Transcript
Polarized PDFs and Hall C Experiments at 6 and 11 GeV Xiaodong Jiang, Rutgers University. August 9, 2007 @ JLab Hall C workshop.
With the high intensity and high polarization electron beam at JLab 6 and 11 GeV, deep inelastic scattering experiments on polarized targets provide new constraints on polarized parton distributions.
Inclusive DIS data and constraints on polarized PDF.
.
( He)
.
,
Constraints on
,
Measurements of
Semi-inclusive DIS and constraints on polarized PDF.
.
( He)
.
,
,
More constraints on
Upcoming experiment:
Access quark angular momentum, measurements of
in SIDIS.
1
Jefferson Lab E99-117 (Hall A)
&%
DIS. Measured asymmetry
#"!
=5.73 GeV beam. Polarized He target
.
$ Phys. Rev. Lett. 92, 012004 (2004) and Phys. Rev. C 70, 065207 (2004). 2
'
'
Hall B eg1b: polarized NH and ND targets 1.2
1.2
This work
This work
pQCD
HERMES
1
SLAC - E155
0.8
SMC
Ad1 ( D-state corrected )
SMC
SLAC - E155
0.8
SLAC - E143
SLAC - E143
0.6
SU(6)
Ap1
0.6
pQCD
HERMES
1
0.4
0.4
SU(6)
0.2
0.2
0
0 0
0.2
0.4
x
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0.8
1
0
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0.4
x
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1
(nucl-ex/0605028)
3
0.5
∆u/u
)+
)*
7>= 6<
G : F3 1
C 6 4;2 3 B A2 6 7 C 6 >@ 4 : B D2 7 ?>= 9D A2 6< 7 6 >@ : 7 6 :;9 3 4 D2 DF 7 6 8 452 3 1
E
∆d/d
(
( E
x
E / , - / , E 0 . / . . / . -
-0.5
-
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1 0.8 0.6 0.4 0.2 0
, GRV AAC GS LSS
0 0.5
,
This work HERMES JLab/HallA
0.25
data and Spin-flavor decomposition from
1
0.75
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After JLab 12 GeV Upgrade
5
H
QRO
%
O
P
L &NM
.
.
L M
S
WVM S
UTM
L NM
S
S
&NM S
QRO
%
At
at
).
L I
KJI
PDFs from CTEQ5M (
P
, inclusive spin structure measurements on polarized proton and “neutron”
provide enough information on polarized parton distributions.
6
2
x, Q :
X
L MY
Inclusive DIS access only
LO approximation
TMY
a b _` ]\ s p te
n qrp e
∆ q , ∆ q (x) f f
ik h ij gfe
vu vu vu vu vu vu vu vu vu vu vu uv
a onm e l
a dcb
_` ^]\ [Z
−
f
(pol)
a
evolution, at NLO:
w
Inclusive DIS access gluon via
vu
vu
vu
vu
p `
n {~ xk a ^}b e
explicitly!
l
\
qb s pe
[Z
e
nq e p \ n |{z a yxe l ik h ij fge
c
term can be
b
k } \
Scheme dependence
involves gluons
attributed either to singlet quark or to gluon distribution
7
X
QCD evolution: singlet vs. non-singlet
V
T
M J
MT
M
I
u, d, s
L M L M
V
M
according to
V M
T
J
J
T
J M
I
J M
“Organize” PDFs
−− u, d, s−
S
M S
singlet
u
− u
5M S
M 5 S
flavor/charge
all
S
non-singlet
M and valence quark distributions do not
Flavor–non-singlet
“mix with” gluon distribution . . . Individual flavors
do! 8
Global fits to the inclusive DIS data 0.15
0.5
0.1
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0.05
0.3
Assume sea behavior.
0
X
.
-3
10
-2
10
-1
MY Y Y
J¢
L M
0.01
Only access one flavor non-singlet:
X
1.25
Inclusive data can not distinguish from since .
M
x
0.02
1.5
evolution of
X
x
10
L I
-1
as in BB: .
