1

Flavor Symmetry of Parton Distributions and Fragmentation Functions

Jen-Chieh Peng

Workshop on “Future Prospects in QCD at High Energy” BNL, July 17-22, 2006

University of Illinois at Urbana-Champaign

2

Outline Flavor asymmetry of the nucleon

Sea-quark Boer-Mulders functions from

p+p and p+d Drell-Yan

Connection between PDF and Fragmentation

Funct

, , ,

Flavor asymmetry of fragment

ions

ati

d d s d

u u s u

on

functions?

3

Is in the proton? u d

Test of the Gottfried Sum Rule 1

2 20

1

0

[( ( ) ( )) / ]

1 2( ( ) ( ))

3 3

( )1

3 p p

p nG

p p

S F x F x x dx

u x d

i

x dx

f u d

New Muon Collaboration (NMC) obtainsSG = 0.235 ± 0.026

( Significantly lower than 1/3 ! )

=

4

Drell-Yan 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

5

Unpolarized Semi-Inclusive DIS2

2

((

( )(

)

)

)1

h

qqq

qq

q

q

f xed

ep hXdz e x

D z

f

: parton distribution function

: fragmentation functi( )

(

o

)

n

q

hq

f

D z

x

Use SIDIS to extract parton distribution functions

Universality of fragmentation functions (hep-ph/0011155)

e e h X pp h X e p h X

6

Flavor structure of sea-quark distribution via SIDIS( ) ( ) [1 ] [( , ) ( , )

( ,

1 ]

( ) ( ) ( , )

( )

) [1 ] [1 ]( )

r x z r x z

r x z

d x u x

u r x zx d x

J z

J z

3 1 ( )( ) ; ( ) ( ) / ( )

5 1 ( ) u u

D zJ z D z D z D z

D z

( , ) ( , )( , )

( , ) ( , )

p n

p n

Y x z Y x zr x z

Y x z Y x z

• Assuming factorization is valid• Require knowledge on the fragmentation function D’(z)

SIDIS from HERMES Drell-Yan vs SIDIS

7

Future experiments to measure at large x/d u

8

Future SIDIS for at small x ? d u

HERMES: Semi-Inclusive DIS2 2 2 2: 2.866 : 54 3; HEE Q GeV RMES Q GeV

1

0[ ( ) ( )] 0.118 0.011 ( 866)d x u x dx E

1

0[ ( ) ( )] 0.16 0.03 ( )d x u x dx HERMES

1

0[ ( ) ( )] 0.147 0.039 ( )d x u x dx NMC

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/ 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

Independent of nuclear effect in deuteron!

21 21 2 1 2

1 2

2( ) cos ( ) ( ) ( ) ( )

3 F cF

x xdpp W X G u x d x d x u x

dx x x

21 21 2 1 2

1 2

2( ) cos ( ) ( ) ( ) ( )

3 F cF

x xdpp W X G u x d x d x u x

dx x x

21

21

( )( )

(

( )(

( ) ))

( )

FF

F

dpp W X

dx u xR x

d d xpp

d x

uW xXdx

10

/ from W production at RHICd u

Garvey and Peng, nucl-ex/0109010

21

21

( )( )

(

( )(

( ) ))

( )

FF

F

dpp W X

dx u xR x

d d xpp

d x

uW xXdx

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Models for asymmetry /d uMeson Cloud Models Chiral-Quark Soliton Model Instantons

• Quark degrees of freedom in a pion mean-field

• nucleon = chiral soliton

• expand in 1/Nc

Theses models also have implications on

• asymmetry between and ( )s x ( )s x

• flavor structure of the polarized sea

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Meson cloud model

Signal and Thomas

Brodsky and Ma

Melnitchouk and Malheiro

Christiansen and Magnin

Analysis of neutrino DIS data

( )x s s /s s

Barone et al.

( ) ( ) ?s x s x

p K (( ))us uds

13

Result from NuTeV

D. Mason, DIS 2005 talk

s(x) s-bar(x)

1

0[ ( ) ( )]S x s x s x dx

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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

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1

0

Predictions of

[ ( ) ( )]u x d x dx

JCP, Eur. Phys. J. A18 (2003) 395

16

Flavor Structure of the Helicity Distributions

• No evidence for u d

• Measurement of W± production at RHIC-spin would provide new information

17

Drell-Yan decay angular distributions

Collins-Soper frame

Θ and Φ are the decay polar and azimuthal angles of the μ+

in the dilepton rest-frame

A general expression for Drell-Yan decay angular distributions:

