Possible studies of structure functions at JLab
Shunzo Kumano
High Energy Accelerator Research Organization (KEK)
Graduate University for Advanced Studies (GUAS)
http://research.kek.jp/people/kumanos/
Our codes are available for
Nuclear PDFs:
http://research.kek.jp/people/kumanos/nuclp.html
Polarized PDFs:
http://spin.riken.bnl.gov/aac/
Fragmentation functions: http://research.kek.jp/people/kumanos/ffs.html
Q2 evolutions:
http://research.kek.jp/people/kumanos/program.html
Workshop on the Jefferson Laboratory Upgrade to 12 GeV
Sept. 14 - Nov. 20, 2009, INT, Seattle, USA
http://www.int.washington.edu/PROGRAMS/09-3.html
November 5, 2009
Outline
Three different topics.
I will stop when time runs out.
1. Nuclear modifications of R = FL / FT at large x
We (M. Ericson and SK) insist that
nuclear modifications of R = FL / FT should exist at large x.
2. From nucleon-spin crisis to tensor-structure crisis (?)
Tensor structure functions of spin-1 hadrons (b1, b2, …).
3. ∆ g(x) determination by accurate g1 measurements
Accurate g1 by JLab E07-011
 NLO gluon term in g1 could be determined.
Nuclear modifications
of R = FL / FT at large x
Ref. M. Ericson and SK, Phys. Rev. C 67 (2003) 022201.
Nuclear effect on R = FL / FT by HERMES
HERMES, K. Ackerstaff el al., PL B 475 (2000) 386;
Erratum, PL B567 (2003) 339 [hep-ex/0210067; hep-ex/0210068].
Longitudinal and transverse components

WT = 1 (W = + 1 + W = – 1) = W1
2

WL = W = 0
W  =   *
  W, 
2

= (1 + 2 ) W2 – W1
Q
X
'
L, T
p
RA /RD
(2000)
Q2 (GeV2)
(2003)
Nuclear effects on R by CCFR/NuTeV
U.-K. Yang et al., PRL 87 (2001) 251802.
CCFR
SLAC
HERMES
note
No significant deviation is measured
from the nucleon case (
).
No large nuclear modification
of R is observed in +Fe!
(note: CCF/NuTeV target is Fe)
M. Ericson and SK, Phys. Rev. C 67 (2003) 022201
 Submitted (Nov. 30, 2002) just after the HERMES correction paper (Oct. 31, 2002).
 Nuclear modifications of transverse-longitudinal ratio
do exist in medium and large-x regions,
although the modifications do not seem to exist at small x
within experimental errors according to the revised
HERMES paper.
 Mechanisms
(1) Transverse nucleon motion
 T-L admixture of nucleon structure functions.
(2) Binding and Fermi-motion effects in the spectral function.
Formalism
A, N
W
 W
A, N
1
q q 

1 A, N A, N
A, N
g


W
p p
2
 
q 2 
M N2
pq
p  p  2 q
q

Q2 
F1  M N W1 , F2   W2 , FL 
W  1  2  F2  2xF1
 L 
 
Q2
Projection operators of W1A and W2A

P̂1
2
 


1   p A pA 
p
3
p


A
A pA
 g 
, P̂2   2  g 
2
p 2 
2 pA 
p 2 

A
P̂1,2
WA  W1,2
Convolution: WA ( pA , q)   d 4 p S( p) WN ( pN , q)
A

W1,2
( pA , q)   d 4 p S( p) P̂1,2
WN ( pN , q)
Longitudinal and transverse components
WTA, N
1
 (WA, 1N  WA, 1N )  W1A, N
2
2
(
p

q)
 A2   2  N 2
pN
WA, N    *  WA, N
WLA, N  WA, 0N
  A,2 N  A, N
  1  2  W2  W1A, N
Q 

Formalism (continued)
Q2
MN
Q2
x
Q2
pN  q
Scaling variables: x A 

x, x N 
 , x
, z
2 pA  q M A
2 pN  q z
2M A
M A
A, N
L
Longitudinal structure functions F1 and F2 : F
Transverse-longitudinal ratio: RA,N