S
10
from
;
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L J
10
S
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-0.25
1.75
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L V
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Can not access
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.
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X
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Obtain
-0.15
0
L J
-0.1 0.1
S
S
0.2
L JM
-0.05
-3
10
-2
10
-0.04
-1
x
10
-3
10
-2
10
-1
x
9
¥¤
is more sensitive to
X
S
term drops out in , leads to a relatively larger contribution.
§
T¦
M
S
X
High precision data over a wide range of will constrain through global fit.
$¨
¡
S
;
X
COMPASS measured
$¨
at low-x.
¡
² S
¥
S¯ ´µ
´µ
°
T
T
° ·
¶ ³
³
«
TM S ¥ R T M S ® R ¬
±
; ² ±
¥ J " $ ©ª¡
¸ 10
A1d
1
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COMPASS data on COMPASS 2002-04, Q2 >1 (GeV/c) 2 COMPASS 2002-03, Q2 <1 (GeV/c) 2
0.8
E143, Q2 >1 (GeV/c) 2 E155, Q2 >1 (GeV/c) 2
0.6
HERMES, all Q
2
2
SMC, all Q
0.4 0.2 0 -0.2
10-4
10-3
10-2
10-1
x
hep-ex/0701014.
11
reduced error on
¥¤
CLAS eg1b data on
¹
Fit of LSS-06, including higher-twist terms.
¹
CLAS eg1b-06 data significantly shrunk error size of
º
¾
&½¼ »
¹
12 GeV data will reduce error by a factor of 4. Similar conclusions from AAC-06 analysis.
º
½¼
»
¾
¹
12
¥
data to come
JLab @ 6 GeV: more
Experiment E07-011 (Hall C). 13
will reduce error band on
S
!
JLab 6 GeV experiment on
$¨
X
Will collect data in late-2008, share beam time with E04-113. Same constrain power on as of RHIC 2006 data (AAC-07).
X
S
Á ÂÂ
À¿!
14
Constrain Polarized PDF with Semi-Inclusive DIS Data L M
MT
through differences in fragmen-
L M
from
S
S
In SIDIS, final state hadron tagging separates
M
.
L M
S
V M
S
tation, data provide constraints on
.
S
S
Inclusive DIS data provide constraints on
.
Ä Ã
Measure SIDIS double-spin asymmetries in
X S
M
results from HERMES. and
Å#!
X
Å#!
Upcoming JLab experiment E04-113: precision data on
$¨
$© .
Ë
S
S Ê
Ë L
.
S
.
M
S
S
and
L M
X
Inputs to NLO global fit to constrain
S
L V S Ö Õ Ê ÔÈ ÒÕ Ó Ò JË
S
:
ÑVË S Ì Ð
ÌÏ Î Í
X
To obtain
È ³ É
X
V Ædz
Flavor/charge non-singlet combination
.
15
Å ¢á
Leading order cross section: u
S
π
&ç Y Å æ % MY S Y
π
dÙØ
d
h
J Å ¢
u
N
Å¢
q
S
J$ Å!
(E, p) γ*
Results
Detect the leading hadron from the current fragmentation and measure double-spin asymme. try:
(E,’ p’ ) e
×
Flavor Tagging in SIDIS and HERMES
¶ äå¶ã â^Y
Ø
+
π
àßÝ Þ Ü ÛÚ HERMES calculated “purity” from a LUND based Monte Carlo:
é
% &% Mé é M S î ç& &ç ê é Å Å ç ?æ ?æ %& íì % &% ê é éM M Å ï ê é ê ë
J$ Åè!
Fragmentation “tags” flavor and charge of struck quark.
16
x⋅∆u
ð ñò
Solve for
ý
ý
ý
0.2
x⋅∆d
–
–
x(∆u-∆d)
0
Q2 = 2.5 GeV2 0.1
-0.2
0 –
-0.1
ý
ý ÿ
ü þý
0
ð û ý úùø ý ^÷ö õ Wôó ý
0.2
x⋅∆u
Q2 = 2.5 GeV2
0
GRSV2000 LO std BB01 LO
-0.1
χQSM B. Dressler et al., EPJ C14 (2000) 147.
