1
Jen-Chieh Peng
Workshop on “Parity-Violating Spin Asymmetries at RHIC” RIKEN-BNL, April 26-27, 2007
University of Illinois
/ asymmetry and W-production
Charge-symmetry violation and
W-production
/ ratios at large and W-production
d u
d u x
Flavor Structure of the Nucleon and W - Production
2
Violation of the Gottfried Sum Rule
New Muon Collaboration (NMC) obtains
SG = 0.235 ± 0.026
( Significantly lower than 1/3 ! )
What do we know about the / asymmetry?d u
1
2 20
1
0
[( ( ) ( )) / ]
1 2( ( ) ( ))
(assuming charge symmetry)3
(if 1
3)
3
p nG
p
p
p
p
S F x F x x dx
u x d x
u d
dx
3
Explanations for the violation of Gottfried Sum Rule:
• Uncertain extrapolation for 0.0 < x < 0.004
(Can be studied at EIC)
• Nuclear effects for deuteron
• Charge-symmetry breaking
• in the proton
,( ), More later ....n p n pu d d u
( ) ( )u x d x1
0( ( ) ( )) 0.148 0.04d x u x dx
Need independent methods to check the
asymmetry, and to measure its x-dependence !
4
The Drell-Yan Process: pN X
The x-dependence of can be directly measured( ) / ( )d x u x
1 ( )[1 ]
2 2 ( )
pd
pp
d x
u x
5
Fermilab E866 Measurements
800 ( ) / ( )GeV p d X p p X
1/ 2 [1 ( ) / ( )]:
/
21
/ 2 [1 ( ) / ( )], :2
pd pp
pd ppn p
Drel d xl Yan
J
u x
g x g x
6
Extraction of / d u
Assume no shadowing/binding corrections for deuteron
Validity of the charge-symmetry is assumed
( = , = )n p n pd u u d
7
is more suppressed than in the proton since
(Field and Feynman 197
(pQCD calculati
Paul
ons b
Origins of ( ) ( )?
y Ross and Sachrajda)
(Bag model calculation by Signal, Thomas, Schreib
7
i blocking by the valenc
)
e quarks
u x d x
g uu g dd
p uud
Quark spectrum includes a bound state plus the
polarized negative
er)
(Diakonov
Chiral quark-soli
, Pobylitsa, Poly
and positive D
akov, Wakamats
irac continuu
u, Kubota)
ton model
Instanton m l
m
ode
,
Sta
(Dorokhov, Kochelev)
(Bourrely, Butistical model ccella, Sof
,
f er)
etc. L R R L L R R Lu u d d d d u u
The valence quarks affect the Dirac vacuum and the quark-antiquark sea
8
0
0
Sullivan Processed in DIS
| | | |
( )
( )
Goldstone bosons couple to va
Meson cloud in the nucleon
Orig
s
Chir
lence qua
al quark
ins of ( ) ( )?
model
rks
p p a N b
p ud n
p ud
u d
u K s
u x d x
The pion cloud is a source for antiquarks in the proton,
and it leads to d u
9
Spin and flavor are closely connected
0 ( ( )) u Ku uu u us s
,L R LR RR LL du u d d u ud
( ) ( ) ( ) ( )u x d x d x u x
( ) ( ) ( ) ( )u x d x d x u x
• Meson Cloud Model
• Pauli Blocking Model
A spin-up valence quark would inhibit the probability of generating a spin-down antiquark
• Instanton Model
• Chiral-Quark Soliton Model
• Statistical Model
10
1
0Predictions of [ ( ) ( )]u x d x dx
Peng, Eur. Phys. J. A18 (2003) 395
11
What's next for / ?d u2
21 2 1 2
1 2 1 2
4[ ( ) ( ) ( ) ( )
1]
3DY
i ii
de q x q
sx q x q x
dx dx x x
J-PARC 50 GeV
Intriguing / behavior at large
can be studied at lower beam energies
d u x Drell-Yan at RHIC can explore small x
region where is larged u
12
/ from W production at RHICd u production in collisionW p p
p p W x p p W x
( )u d W ( )d u W
No nuclear effects !
No assumption of charge-symmetry !
Large Q2 scale !