Calculating
A
1
2 xA F =
A
L
F =

MN
d p N S(pN) z
p N2
4
MN
d pN S(p N) z
p N2
4

A
A
W1,2
= P1,2 W
= P1,2
[(
[(

Q2  A, N
  1  2  F2  2x A, N F1A, N
 A, N 

FLA, N

2x A, N F1A, N
N
d 4p N S(p N) W
,
2
2
p N
p N
N
2
1+
2 x N F1 (x N, Q ) +
FLN(x N, Q 2 )
2
2
2 pN
2 pN
)
2
2
p N
p N
N
2
1 + 2 FL (xN, Q ) + 2 2 x N F1N(xN, Q 2)
pN
pN
)
pN
]
pN
q
]
Results


(M A – i = M A – M N –  i)
Spectral function
2
S(p N) =  (p N)
i
(
 p 0N – M A +
2
2
M A – i + pN

Transverse –longitudinal ratio: R 1990

F2N (PDFs): MRST98 –LO
0.4
)
for
1.1
2
Q 2 = 1 GeV 2
10 GeV 2
100 GeV 2
2
Q = 1 GeV
0.3
1.05
R
N
14
0.2
2
10 GeV
0.1
admixture effects
R 14N
RN
1
100 GeV2
0
0
0.2
0.4
0.6
x
without L-T mixing
0.8
1
0.95
0
0.2
0.4
0.6
x
0.8
1
After the HERMES (CCFR/NuTeV)
re-analysis, people tend to lose interest
in the nuclear effect on R.
However, we claim that nuclear
modification should exist in medium
and large-x regions.
Physical origins
 transverse-longitudinal admixture
due to the transverse Fermi motion
 binding and Fermi motion effects
in the spectral function
In the kinematical region of
our prediction, data does not
exist.
Need future experimental
investigations at
JLab, EIC,  factory, …
JLab measurements in 2007
• V. Tvaskis et al., PRL 98 (2007) 142301.
• Lingyan Zhu (Hampton Univ),
personal communications (2009).
Badelek, Kwiecinski, Stasto (1997)
E99-118
Ee  2.301, 3.419, 5.648 GeV
MRST-2004
0.007  x  0.55, 0.06  Q2  2.8 GeV 2
proton, deuteron
GRV-1995
x  0.07
x  0.32
Almost same for p an d, but at 0.04 < x < 0.32.
 In any case, nuclear modifications
should be small for the deuteron.
 Importance of future JLab measurements
for heavier nuclei, especially at large x (>0.4).
From nucleon-spin crisis
to tensor-structure crisis (?)
Refs. F. E. Close and SK, Phys. Rev. D 42 (1990) 2377,
M. Hino and SK, Phys. Rev. D 59 (1999) 094026;
D 60 (1999) 054018,
SK and M. Miyama, Phys. Lett. B 497 (2000) 149,
T.-Y. Kimura and SK, Phys. Rev. D 78 (2008) 117505.
References on tensor structure function b1
Theoretical formalism for polarized electron-deuteron
deep inelastic scattering
P. Hoodbhoy, R. L. Jaffe, and A. Manohar, NP B312 (1989) 571.
[ L. L. Frankfurt and M. I. Strikman, NP A405 (1983) 557. ]
HERMES experimental result
A. Airapetian et al., Phys. Rev. Lett. 95 (2005) 242001.
Our works
Sum rule for b1
F. E. Close and SK, Phys. Rev. D 42 (1990) 2377.
Projections to F1, F2, g1, g2, b1, …, b4 from W 
T.-Y. Kimura and SK, Phys. Rev. D 78 (2008) 117505.
Motivation
 Spin structure of the spin-1/2 nucleon
Nucleon spin puzzle: This issue is not solved yet,
but it is rather well studied theoretically and experimentally.
 Spin-1 hadrons (e.g. deuteron)
Tensor-structure puzzle (???)
There are some theoretical studies especially on tensor structure
in electron-deuteron deep inelastic scattering.
 HERMES experimental results
A few investigations have been done for polarized
proton-deuteron processes.
 J-PARC, COMPASS, U70, GSI-FAIR, RHIC … experiment ?
Structure function b1 in a simple example
Spin-1 particles (deuteron, mesons)
b1 = 0
only in S-wave
b1  0: New field of high-energy spin physics
with orbital angular momenta.
The b1 probes a dynamical aspect of hadron structure
beyond simple expectations of a naive quark model.
 Description of tensor structure
by quark-gluon degrees of freedom
Electron scattering from a spin-1 hadron
P. Hoodbhoy, R. L. Jaffe, and A. Manohar, NP B312 (1989) 571.
[ L. L. Frankfurt and M. I. Strikman, NP A405 (1983) 557. ]
W   F1 g  F2
p p

i
i
 g1   q  s  g2 2   q  p  qs  s  qp








1
1
1
 b1 r  b2 s  t  u  b3 s  u  b4 s  t
6
2
2
Note: Obvious factors from q W  q W  0 are not explicitly written.
  p  q,   1  M 2 Q 2  2 , E 2   M 2 , s  
i
  E E p
2
M
2 
1 2  p p

q

E
q

E

 