–
x⋅∆d
-0.2
0
0.03
Assume:
-0.1
0 x⋅∆s
-0.1 0.03
0.1
0.6
0.1
0.6
x
Leading order cross section and current fragmentation. Isospin symmetry and charge conjugation. “Purity” calculated from Monte Carlo depends on the detailed knowledge of the fragmentation process.
x
17
S
S
T %&
&%
V
Ë
%
Q S &% Ë S
¥ V &% M S ¥ J L
% S V &% L
Q % $ " ¡
%& M
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V % $ ©;¡ J
S
¥
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Q S VË S V &% $ " ¡
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V &% $ © ¡ J L &
% S
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%& $ " ¡ V %& $ © ¡
%
L
S
L
S
S
S
Ë
M S
X
S
VË
S
through SIDIS data, rather than
X
Obtain
Q L
%&
V S
% M
T &% S
L
J S
S
V &% L S
separately.
and , ,
. through inclusive data
Obtain non-singlet
An alternative method to obtain flavor non-singlet Flavor non-singlet:
At the leading order:
18
at LO
Flavor Non-Singlet
Frankfurt et al. 1989, Christova and Leader, 2001.
S
VË VË
S
R
Ë
J
J ¦
¿¢©
S
S
R
Ë
¿¢©
V V ¿¢© ¿¢©
¿ È $©
¿ !
S
S
¿¢
S
S
Ë
TË
¨ J
J §
T ¦
È ¿ $¨
¿¢
TË Ë
TË
¨
V V ¨ ¨ ¿¢ ¿¢
W¿!
¥
®
Â
Ë
Ë
Ë
È ¿ $¨
¿ !
V
È¿ $ ©
R
¿ !
VË
J S
VË S
X
Fragmentation functions drop out at LO (isospin symmetry and charge conjugation).
X
Measurements on three polarized targets, proton, deuteron and Helium-3, over-constrain
S
 Ë
VË S
.
19
SIDIS Beyond the Leading Order Extend SIDIS cross sections beyond LO (Christova and Leader 2001, de Florian, Navarro and Sassot 2005). # ''
%&" !
# '(
%"
!
$ $
# '(
#"
! %" !
$
X
Extension to NLO is well known (Wilson coefficients, D. Graudenz, 1994). - ) .
,
* ) +
X
Flavor non-singlet observables related to
are theoretically clean, do not mix with gluon
density and gluon fragmentation function at any QCD order. 20
At the Next-to-Leading-Order: 1
]
6 51
]
675
6
c 0
0 b
x {
{p
\
1_ ^]\
6;
p
_`
21
x
a 34b
0
a/ b
_` ]\ p
:
6 91
:
689
]
6 1
]
6 8
x
are well-known Wilson coefficients (D. Graudenz, 1994).
}
l
x
?
? p
{ zz
q
{
A @ B
n
= 0
k n
a
c
= < >
n
zE D
C )
?
}
} a
k n
= 0
n
n
= 0
k n
a
l
l x ?
p
{ z~
?
qF
?
{ z~
{
x {
q zE
C
C )
) ?
? - )
gluon terms drop out.
a
G = 0
?
l?
?
.
H
H
zE
c zE
= 0
l?
F
F
,
a
G = 0
c
= 0
X
Isospin symmetry and charge conjugation:
,
* )
X
In flavor/charge non-singlet combinations
È ³
V Ƴ
is theoretically clean.
¥ 21
È ³ É V Ƴ
From
and
NLO
¥
E. Christova and E. Leader, 2001.
È¿ ¿
¿¢©
µ
æ
S
³ ²á ±
T ¥
S
S
°
°
Ë
R
VË
S
I
¶¶
J
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¿¢©
µ
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æ °
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V V ¿¢© ¿¢©
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¿ È ¿ æ ¿ °
S
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S
TË S
¿¢
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¿¢ µ
°
°
æ
³ ²á ±
I
T ¥ Ë
TË
¨
V V ¨ ¨ ¿¢ ¿¢
S
¶¶
n
Xn
and
5
J
K
K
are non-singlets which do not mix with gluon and sea.