21
21
( )( )
(
( )(
( ) ))
( )
FF
F
dpp W X
dx u xR x
d d xpp
d x
uW xXdx
13
W and Z production cross sections
28factor: 1 ( ); at mass, 0.116, 1.32
9
o
3
, f r ( )F
S SK K
du d u d pp W X
d
Q W K
x
1 2
1 2
2 21 2 1 2 1 2 1 2
2( )
3
cos ( ) ( ) ( ) ( ) sin ( ) ( ) ( ) ( )
FF
c c
x xdpp W X K G
dx x x
u x d x d x u x u x s x s x u x
2 0
Higher-order QCD corrections are relatively unim
si
portant for W/Z produ
n 1.317 at mass scale
ctionW W K Z
0 1 2
1 2
2 21 2 1 2 1 2 1 2
2( )
3
8 32 4 8(1 ) ( ) ( ) ( ) ( ) (1 ) ( ) ( ) ( ) ( )
3 9 3 9
FF
W W W W
x xdpp Z X K G
dx x x
u x u x u x u x d x d x d x d x
14
W and Z production cross sections
1 2
1 2
2 21 2 1 2 1 2 1 2
2( )
3
cos ( ) ( ) ( ) ( ) sin ( ) ( ) ( ) ( )
FF
c c
x xdpp W X K G
dx x x
u x d x d x u x u x s x s x u x
0 1 2
1 2
2 21 2 1 2 1 2 1 2
2( )
3
8 32 4 8(1 ) ( ) ( ) ( ) ( ) (1 ) ( ) ( ) ( ) ( )
3 9 3 9
FF
W W W W
x xdpp Z X K G
dx x x
u x u x u x u x d x d x d x d x
Peng and Jansen, Phys. Lett. B 354 (1995) 460
15
1 2 1 2
1 2 1 2
11 2
1
1 2
1
2
2
2
( )
( )( )
( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
( )At large ( ), ( )
( )
( )
; ( )
At 0 (
( )
( )
( )
( ))
( )
), (( )
FF
F F
F
F
F
F
F
F
x x x
dpp W X
dxR x
dpp W X
dx
u
d x
u x
x d x d x u x
u x d x d x u x
u xx x
d x
u x
x R xd x
u xx x x
R
x R x
x
x
x R
d
Peng and Jansen, Phys. Lett. B 354 (1995) 460
/ from W production at RHICd u
u d
( ) / ( ) at 500 GeVpp W pp W s
u d
16
u d
u d
Using more recent PDFs
R. Z. Yang and Peng (2007)
( 0.16) ( 0.16) ( 0.16)( 0) 2
( 0.16) ( 0.16) ( 0.16)F
u x d x d xR x
d x u x u x
/ from W production at RHICd u/ ( )
( ) at 500 GeV/ ( )
FF
F
d dx pp W xR x s
d dx pp W x
17
/ from W production at PHENIXd u
R. Z. Yang and Peng (2007)
/ ( )( ) at 500 GeV
/ ( )
d dy pp W x l xR y s
d dy pp W x l x
detectione
detection
u d
u d
950 pb-1 integrated luminosity
18
Charge Symmetry Violation in PDF?
2 2
Charge symmetry : rotation around isospin axis by 180
Charge symmetry in PDF is generally assumed, bu
( ; .)
A compari
t not tested
son of with shows upper limit o f
n
y
p n pp n u d u d u d u d etc
F F
I
The NuTeV anomaly in the Weinberg angle could be explained
by charge
(Lon
sym
CS breaking
of 5 1
metry violation
dergan and Thomas, hep-ph/0407247)
(Londergan and Thomas,
PL B558
0%
(
2003) 1
32)
19
Charge Symmetry violation from MRST Global fits
(Eur. Phys. J. C35, 325 (2004))
4 0.5(
(
) (1 ) ( 0.0
) ( ) ( )
Best fit: 0.2
0.8 0.65 (90%
( ) ( ) ( )
( )
C.L.)
90
(
9
)
)
( )
V V
p nV V V
p nV V V
u x d x f x
d x d x u x
u x u
f x x x
x
x
x d
Best fit: 0.08
(8% of C
0.08 0.18 (90
( ) ( )[
BV
1 ]
( ) ( )[
fo
% C
1 ]
r
.L
.
