1 flavor symmetry of parton distributions and fragmentation functions jen-chieh peng workshop on...
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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
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
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
12
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
15
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
19
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
20
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
21
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
22
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
24
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
25
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
26
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
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
28
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
29
/ 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)
30
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
32
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
33
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
34
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
35
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
36
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
37
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?
38
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.