X
n
n
, neutron data is sensitive to
J
5
K
.
K
Proton data is sensitive to
“Bjorken-type Sum Rule” links the moments at all orders of QCD
(Sissakian et al. PRD68, 031502 (2003))
.
$
$ L
L
¡ J
®
O
O
QO
O
N
Q
¥
J%
S
% T
Ë
VË S
S
L V S
M
¡
22
Semi-SANE (E04-113): A Hall-C 6 GeV Experiment X. Jiang, P. Bosted, D. Day and M. Jones co-spokespersons O
Duke, FIU, JLab, Kentucky, Norfolk, RPI, Rutgers, Temple, UVa, W M, Yerevan, IHEP-Protvino.
V
UTRS
J
O
\
QO
-Arm: a calorimeter array
J
.
X
GeV, P
).
X
ZYS XW
Q
,
X
E
(
PQ
Ä Ã
High precision asymmetry data in deep-inelastic
[
O
®
^ _
]
. ^
-Arm: HMS spectrometer @10.8 , 2.71 GeV/c, .
X
Ä
QO
Nç
`
LiD
).
§
T¦
J
(
and
( ), ND
¦
X
Target: polarized NH
23
a
UVa/SLAC/Hall-C Polarized Target ( , ) a
Signal
b
Microwave Input
NMR Signal Out
Refrigerator To Pumps
Frequency
To Pumps
X
Dynamic nuclear polarization.
LN2
LN2
Strong field (5 T), low temperature (1K).
Liquid Helium
X
Liquid Helium
d
d
e
e
Ci
hj g
hg
.
Å l
J
X
Dilution factor: (NH ), (LiD).
LiD)
c
c
c
(ND ,
f
X
(NH )=0.8,
N
Q¥O k l
QRO
O
QRO
QO
Magnet e– Beam
4-94
Target (inside coil) 1° K
NMR Coil B 5T
7656A1
24
¥
Ä Ã
The Expected Results: Double-Spin Asymmetries
qr
.
p
. First data on
o
o
m n
Expect significant improvements on
25
¥
T Ã ¥
È ³ V à Ƴ
and
È ³
Ƴ
Combined Asymmetries:
u s
: flavor/charge non-singlet, gluon den-
tm m
p
sities do not contribute. Need well-controlled hadron-arm phase space and PID to determine: u y x z }
}|
Z~ }|
w s
Uwv { y x
u
u s
s
y
y
º
º
v
y
w
w
}
u z y x
z y x
u s y
s
v
y x
y x
26
and
E04-113: Expected Results on
× S
L L
S
V
S
S
V
S
JË
JË
S
ç
Tow independent methods of flavor decomposition: i, Christova-Leader method. ii, “Purity” at a fixed- .
L
L V
L
S
L V
S
One expects at least
!!!
27
E04-113: Access Flavor Asymmetry in the Nucleon Sea 1.2 E866/NuSea Peng et al. Nikolaev et al. Szczurek et al. Pobylitsa et al. Dorokhov and Kochelev
1 0.8
_
_
d-u
0.6 0.4 0.2 0
Systematic Uncertainty
-0.2 0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
x
È Æ
¦
data. Many
s ,
,
J
5
n
5
J
s
s
a
)
,
n
5
J
n
n s cJ
s
s c5
ns
g
,
models explain , including the meson-cloud model ( ) which predicts .
s
s n
5
J
model, while
¦
s
model predicted large In Chiral-quark soliton appears in LO ( ) appears in NLO ( ).
Fermilab
other .
¦
Many
¢£ ¡
.
Pauli-blocking model:
28
After 12 GeV Upgrade: Spin-Flavor Decomposition through SIDIS
11 GeV beam on NH (1200 hours) and He (400 hours) targets.
(X. Jiang, JLab 12 GeV upgrade CD1 report.)