 
2 
3
r 
1 
1

q  E q  E   2  g ,
2 

 
3
t 
1 
4

q  E p E  q  E p E  q  Ep E  q  Ep E   p p 
2 

2 
3
u
s 
1
2
2

  E E  E E  M 2 g  p p 


3
3


spin-1/2, spin-1
spin-1 only
E   polarization vector
b1 ,  , b4 tems are defined so that
they vanish by spin average.
b1 , b2 tems are defined to satisfy
2xb1  b2 in the Bjorken scaling limit.
2xb1  b2 in the scaling limit ~ O(1)
M2
b3 , b4  twist-4 ~ 2
Q
Projections to F1, F2, …, b4 from W
Calculate W  in hadron models  need to extract structure functions b1 , b2 , 
Projection operators are needed to extract them from the calculated W  .
For F1 and F2 , they are well known:
1     1 p  p 
x     1 3 p  p 
F1    g 
W , F2    g 
W ,   1  Q2  2
2 
2 
2
 M 


M 
Try to obtain projections
in a spin-1 hadron by combinations of
Results on a spin-1 hadron
p  p
g ,
,   q s ,...
2
M

Bjorken scaling limit
1
1
1
 
F2   g    f i Wf i
2x
2
3
i 
 
g1  
 q s   f 1 i 1Wf i
2
1
1
 
b1 
b2  g    f 1 i 1    f 0 i 0 Wf i
2x
2
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ÅB
F1 


T.-Y. Kimura and SK,
PRD 78 (2008) 117505.
Structure
Functions
F1  d



g1  d , 1  d , 1

d 1  d 1
b1  d 0  
2
note:  (0) 
 (1)   (1)
2
Parton
Model
F1 
3  
3
 (1)   (1)
2

1
ei 2 qi  q i

2 i

qi 

1
g1   ei 2 qi  q i
2 i


 qH x,Q2 



1
b1   ei 2  qi   q i
2 i


1 1
qi  qi 0  qi 1
3

qi  qi 1  qi 1
1
1
q

q
i
 qi  qi 0  i
2

Sum rule for b1
2
dx
b
(x)

dimensionless
:
QM
???
 1
F.E.Close and SK,
PRD42, 2377 (1990).
M  hadron mass


dx
 






Q  quadrupole moment
q0

 

1
4

D
dx
b
(x)

dx

u


u


d


d


s


s
D
D
D
D
D
 1
  9 D

9
5
1
 Q   Q
  dx  uv (x)   uv (x)  Q   Q

sea
sea
9
9



 

  dx  5  u   u   d D   d D  2  s D   s D 
sea
Elastic amplitude in a parton model
 H, H  p, H J0 (0) p, H   ei  dx  qi H  qi H  qiH  qiH 
i
1
1
1









e
dx

q


q

dx  uv (x)   dv (x)
 i  D
0,0
1,1
1,1 
D

2 
2
3

i


D
dx
b
(x) 
1


5
1
 1





Q   Q
0,0
1,1
1,1  
6 
2
9



sea
Macroscopically
t 0
t


 0,0  lim  Fc (t) 
F
(t)
Q

t0 
3M 2
t


 1,1   1,1  lim  Fc (t) 
F
(t)
Q

t 0 
6M 2
5

 dx b (x)  lim
t 0
12
5
 lim 
t 0
12
D
1


t
1
F (t)   Q   Q
2 Q
M
9
t
F (t)
2 Q
M
sea
dx
1
2
p
n
 F2 (x)  F2 (x)    dx uv  dv   dx  u  d 
x
3
3
Note: FQ (t) in the unit of
1
M2
If the sum-rule violation
is shown by experiment,
it suggests antiquark
tensor polarization.
HERMES results on b1
27.6 GeV/c
positron
A. Airapetian et al. (HERMES), PRL 95 (2005) 242001.
, 0
deuteron
b1 measurement in the kinematical region
0.01  x  0.45, 0.5 GeV 2  Q2  5 GeV 2
b1 sum rule