*"Naive" Drell-Yan (transversely polarized ,

no transverse mo 1, 0, 0mentum)

In general : 1, 0, 0

2 21 31 cos sin 2 cos sin cos 2

4 2

d

d

*1 2

*( )h h x l l q qx

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Drell-Yan decay angular distributions

Collins-Soper frame

Θ and Φ are the decay polar and azimuthal angles of the μ+

in the dilepton rest-frame

2 21 31 cos sin 2 cos sin cos 2

4 2

d

d

A general expression for Drell-Yan decay angular distributions:

Reflect the spin-1/2 nature of quarks

(analog of the Callan-Gross relation in DI

Ins

Lam-Tung relation:

ensitive to QCD -

S

c

)

orrection

2

s

1

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Decay angular distributions in pion-induced Drell-Yan

Z. Phys.

37 (1988) 545

T0 and increases with p

Dashed curves are from pQCD

calculations

NA10 π- +W

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Decay angular distributions in pion-induced Drell-Yan

Data from NA10 (Z. Phys. 37 (1988) 545)

Is the Lam-Tung relation violated?

Violation of the Lam-Tung relation suggests

non-perturbative origin

140 GeV/c 194 GeV/c 286 GeV/c

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Boer-Mulders function h1┴

1=0.47, MC=2.3 GeV

221 12 2

( , ) ( )T TkC HTT H

T C

M Mh x k c e f x

k M

1

1

1 represents a correlation between quark's and transverse

spin in an unpolarized hadron. Ana

is a time-reversal odd,

log of Collin

s frag. fun

depend

cti

ent parton distributi

on.

o

n

T

T

h k

h

h k

1 1

1 1

can lead to an azimuthal dependence with h h

f f

2 2

1 2 2 216

( 4 )T C

T C

Q M

Q M

Boer, PRD 60 (1999) 014012

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Motivation for measuring decay angular distributions in p+p and p+d Drell-Yan

• No proton-induced Drell-Yan azimuthal decay angular distribution data

• Provide constraints on models explaining the pion-induced Drell-Yan data. (h1

┴ is expected to be small for sea quarks. The vacuum effects should be similar for p+N and π+N)

• Test of the Lam-Tung relation in proton-induced Drell-Yan

• Compare the decay angular distribution of p+p versus p+d

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2 21 31 cos sin 2 cos sin cos 2

4 2

d

d

E866 Preliminary

<λ> 1.07±0.07

<µ> 0.04±0.013

<ν> 0.03±0.01

<2ν-1+λ> -0.13±0.07

p+d at 800 GeV/c

Decay angular distributions for p+d Drell-Yan at 800 GeV/c

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Comparison of NA10 versus E866 194 GeV/c W

2 2

1 2 2 216

( 4 )T C

T C

P M

P M

1 0.466 0.135

2.41 0.51CM GeV

1 0.04 0.01

0.6 0.15CM GeV

800 GeV/c p d

1 1

1 1

h h

f f

Sea-quark Boer-Mulders function is relatively small

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Comparison of p+d versus p+p

800 GeV/c p d 800 GeV/c p p

1 1No noticeable flavor asymmetry between ( ) and ( )h u h d

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Many Quark Distributions Are Probed in Semi-Inclusive DIS

4

26 4

Q

sxd

),()(])1(1{[ 211

,

22 h

qq

qqq PzDxfey

),()()sin()1(||

),()()2sin(4

)1(||

),()()2cos(4

)1(

2

,11

2

2

,1

)1(1

22

2

2

,1

)1(1

22

2

hqq

qqq

lS

lh

h

hT

hqq

qqLq

lh

hN

hL

hqq

qqq

lh

hN

h

PzHxhezM

PyS

PzHxheMMz

PyS

PzHxheMMz

Py

)},()()cos()2

11(||

),()()2

11(||

),()()3sin(6

)1(||

),()()sin()2

11(||

21

)1(1

,

2

21

,1

2

,

21

)2(1

223

3

21

)1(1

,

22

hqq

Tqq

qlS

lh

N

hTe

hq

qq

qqLe

qqh

qqTq

lS

lh

hN

hT

hqq

Tqq

qlS

lh

N

hT

PzDxgezM

PyyS

PzDxgeyyS

PzHxheMMz

PyS

PzDxfezM

PyyS

Unpolarized

Polarized target

Polarzied beam and

target

SL and ST: Target Polarizations; λe: Beam Polarization

Sivers

Transversity

Boer-Mulders

27

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

( ) / ( ) at large d x u x x

Is the / asymmetry related to asymmetry?v v

dd u

u

S = 0 dominance d/u→0

SZ = 0 dominance d/u→1/5

SU(6) symmetry d/u →1/2

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Can one probe the meson cloud directly?Scattering of electron off virtual pion was studied at

