aac analysis of polarized parton distributions with uncertainties shunzo kumano, saga university...
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AAC analysis of polarized parton distributions with uncertainties
Shunzo Kumano, Saga University
kumanos@cc.saga-u.ac.jp, http://hs.phys.saga-u.ac.jp
12th International Workshops on Deep Inelastic Scattering (DIS04)
Strbske Pleso, Slovakia, April 14-18, 2004
Refs. (1) Y. Goto et. al., Phys. Rev. D62 (2000) 034017.
(2) M. Hirai, SK, N. Saito, Phys. Rev. D69 (2004) 054021.
April 15, 2004
Contents
Introduction
Polarized PDFs of AAC03 analysis
- global analysis
- uncertainty estimation
- analysis with g=0
Summary
• proton-spin issue
polarized e/-proton scattering measurement of g1 g
1
LO 1
2e i
2 (q ii q i)
proton, deuteron, 3He g1 data
with isospin symmetry valence and sea polarization uv ,dv ,q
quark spin content uv dv 6q
experimentally dx0
1
(x)0.1 0.3
rest of the spin ???
Papers on the polarized PDFs
D. de Florian, L. N. Epele, H. Fanchiotti, C. A. Garcia Canal, and R. Sassot, Phys. Rev. D51 (1995) 37; D57 (1998) 5803; D62 (2000) 094025.
M. Glück, E. Reya, M. Stratmann, and W. Vogelsang, Phys. Rev. D53 (1996) 4775 (1996); D63 (2001) 094005.
T. Gehrmann and W. J. Stirling, Phys. Rev. D53 (1996) 6100.
G. Altarelli, R. D. Ball, S. Forte, and G. Ridolfi, Nucl. Phys. B496 (1997) 337; Acta Phys. Pol. B29 (1998) 1145.
C. Bourrely, F. Buccella, O. Pisanti, P. Santorelli, and J. Soffer, Prog. Theor. Phys. 99 (1998) 1017; Eur. Phys. J. C23 (2002) 487.
L. E. Gordon, M. Goshtasbpour, and G. P. Ramsey, Phys. Rev. D58 (1998) 094017.
SMC (B. Adeva et. al.), Phys. Rev. D58 (1998) 112002.
E. Leader, A. V. Sidrov, and D. B. Stamenov, Phys. Rev. D58 (1998) 114028; Eur. Phys. J. C23 (2001) 479.
AAC (Y.Goto et al., M. Hirai et al.), Phys. Rev. D62 (2000) 034017; D69 (2004) 054021.
J. Bartelski and S. Tatur, Phys. Rev. D65 (2002) 034002.
J. Blümlein and H. Böttcher, Nucl. Phys. B636 (2002) 225.
Initial distributions fi(x,Q0
2) = A i x i (1 + i x i) fi(x,Q02)
i = uv, dv, q, g A i , i , i , i : parameters
χ2 fit to the data [p, n (3He), d]
A 1
g1
F1= g1
2 x (1 + R)F2
R =
FL
2 x F1=
F2 – 2 x F1
2 x F1
2 =
i
(A 1 idata – A 1 i
calc)2
(A 1 i
data)2
We analyzed with the following conditions.
• unpolarized PDF GRV98• initial Q2 Q0
2 = 1 GeV 2
• number of flavor Nf = 3
positivity f(x) f(x) (to be precise, )
antiquarkflavor: u = d = s
Experimental data on spin asymmetry A1(x,Q2)
• A1 data– Proton : E130, E143, EMC, SMC, HERMES, E155
– Deuteron: E143, E155, SMC
– Neutron : E142, E154, HERMES, JLab
Total data 399 points (Q2>1GeV2)
1
10
100
0.001 0.01 0.1 1
x
E130(p)
E143(p)
E155(p)
EMC(p)
SMC(p)
HERMES(p)
E143(d)
E155(d)
SMC(d)
E142(n)
E154
HERMES(n)
(GeV
2 )
Error estimation Hessian method
2() is expanded around its minimum 0 ( =parameter)
where the Hessian matrix is defined by
2(0 ) 2(0) 2(0) i
ii
12
2 2 (0 ) i j
i ji, j
In the 2 analysis, 1 standard error is
The error of a distribution F(x) is given by
H ij 1
22 2(a0) i j
2 = 2(0 ) 2(0) i Hij ji, j
F( x)
2 2 F( x) i
ij– 1 F( x)
ji, j
P(s) N: 2(= s) distribution with N degrees of freedom
ds0
2
P(s) N = 11 = 0.6826 2=12.64 (N = 1 case, 2= 1)
Results • Total 2
2/d.o.f. = 0.893
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.001 0.01 0.1 1
x
AAC00
New
dg=0
Q2=1 GeV2
xuv(x)
xdv(x)
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.001 0.01 0.1 1
x
AAC00
New
dg=0 xg(x)
x6q(x)
Comparison of AAC03 with AAC00AAC00: Y.Goto et al., Phys. Rev. D62 (2000) 034017
AAC03: M.Hirai et al., Phys. Rev. D69 (2004) 054021
Spin asymmetry A1p