0.85
0.002
dx b1 (x)  1.05  0.34(stat)  0.35(sys)  10 2
at Q2  5 GeV 2
In the restricted Q2 range Q2  1 GeV 2

0.85
0.02
dx b1 (x)  0.35  0.10(stat)  0.18(sys)  10 2
at Q2  5 GeV 2
D
dx
b
 1 (x)  lim 
t0


5 t
1
F
(t)

Q Q
Q
2
12 M
9
sea  0 ?
dx
1
2
 F2p (x)  F2n (x)    dx uv  dv   dx  u  d   1 / 3
x
3
3
Drell-Yan experiments probe
these antiquark distributions.
Actual experimental proposals at J-PARC: P04, P24
q
E866
J-PARC
Antiquark
distributions

+
–
q
Drell-Yan: p  p       X, p  d       X
E906
 DY ( pd) 1  d (x2 ) 
 1
2 DY ( pp) 2 
u(x2 ) 
E866: existing measurements by the Fermilab-E866
E906: expected measurements by the Fermilab-E906
(from 2010)
J-PARC: proposal stage
 It should be possible to use polarized proton-deuteron Drell-Yan processes
to measure the tensor polarized distributions.
References for tensor structure in Drell-Yan
• General formalism for polarized Drell-Yan processes
with spin-1/2 and spin-1 hadrons
p  d    X
( p  d       X is
enough for tensor structure)
M. Hino and SK, Phys. Rev. D59 (1999) 094026.
• Parton-model analysis of polarized Drell-Yan processes
with spin-1/2 and spin-1 hadrons
M. Hino and SK, Phys. Rev. D60 (1999) 054018.
• An application: Possible extraction of polarized
light-antiquark distributions from Drell-Yan
SK and M. Miyama, Phys. Lett. B497 (2000) 149.
Comments on the situation
• There was a feasibility study for polarized deuteron beam at RHIC:
E. D. Courant, BNL-report (1998).
• No actual experimental progress with hadron facilities.
• Future: J-PARC, COMPASS, U70, GSI-FAIR, RHIC, …
Spin asymmetries in the parton model
longitudinally polarized: qa ,
tensor polarized:  qa
unpolarized: qa ,
transversely polarized:  T qa ,
Unpolarized cross section
d
2
1
2

1

cos

ea2  qa x A qa x B   qa x A qa x B 

2
dx A dx B d
4Q
3 a


Spin asymmetries
ALL


2
 qa x A qa x B   qa x A qa x B 
e
a
a

2
 qa x A qa x B   qa x A qa x B 
e
a
a
2
sin2  cos 2   a ea   T qa x A  T qa x B    T qa x A  T qa x B 
ATT 
1  cos 2 
 a ea2  qa x A qa xB  qa x A qa xB 
AUQ0
e  q x  q x   q x  q x 


 e  q x q x  q x q x 
2
a
a
2
a
a
a
A
a
A
a
B
a
A
a
B
a
A
a
a
B
B
Advantage of the hadron reaction ( q measurement)
AUQ0 large xF
e q x  q x 


 e q x q x 
2
a a a
2
a
a
a
A
A
a
a
B
B
ALT  ATL  AUT  ATU  ATQ0  AUQ1
 ALQ1  ATQ1  AUQ2  ALQ2  ATQ2  0
Note:   transversity in my notation
Possible JLab measurements
F2
"Rough" order of magnitude estimate
in a conventional model for the deuteron
HERMES
(2005)
 p2 
b1
~ O  2   (D state admixture)
F1
M 
See P. Hoodbhoy et al.,
NP B312 (1989) 571.
1
F2
2
x  0.35
2


1
p
xb1 ~ F2  O  2   (D state admixture)
2
M 
xF1 ~

x  0.18
Q2
1
1 1
 (0.3)  
 0.001 at medium x
2
10 20
 expected to be a small quantity!
(suitable for JLab experiment)
Possible JLab measurements
in this x region.
• HERMES data have large errors
See also a theoretical model by G. A. Miller,
in Topical Conference on Electronuclear physics
with Internal Targets, edited by R. G. Arnold
(World Scientific, 1990).
 Important contribution from JLab.
Possibly, opening of tensor-structure crisis at JLab!?
Determination of gluon polarization
by accurate g1 measurements
Refs. AAC (Asymmetry Analysis Collaboration),
Y. Goto et al., Phys. Rev. D 62 (2000) 034017;
M. Hirai, SK, N. Saito, Phys. Rev. D 69 (2004) 054021;
74 (2006) 014015;
M. Hirai, SK, Nucl. Phys. B 813 (2009) 106.
Nucleon Spin
Naïve Quark Model
  uv  dv  1
Electron / muon scattering
  0.3
Almost none of nucleon spin
is carried by quarks!
QCD
Sea-quarks and gluons?
Orbital angular momenta ?
Gluon: G
Sea-quarks: qsea
Lq , Lg
Recent data indicate
G is small at x ~ 0.1.

