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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
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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?
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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 ! )
=
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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
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Unpolarized Semi-Inclusive DIS2
2
((
( )(
)
)
)1
h
qqq
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
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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
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Future experiments to measure at large x/d u
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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
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/ 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
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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
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Flavor Structure of the Helicity Distributions
• No evidence for u d
• Measurement of W± production at RHIC-spin would provide new information
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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
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
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
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
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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
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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.