29
1.0
RHIC pp √s = 500 GeV ∫L dt = 800 pb−1
¤
... and from RHIC-II
decay one expects
DGLAP evolution equation links high- lowregion to low- highregion.
∆q/q
¦ ¥
0.5
§ ¦ ¥
AL (W +) _ AL (W )
∆u/u ∆d/d
0
−0.5
∆d/d
∆u/u
Q 2= MW2
¦ ¥
−1
10
¦ ¥
GS95LO(A) BS(∆g=0)
−1.0 −2 10
Data at increasing probe higher and . higher in input PDF at Non-singlet evolution is straight forward.
x 30
. « ¨
ª © ¨
and
COMPASS-2007:
¬ - hA h+ d
1
1
0.8 0.8
0.6
0.4
-
+
N /N
0.2 0
σh-/ σ h+
0.2 0
0.4
unmeasured
0.6
-0.2 -0.4
10-2
10-1
x
10-1
x
1
GeV ¯
A ´
² ± ³
° ¯ ®
f
arXiv:0707.4077. LiD target,
10-2
1
31
0.7
∫x(∆u +∆d )dx
x(∆ uv+∆ dv)
min
0.4
0.6
From diff asymmetry d
From Inclusive g
1
(∆ u=∆ d=∆ s=∆ s)
0.5
DNS fit (without COMPASS)
0.3
0.4
0.2
0.3
0.1
(∆ u=-∆ d)
0.2
0
0.1
-0.1 -0.2
v
unmeasured
0.5
v
10-2
10-1
x
0
1
10-2
10-1
xmin 1
¶
µ ¢
¡Â
¿Ã ¿
ÀÁ
¢¡
¾
¢ ¿À
¡N
¢¡
¾¡
ȼ
¹
¹
¢½ ¡
.
¼
µ
¸·`
32
Æ
Ç
Å
Å
and
Ä
Ä
Ä
,
: NLO global fits to DIS and SIDIS data
de Florian, Navarro and Sassot. PRD71, 094018, (2005). X. Jiang, Navarro and Sassot. EPJC47, 81, (2006).
È
Gives error bands on polarized PDF. Translate into error bands on observables.
È
Constraints on
Í Ì Ë
Ê
Ï
Ï
, compare with RHIC
Î
È
Allow different parameterizations of F.F. (KRE and KKP).
É
È
Fit inclusive and semi-inclusive DIS data to NLO in PDFs and fragmentation functions.
data.
33
Inclusive:
¬
Ò
×
¥ Ò
Ù
¦Ú¥
¦
¦
Ñ Ð
Ó
£
Ø Ó
Õ ÓÔ Ö
ß
Ü
¦ ¥ Û
¢
Ò
¦Ú¥
à
Ð
Ó
£
ß
ß
á
ß
ß
º Ò Ù
¦Ú¥
à
ß
º
Ý
Þ
â
Semi-inclusive:
¬
¦
é
º æ ¥ Ò ß å
×
Ù
å
Ò
çèæ
¦ ¥ ä
¦
¥ Ò ßÒ
ãäÐ Ñ
Ó
Ó
£
Ø
Ó Õ ÓÔ
ß
ê ß ê §
îïà
º Ò
Ó
Ó Ó
í
£
Ý
ê
ê ß
Ù
ê ì
í
ê ìß
¦ ¥ ä
é ç Ò
¦ ¥ ä
¦ ¥ ä Ò
ê ßÒ ê ð
¦¥ Ü Û
ë
Þ
ß
ß
Ò
Ð
Ó
Ó
á
í
í
ê ì
í
ê ìß
¦ ¥ ä
é ç Ò
¦ ¥ ä
îïà
Ò
ê ßÒ ê ð
¥ Ò
Ó
á
á
í
ê ìß
¥ Ò
ç
º
¦ ¥ ä
¦
é
¦
îïà ¥
Ù
ê ì
Ò
ê ßÒ ê ð
¦
34
Fit Compared with Inclusive Data 1 0.5 0 1 0.5 0 0.5 0 10
-2
10
-2
1 10
-2
1 10 -2
35
Fit Compared with Semi-Inclusive DIS Data 0.5 0 0.5 0 0.5 0 0.5 0 10
-2
1 10
-2
1 10
-2
1 10
-2
1
36
Error bands of NLO polarized PDF 0.4
0.4 –
x(∆u+∆u)
–
x∆uv
x∆g
0.2
0.2
0
0 –
-0.2
x(∆d+∆d)
x∆dv
-0.2
0.06 0.04
0.06 –
–
x∆u
–
x∆d
x∆s
KRE (NLO) 0.04 KKP (NLO) unpolarized 2 KRE χmin+1 0.02 2 KRE χmin+2%
0.02 0
0
-0.02
-0.02
-0.04
-0.04
-0.06
10
-2
xBj
10
-2
xBj
10
-2
-0.06
xBj
37
Impacts of semi-SANE proton data on NLO global fit X. Jiang, G.A. Navarro and R. Sassot, 2006.