HERA by tagging forward-going proton/neutron

Pion structure functions at 10-4 < x < 10-2 were measured

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/ measurement with taggingd u

BONUS at Hall-B 2 2Expected / sensitivitiesn pF F

Measuring ( , ) using

( , )

n e e X

d e e p X

Tagging slow-moving spectator protons

This setup is ideal for detecting the scattering off the meson cloud:

a) ep→e’pX (π0 cloud) b) ep→e’ΛX (K+ cloud)

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Connections between parton distribution functions and fragmentation functions

Implications on the flavor structure of the proton

fragmentation functi

Gribov-Lipatov "recipro

Flavor struct

city" relation at

ure of the meson f

1

r

(

agmentation

) (

functions

)

?

ons?

h hi izq z

z

D z

31

Gribov-Lipatov reciprocity relation

( ) ( )h hi iD x xq x

( ) ( ) at large

( ) ( )

pdpu

D x d xx

D x u x

( )Is constant or

( )

(1- ) at large ?

pdpu

D x

D x

x x

The KKP (Kniehl, Kramer, Potter)

proton fragmentation function assumes

( ) 2 ( )p pu dD x D x

e e ppX

91.2 GeVs

22 GeVs

34 GeV

29 GeV

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Ma, Schmidt, Soffer, Yang assumes the following relations between fragmentation function and parton distributions:

( ) ( ); ( ) ( )v v v s s sD z C z q z D z C z q z

e e ppX

CTEQ5 PDF BSB PDF

Solid: 1, 1,

Dotte

Dashed: 1, 3,

d: 1, 0,

0 5

1

0

.v

s

v

s

s

v

C C

C C

C C

(hep-ph/0208122)

Precise e+e- data at large z from Belle could shed light on the connection between PDF and fragmentation functions

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Connection between PDF and FF for mesons?

SMRS pion PDF

Pion valence quark distribution from E615 Drell-Yan

( )xu x 3 ( )ux D x

Kretzer pion fragmentation function

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Connection between PDF and FF for mesons?( ) / ( ) from NA3 Drell-Yan experimentKu x u x

3 ( ) / ( )Ku uD x D x

Kretzer pion fragmentation function

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Flavor structure of the fragmentation functions

/ sea-quark flavor asymmetry is observed for the pr

Can one observe / asymmetry in other

oton

hadrons?d

d u

u

1) Hyperons

Pion-cloud model and Pauli-blocking predict in d u

(Alberg et al. hep-ph/9809243)

Can be measured with Drell-Yan using Σ+ beam. Difficult experiment!

2) Pions

Is ( ) ( ) in ?sea sead x u x Isospin and charge-conjugation symmetries

( ) ( ) in sea sead x u x

Σ+ contains uus valence quarks( ) ( ) in d x u x

X

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Flavor structure of the fragmentation functions

3) Kaons

Is ( ) ( ) in ?sea sead x u x K contains valence quarks

Pauli-blocking implies sea is blocked, but not the sea

Hence, one expects ( ) ( ) for

K us

uu dd

d x u x K

Difficult to measure sea-quark distributions in K+ !

Can the / flavor asymmetry be observed in the

kaon fragmentation functions?

u d

Is ( ) ( )?K Kud

D z D z

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What is known about kaon fragmentation functions?

KKP global fit:

This implies:

Lingyan Zhu (PR-04-114)

1 12 2, 0 00.05 0.05

( , ) 0.19, ( , ) 0.25K Ku s ddz z D z Q dz z D z Q

1 12 2

0 00.05 0.05( , ) 0.065, ( , ) 0.25K K

u ddz z D z Q dz z D z Q

( ) ( )?K Kud

D z D z

4

K K K KK

n n p pd

K K K K Ku p p n n

Y Y r Y YD

D Y Y r Y Y

Connections between the parton distribution and fragmentation functions?

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Summary• The flavor asymmetry of light sea quarks provides

insight on nucleon sea. Future measurements of the sea quarks at higher and lower x and polarized sea are anticipated.

• Flavor and spin structure of the nucleon are connected.

• Complementarity between electron and hadron probes.

• Connection between the parton distribution function and the parton fragmentation functions need to be better understood.

• The flavor structure of nucleon and meson fragmentation functions could be an interesting area for further investigations.