!
)
sea )
n p
n p
u x d x
d x u x
CSV for sea quarks
CSV for valence quarks
20
Comparison between MRST and quark-model calculation
Charge symmetry violation for valence quarks
MRST Quark-model
(Rodionov, Thomas, Londergan)Eur. Phys. J. C35, 325 (2004)
21
CSV from W production at RHIC2 / ( )
( ) at 500 GeV/ ( )
FF
F
d dx pp W xR x s
d dx pd W x
2 2
2 2
/ ( )( )
2 / ( )
( ) ( )11
2 (
for 0, ( ) is sensitive to
valence-quar
) ( )
k CSV
FF
F F
F
d dx pd W xR x
d dx pp W x
d x d x
u x u x
x R x
(S. Yoon and Peng, 2006)
Charge-symmetric
Charge symmetry violating
22
CSV from W production at RHIC2 / ( )
( ) at 500 GeV/ ( )
FF
F
d dx pp W xR x s
d dx pd W x
2 2
2 2
/ ( )( )
2 / ( )
( ) ( )11
2 ( ) ( )
for 0, ( ) is sensitive to
sea-quark CSVF F
FF
F
d dx pd W xR x
d dx pp W x
d x d x
u x
x
u x
R x
(S. Yoon and Peng, 2006)
Charge-symmetric
Charge symmetry violating
23
CSV from W production at PHENIX/ ( )
( ) at 500 GeV2 / ( )
d dy pd W x xR y s
d dy pp W x x
For y 0, ( ) is sensitive to
valence-quark CSV
R y
(S. Yoon and Peng, 2006)Charge-symmetric
Charge symmetry violating
800 pb-1 integrated luminosity
24
0, 0 1, 0 1, 1
1, 0 1, 1
1 1 1| ( ) ( ) ( )
32 18
1 2( ) ( )
3 3
z Z Z
Z Z
S S S S S S
S S S S
p u ud u ud u ud
d uu d uu
2
2
2
2
1) SU(6) symmetry
2) Dominance of 0 diquark configurations (Close,
Ignoring terms with 1diquark
Carlitz)
3) Domina
1 2
2
nce of
3
10
s, th n
4
e
n
p
n
p
Fd
u F
Fd
u F
S
S
2
2
Ignoring terms with
0 diquark conf
=1
igurations (Farrar, Ja
diquarks, t
ckson)
h
1
en
3
7
5
Z
n
p
Z
Fd
u F
S
S
( ) / ( ) at large d x u x x
25
2
2
( ) ( )(1 4 ) / (4 )
( ) ( )
n
p
F d x d x
F u x u x for large x
2 2Model dependence of extracting from n dF F
Is the / asymmetry related to asymmetry?d
d uu
S = 0 dominance d/u→0
SZ = 0 dominance d/u→1/5
SU(6) symmetry d/u →1/2
Extraction of ( ) / ( ) at large d x u x x
26
/ from W production at CDFd u
asymmetry from CDFW
CDF, hep-ex/0501023
/ ( ) / ( )( )
/ ( ) / ( )l
d dy l d dy lA y
d dy l d dy l
Melnitchouk and Peng (PL B400 (1997) 220)
27
/ from W production at RHIC?d u
1 2 1 2
1 2 1 2
11 2
1
1 2
1
2
2
2
( )
( )( )
( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
( )At large ( ), ( )
( )
( )
; ( )
At 0 (
( )
( )
( )
( ))
( )
), (( )
FF
F F
F
F
F
F
F
F
x x x
dpp W X
dxR x
dpp W X
dx
u
d x
u x
x d x d x u x
u x d x d x u x
u xx x
d x
u x
x R xd x
u xx x x
R
x R x
x
x
x R
d
( ) / ( ) at 500 GeVpp W pp W s
Melnitchouk and Peng (PL B400 (1997) 220)
28
Summary• W-production at RHIC provides unique
information on the flavor asymmetry of unpolarized parton distributions.
• The connection between flavor and spin structure remains an interesting area to explore.
• W-production can disentangle the charge-symmetry violation effects from the sea-quark flavor asymmetry effect.
• More simulation studies are required.