Future experiments

1 1
 uv  dv  qsea  G  Lq  Lg
Nucleon Spin:
2 2

Gluon polarization from lepton scattering
F. Kunne (COMPASS), AIP Conf. Proc. 1149 (2009) 321.
Gluon polarization from RHIC π0 production
Parton distribution functions
Parton interactions
p  p 0  X
(Torii’s talk at Pacific-Spin05)
Fragmentation functions
Gluonic processes dominate.
Determination of ∆g
however with uncertainties of
gluon fragmentation functions.
0.1
RUN05
0.08
0.06
0.04
0

ALL
0.02
Uncertainty range of
gluon fragmentation functions in LO.
(See the next page.)
In the NLO, the range is smaller.
0
-0.02
-0.04
-0.06
1
2
3
4
5
6
pT (GeV)
7
8
9
10
Comparison of fragmentation functions in pion
NLO
(KKP) Kniehl, Kramer, Pötter
(AKK) Albino, Kniehl, Kramer
(HKNS) Hirai, Kumano, Nagai, Sudoh
(DSS) de Florian, Sassot, Stratmann
• Gluon and light-quark
fragmentation functions have
large uncertainties, but they
are within the uncertainty bands.
 The functions of KKP, Kretzer,
AKK, DSS, and HKNS are
consistent with each other.
All the parametrizations agree
in charm and bottom functions.
M. Hirai, SK, T.-H. Nagai, K. Sudoh,
PRD75 (2007) 094009.
A code is available at
http://research.kek.jp/people/kumanos/ffs.html
Global analyses of polarized PDFs: Asymmetry Analysis Collaboration (AAC)
AAC codes for polarized PDFs: http://spin.riken.bnl.gov/aac/
2000 version (AAC00)
Y. Goto et al., PRD 62 (2000) 034017.
- Q2 dependence of A1, positivity
- q at small and large x   issue
2004 version (AAC03)
M. Hirai, SK, N. Saito, PRD 69 (2004) 054021.
- uncertainty estimation
(very large g uncertainty, impact of accurate g1p (E155))
- error correlation between g and q
2006 version (AAC06)
M. Hirai, SK, N. Saito, PRD 74 (2006) 014015.
- include RHIC-Spin 0 (g uncertainty is significantly reduced)
- g at large x ? (from Q2 difference between HERMES and COMPASS)
- g < 0 solution
2008 version (AAC08)
M. Hirai, SK, NPB 813 (2009) 106.
- impact of g by JLab E07-011 ?
Today’s talk
(g uncertainty could be significantly reduced.)
General method for determining polarized PDFs
F
F  2xF
2x 1  R 
g1
R


Spin asymmetry: A
g
L
1
F1
1
F2
2xF1
2
e  p  e  X
1
2xF1
1 dy


1
 s (Q2 )
2
2
2
 q(x / y, Q )  q(x / y, Q )   (1  y) 
g1 (x, Q )   eq 
Cq (y)     
x y
2 q
2


2
1
+ eq2
2

1
x

dy
 s (Q2 )
2 
g(x / y,Q )  n f
Cg (y)     
y
2


Leading Order (LO)
eq2 
1
nf
e
2
q
q
Next to Leading Order (NLO)
Cq (Cg )  quark (gluon) coefficient function


dy
 s (Q2 ) (2)
2
2
 q(x / y, Q )  q(x / y,Q )   (1  y) 
F2 (x,Q )  x  e 
Cq (y)     
x y
2
q


