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.