0.5
0.3
0.45
0.25
πAp
Aπ+ p
0.2
0.4
0.15
0.35 0.1
0.2
x
0.3
0.4
0.1
0.2
x
0.3
ò ñ
and
ö
ô ò ñ ó
Existing constraints compared with semi-SANE projected error bars on
0.1
0.4
.
õ
õ
38
Improved constraints on the moments of polarized PDF Standard Fit Improved Fit
460
460
2 χ +5%
450
χ
450
2
440
430
2 χ +2%
440
χ2+1
-0.3
430 -0.2
-0.1
–0
δu
0.1
0.2 -0.4
-0.2
– 0
δd
0.2
460
460 2 χ +5%
450
χ
450
2
440
2 χ +2%
440
2
430
χ +1
-0.1
-0.08
430 -0.06
-0.04
δs
-0.02
0 -0.5
0
0.5
δg
1
Adding the projected semi-SANE proton data significantly improves the
moment.
39
¨
SIDIS with a longitudinally polarized He target: ÷
¬ø ×
È
A JLab 6 GeV proposal (PR05-112). Will improve HERMES-95 data.
High luminosity polarized He target to obtain .
È
ã ñ
ù
È
Add strong constraints to through NLO global fit.
È
Sensitive to
¹
. ú
40
÷
Adding He SIDIS data: indirect constraints to X. Jiang, Navarro and Sassot. EPJC47, 81, (2006). ÿ
evolution of
.
û
in
¯ ®
Ê
þ
is fixed in SIDIS, there’s less freedom for
É
É
, once
þ
þ
üýû
Since
0.03
460
Run 5
0.02
2 χ +5%
2006-7
450
χ
0.01
2
AπLL 0
440
0
2
χ +2%
-0.01
2
χ +1
KRE NLO 2 KRE NLO ∆χ =2% 2 KRE NLO∆χ =2% with Helium data (only pions)
430 -0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
-0.02
0
2
4
δg
É Ê
10
12
14
Ï
as strong as RHIC
Ï
Constrain
8 (GeV/c)
Î
Ê
by a factor of 4.
pT
n Ì Ë
É
Improve
6
2006.
41
Summary: JLab Experiments The high luminosity at JLab allows precision measurements of inclusive and semi-inclusive asymmetries on polarized targets.
( He):
ñ
ù
,
ñ
,
ñ
Inclusive
õ ÿ
ÿ É
É
É
.
Ê
through global fits.
( He):
,
ã ñ ù
ã ñ
,
ã ñ
Semi-inclusive
É
È
Constrain
É
È
Spin-flavor decomposition
õ
È
In addition to asymmetries, one needs to determine relative cross section ratio
É
.
þ
þ
from
ÿ
È
Flavor non-singlet observable
É
È
Flavor tagging separates
ö ÿ
ô
ÿ
Ì
É
É
É
É
Ì Ë
.
Ì
Ì
provide clean access
.
Combine inclusive and semi-inclusive data:
ÿ É
ÿ É ²
.
È
É
É
ÿ
È
Ê
þ
þ
and
É
É
É
Constrain
through NLO global fits.
42