• Precise data (E155-proton) reduce asymmetry uncertainties• Agreement with polarized DIS data
– Quark and antiquark distributions are constrained– Gluon distribution need other constraint
-0.5
0
0.5
0.01 0.1 1
-0.5
0
0.5
0.001 0.01 0.1 1
-0.5
0
0.5
0.01 0.1 1
x
EMC (p)
SMC(p)
HERMES(p)
-0.5
0
0.5
0.01 0.1 1
-0.5
0
0.5
0.01 0.1 1
-0.5
0
0.5
0.01 0.1 1
x
E130 (p)
E143 (p)
E155 (p)
-0.2
0.2
0.6
1
1.4
1.8
0.001 0.01 0.1 1
x
AAC03
AAC00
Proton
Q2 = 5 GeV2
(Dat
a-th
eory
)
AAC03 uncertainties
AAC00 uncertainties
AAC00 AAC03 (with E155-p)
Polarized PDFs (AAC03)• PDF uncertainties reduced by
including precise (E155-p) data
• Valence-quark distributions are well determined
– Small uncertainty
of uv, dv
• Antiquark uncertainty is significantly reduced– g1
p 4uv+ dv+12q
• g(x) is not determined– Large uncertainty– Indirect contribution to g1
p – Correlation with antiquark
0
0.1
0.2
0.3
0.4
0.5
0.001 0.01 0.1 1
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.001 0.01 0.1 1
x
xuv(x)
xdv(x)
Q2 = 1 GeV2
-2
-1
0
1
2
3
0.001 0.01 0.1 1
-0.05
-0.04
-0.03
-0.02
-0.01
0
0.01
0.02
0.001 0.01 0.1 1
x
xg(x)
Q2 = 1 GeV2
xq(x)
AAC03 uncertainties
AAC00 uncertainties
AAC00 AAC03 (with E155-p)
E155 data
Correlation between q(x) and g(x)
• analysis with g(x)=0 at Q2=1 GeV2
2/d.o.f. = 0.915
• qv(x) uncertainties are
not affected
• antiquark uncertainties
are reduced – strong correlation with g(x)– correlation with g(x) is almost terminated in the g=0 analysis
-2
-1
0
1
2
3
0.001 0.01 0.1 1
-0.05
-0.04
-0.03
-0.02
-0.01
0
0.01
0.02
0.001 0.01 0.1 1
x
xg(x)
Q2 = 1 GeV2
xq(x)
0
0.1
0.2
0.3
0.4
0.5
0.001 0.01 0.1 1
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.001 0.01 0.1 1
x
xuv(x)
xdv(x)
Q2 = 1 GeV2
The error band shrinks due to the correlation with g(x).
g=0 uncertainties
AAC03 uncertainties
Comparison with other parameterizations
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
AAC03
GRSV
BB
LSS
xuv(x)
xdv(x)
Q2 = 1 GeV2
-1
0
1
2
0.001 0.01 0.1 1
AAC03
GRSV
BB
LSS
-0.04
-0.03
-0.02
-0.01
0
0.01
0.001 0.01 0.1 1
x
xg(x)
Q2 = 1 GeV2xq(x)
1st moments
– GRSV01 [ Phys. Rev. D63 (2001) 094005 ]– LSS01 [ Eur.Phys.J. C23 (2002) 479 ]– BB02 [ Nucl. Phys. B636 (2002) 225 ]
g
AAC03 0.499 1.268 0.213 0.138
GRSV01 0.420 0.204
LSS 0.680 0.210
BB 1.026 0.138
uv dv 6q
Q2 1 GeV2
W ( g qqq2 ) F1
ˆ p ˆ p pq F2 i
q p2pq F3 where ˆ p p
pqq2
q
i q spq g1i
q(pq s sq p )(pq)2 g2
ˆ p ˆ s ˆ s ˆ p
2pq sq ˆ p ˆ p
(pq)2
g3
sq ˆ p ˆ p (pq)2
g4 ( g qq
q2 ) sq pq g5
new structure functions g3, g4, g5
be careful about “various” definitions of g3, g4, g5 !
d( p 1CC p 1
CC )dx dy GF
2 Q2
(1Q2 / MW2 )2xy
{[ y(2 y)xg1CC (1 y)g4
CC y2xg5CC
]
2 x y M 2
Q2 [ x2y2 g1
CC 2 x2y g2CC 1 y x2y2 M 2
Q2
x g3
CC
x 1 3
2y x2y2 M2
Q2
g4
CC x2y2g5CC] }
0 at Q2>>M2
Polarized neutrino-proton scattering (CC)
Quark spin content
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.000001 0.00001 0.0001 0.001 0.01 0.1 1
xmin
SMC-98
LSS-99
AAC-00-1
factory
1
minmin
)()(x
dxxx
e / scattering = 0 ~30%
It is not uniquely determined.
g1p + g1
p = (u + u) + (d + d)
+ (s + s) + (c + c)
in LO dx (g1p + g1
p) =
independent determination ofquark spin content !
scattering
on factorysee e.g. hep-ph/0310166
Summary • Global analysis for polarized PDFs
– uv(x), dv(x) are determined well– = 0.213 0.138 (Q2= 1
GeV2 )– g(x) could not be constrained
AAC03-polarized-pdfs code could be obtained fromhttp://spin.riken.bnl.gov/aac/
http://hs.phys.saga-u.ac.jp/aac.html (mirror site)
• Uncertainties of polarized
• Effects of E155-proton data
• Global analysis also with g=0
• Error correlation between g and q
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