2
1 dy
  (Q ) (2)

 x eq2 
g(x / y,Q2 )  n f s
Cg (y)     
x y
2
2


2
2
q
1
Unpolarized PDFs
R(x, Q ) : taken from
experimental measurements
Parametrization:  fi (x, Q02 )  Ai x i (1   i x i ) fi (x, Q02 ), i  uv , dv , q, g
Ai ,  i ,  i ,  i are determined by data
Constraint on ∆ g(x)
from current g1 data
Gluon polarization at large x
g1 (x, Q2 ) 
1 dz
1
2
 q(x / z, Q2 )  q(x / z, Q2 ) 
e

q
x z
2 q
AAC, PRD74 (2006) 014015:
Analysis without higher-twist effects


 s (Q2 )
  (1  z) 
Cq (z)     
2


1
+ eq2
2
NLO
CG=0
2
QHERMES
~ 1 GeV 2
2
QCOMPASS
~ 6 GeV 2
Positive contribution to A1 comes
from CG  g at x ~ 0.05.
Note: CG  g  0
if g(0.05 / 0.2  0.25)  0
Gluon polarization is positive at large x.

1
x

dz
 s (Q2 )
2 
g(x / z, Q )  n f
Cg (z)     
z
2


This term is terminated.
x=0.001
x=0.05
x=0.3
However, it may be higher-twist effect.
LSS, PRD73 (2006) 034023.
Leading Twist (LT)
Higher Twist (HT)
LT fit
LT+HT fit
LT+HT fit,
only LT term is shown
At this stage, we cannot conclude that the difference between
the HERMES and COMPASS data should be 100% HT or
HT+g(large x)>0, or 100% g(large x)>0 effects.
Gluon polarization tends to
be positive at large x.
Obtained polarized PDFs by AAC06
0.5
0.4
0.8
2
Q2 = 1 GeV
0.6
0.3
0.2
AAC06
GRSV
BB
LSS
0.4
xuv(x)
xg(x)
0.2
0.1
0
0
0.001
0.01
0.1
1
0
-0.2
0.001
0.01
0.1
1
0.01
0
xdv(x)
-0.1
-0.2
0.001
-0.01
AAC06
GRSV
BB
LSS
-0.02
-0.03
0.01
0.1
x
1
2
Q2 = 1 GeV
xq(x)
-0.04
0.001
0.01
0.1
x
1
Constraint on ∆ g(x)
from future g1 data:
Effects of E07-011 at JLab 12 GeV
3 data sets for global analyses of polarized PDFs
Data set
Current
DIS (g1)
RHIC
0 (run 5)
JLab
E07-011 (g1)
A
Included
—
—
B
Included
Included
—
C
Included
—
Included
Set A: Only DIS data for the determination
of polarized PDFs [g(x)]
Set B: Effects of collider data sets
0 production [Run-5 PHENIX,
PRD76, 051106R (2007)]
Set C: Effect of DIS accurate g1 data
by JLab E07-011.
g1 measurements [E. Brash, et al.,
JLab experiment E07-011;
X. Jiang, personal communications.]
Expected E07-011 data
  g1d (x,Q 2 ) 
A1d (x,Q 2 )Set-A
d
2 
 g1 (x,Q )  E07-011
 A1d (x,Q 2 )E07-011  
Effects of expected JLab E07-011 data
“positive”
Two initial functions for∆ g(x): positive, node
Positive
Node
“node”
x
Gluon
Reduction of
uncertainties
for ∆ g(x)
by E07-011
Antiquark
∆ g(x) with PHENIX run-5 or JLab E07-011 data
Note: π0 data are from run-5
although it may not be a good
idea to compare future data
with past ones.
Δg function
First moment
DIS
DIS+RHIC π
DIS+E07-011
In this table, g 
positive
positive
positive
Δg
(Δg)
(Δg)/Δg
0.53
0.72
1.36
0.36
0.26
0.71
0.53
0.38
0.73
0.40
0.31
0.87
0.47
0.77
0.54
Significant improvements
node
node
Δg
(Δg)
0.87
0.89
node
(Δg)/Δg
1.02

1
0.1
dxg(x).
JLab-E07-011 is comparable
to RHIC run-5 π0
in determining ∆ g(x)
if gluon fragmentation errors
are neglected.
Why such a large improvement of ∆ g(x) by E07-011 data?
g1 (x, Q2 ) 
1 dz
1
2
 q(x / z, Q2 )  q(x / z, Q2 ) 
e

q
x z
2 q


 s (Q2 )
  (1  z) 
Cq (z)     
2


1
+ eq2
2

1
x

dz
 s (Q2 )
2 
g(x / z, Q )  n f
Cg (z)     
z
2


g1g corr
CLAS:
g1g corr ~ g1 errors
E07-011: g1g corr
g1 errors
 NLO gluonic term in g1
could be probed by
the E07-011 experiment.
The End
The End