’qq’– qqqq, qqgg, qqq’q’
• Consistent with unpolarized data– Fragmentation functions (FFs)
• Determined by e+e- data
• Ambiguity of Dg (z)
• Sing problem– gg process dominates at low pT
• ALL0 [g(x)]2, negative or positive ?
,
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
PRD76, 051106 (2007)
7/15
AAC analysis and uncertainty estimation
• Initial distribution of polarized PDF
• Constraint condition– Positivity condition:
• Imposing on positive g(x), but not impose on node type
– 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 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
• Q02 = 1 GeV2
Value of 2
• Hessian method
–
• [K(N,s): 2 distribution ]
• 2 ~ N (N: number of parameters)– 1 error of normal distribution in
multi-parameter space– Not 1 error for PDF uncertainties– Correspondence between
uncertainties and variations of experimental data
• 2=1 : statistically correct– 1 error for 1 degree of freedom
• Asymmetry A1
• X-sections8/15
2
0( , ) 0.683K N s ds
2 2 1
,
( ) ( ) ( ) ij
i j i j
f x f xf x H
a a
Data-theory
AAC08 analysis
• Added new data– DIS: CLAS(p,d), COMPASS(d, renewal data)– 0production: RHIC Run 5 final data (10 points)
• Data sets– Set-A : DIS data only– Set-B : DIS + 0 data– Set-C : DIS + fake data of the E07-011 experiment
• Impact on the determination of g(x) – Set-A vs. Set-B: effect on the functional form, node or positive– Set-B vs. Set-C: an impact on determination of the gluon spin contribution G
9/15
Fake data of the E07-011 experiment
• Update experiment of the J-Lab
• Expected errors for g1(x)– Converted to asymmetry errors
• Expected asymmetry error
10/15
212 2
1 1207 0111
07 011
,, * ,
,
d
d d
dE Set A
E
g x QA x Q A x Q
g x Q
Results
• Minimal 2
• 1st moments:
11/15
Set-A (436 point)Set-B (446
point)Set-C (441 point)
Positive Node Positive Node Positive Node
DIS 381.66 375.87 384.65 381.27 381.66 375.87
0 12.43 11.32
Total 2 381.66 375.87 397.08 392.60 381.66 375.87
2/d.o.f 0.90 0.88 0.91 0.90 0.89 0.87
Set-A Set-B Set-C
Positive Node Positive Node Positive Node
0.24 0.07
0.22 0.08
0.26 0.06
0.25 0.07
0.24 0.05
0.22 0.05
G 0.63 0.81
0.94 1.66
0.40 0.28
-0.12 1.78
0.63 0.45
0.94 1.09
1 2 2
0( ) , 1F f x dx Q GeV
Impact of RHIC 0 data
12/15
• Insensitive to uv(x) and dv (x)– Same center values and
uncertainties between Set-A and –B– gg process dominates
• g(x) becomes small• Gluon uncertainty is reduced by
RHIC data– RHIC data is sensitive to g(x)
• Node type (DIS+0)– Less 2 : 12.43(G>0) , 11.32 (G<0)– Changing sign at x=0.1– Large uncertainty in small-x region
• No data to constraint the behavior
Impact of E07-011 data
13/15
• Converged determination of the valence quark distributions– No changed these uncertainties
– Assuming SUf(3) symmetry
• Fixed 1st moments for uv and dv
• Significant reducing the uncertainty of g(x) – Error correlation with antiquark
distribution via Q2 evolution– Constraint via NLO gluon term
• Low Q2 data• Higher twist term ?
Impact of RHIC 0 and E07-011 data
• Positive type– DIS: large distribution– 0: small distribution
• Node type– DIS: small negative below x=0.02– 0 : large negative at small-x– Large uncertainty in small-x– Positive distribution at high-x
• Relative error G/G (x>0.1)
• Same impact as RHIC Run5 data14/15
Positive
Node
Set-B (DIS+0) 0.71 0.77
Set-C (E07-011)
0.73 0.54
Summary
• Polarized PDF from polarized DIS data– Well determined valence quark distributions– Undetermined anti-quark and gluon distributions
• Rather large uncertainties of these distributions• Reduction gluon uncertainty due to error correlation with antiquark
distribution• NLO gluon term < statistical errors
– Positive distribution of g(x) at medium and large-x region – E07-011 experiment (precise measurement )
• Constraint on g(x) via NLO gluon term• NLO gluon term > statistical errors• Same impact as RHIC run5 0 data
• g(x) from 0 production data– Node type, changing sign around x=0.1
• RHIC data: covering narrow x-region
– Undetermined small-x behavior• No data in the small-x region
• AAC08 numerical library: http://spin.riken.bnl.gov/aac/15/15
16/14
1st moments of g(x)
• Full range x=0~1
• 0.1< X <1
– CLAS data (x=0.175 ~0.55)
– 0 data (s=200 GeV, pT= 1.29 ~ 7.79 GeV)
17/14
Set-A Set-B Set-C
Positive Node Positive Node Positive Node
G 0.63 0.81
0.94 1.66
0.40 0.28
-0.12 1.78
0.63 0.45
0.94 1.09
Set-A Set-B Set-C
Positive Node Positive Node Positive Node
G 0.53 0.72
0.87 0.89
0.36 0.26
0.40 0.31
0.53 0.38
0.87 0.47
G/G 1.36 1.02 0.71 0.77 0.73 0.54
18/14
Comparison of FF for 0 production
• Model dependence of the FF global analysis ?– Kretzer’s FFs within LO uncertainty
– KKP’s FFs without the uncertainty at large-pT
• Cut of z for 2nd moments of FFs (z>0.05)• Heavy quark mass threshold
• Uncertainty from NLO FFs becomes 1/3
19/14
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 g1D
– 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)