parton distribution functions · • the progress of lattice qcd calculations allow direct...
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Parton Distribution Functions
• Unpolarized parton distrbutions
– Flavor structures of the valence and sea quark
contents of the nucleons and nuclei
• Transverse momentum dependent (TMD)
distributions
– Transversity and other novel TMDs
Jen-Chieh Peng
2014 Long-range Plan Joint Town Meetings on QCD
Temple University, Philadelphia, Sept. 13-15, 2014
University of Illinois at Urbana-Champaign
Outline
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Flavor and spin structures of the nucleons
• 99.97% of the visible mass of the Universe is composed of protons and neutrons
• QCD at the confinement scale remains to be better understood
• The progress of lattice QCD calculations allow direct comparison between the experiments and theory
• They provide crucial inputs for describing hard processes in high energy collisions such as at LHC (p+p collider)
Why is it interesting?
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Flavor structure of the proton sea
From Frank
Close’s textbook
(1980)
There was a time when nucleon was nice
and simple……
Actually, the nucleon is full of surprises !!
( ) ( ) ( ) ( ) (3) symmetric seau x d x s x s x SU
Is ( ) 2 ( )?
Is ( ) ( )?
Is ( ) ( )?
Is ( ) (
Quest
)?
Is ( ) ( )?
Is ( ) ( )?
ions
V V
p n
p n
u x d x
u x d x
s x u x
s x s x
u x d x
g x g x
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The Gottfried Sum Rule 1
2 20
1
0
[( ( ) ( )) / ]
1 2( ( ) ( ))
3 3
( )1
3p p
p n
G
p p
S F x F x x dx
u x d
i
x dx
f u d
New Muon Collaboration (NMC) obtains
SG = 0.235 ± 0.026
( Significantly lower than 1/3 ! )
= Expect if sea quarks
are produced in
d u
g qq
?d u
Is in the Proton?u d
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/ flavor asymmetry from Drell-Yand u
2 2
1/ 2 (1 ( ) / ( )Dr )
2ell-Yan: pd pp d x u x
2 2
2
1 2 1 2
1 2 1 2. .
4( ) ( ) ( ) ( )
9a a a a a
aD Y
de q x q x q x q x
dx dx sx x
800 GeV proton beam
on hydrogen and deuterium
mass spectrum
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Meson Cloud Models Chiral-Quark Soliton Model Instantons
• nucleon = chiral soliton
• expand in 1/Nc
• Quark degrees of freedom
in a pion mean-field
Meson cloud has significant contributions to
sea-quark distributions
Some Theoretical Models for / Asymmetryd u
Asymmetry between
These models a
(
Asymmetry between ( ) and (
lso have specific
)
) and ( )
predictions on
s x s
d x
x
u x
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SeaQuest Experiment ( Unpolarized Drell-Yan using 120 GeV proton beam)
Main goals:
2
1) Measure / fla
) Measure EMC ef
vor asymmet
fect of ant
ry up to
iquarks u p to 0.4
0.4
5
5d u x
x
Is there a sign-reversal for ( ) ( ) at large ?d x u x x
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Is the sea-quark polarization flavor symmetric?
W production at RHIC clearly shows ( ) / ( ) asymmetryu x d x
Data show ( ) 0 and ( ) 0 in agreement with chiral soliton model u x d x
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0, 0 1, 0 1, 1
1, 0 1, 1
2
2
1) SU(6) sy
1 1 1| ( ) ( ) ( )
32 18
1 2( ) ( )
3 3
mmetry
2) Dominance of 0 diquark configu
rations (Close, Carlitz)
1 2
2
3
I
Z Z Z
Z Z
S S S S S S
S
n
S S S
p
Fd
u F
p u ud u ud u ud
d uu uu
S
d
2
2
2
2
2) Dominance of 0 diquark configurations (Farrar,
gnoring terms with 1 diquarks, then
Ignoring terms with 1 diquarks, then
1
Jack
04
1 3
s )
5 7
n
o
n
Z
p
n
p
Z
S
S
Fd
u F
Fd
u F
S
Ratios of ( ) / ( ) at large ?d x u x x
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– Extract F2n/F2
p from ratio of
measured 3He/3H structure
functions
How to make a precise measurement of ( ) / ( )?d x u x
1) “spectator tagging”
(BONUS experiment)
2) “Super ratio 3He/3H”
(Marathon experiment)
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Meson cloud model
Thomas / Brodsky and Ma
Analysis of neutrino DIS data
( )x s s
NuTeV, PRL 99 (2007) 192001
Is ( ) ( ) ?s x s x
p K (( ))us uds
x x
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( ) ( ) from NNPDF global fitss x s x
NNPDF2.0 analysis includes fixed-target
Drell-Yan and Tevatron W and Z data
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What is the -dependence of [ ( ) ( )] / [ ( ) ( )]?x s x s x u x d x
A strong dependence for the [ ( ) ( )] / [ ( ) ( )] rati
Ne
CTEQ6.6 suggests an SU(3) symmetric sea at smal
w kaon semi-inclusive DIS data at JLab 12 GeV and at EIC
will be crucia
o
l ?
?
l
x s x s x u x
x
d x
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P. Jimenez-Delgado, E. Reya, PRD 89 (2014) 074049
xuv
xdv
x(d u)
x(s s )
x(u u)
x(d d )
x(s s )
xg
Proton parton distributions from JR14
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Nuclear binding
Fermi motion
of the nucleon
Shadowing
Anti-shadowing
Nuclear Modifications of Structure Function F2
Connection with SRC? Flavor-dependent EMC effect?
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F2 & Drell-Yan data
for nuclei
region of existing nuclear data
Existing Nuclear Data are limited in Q2 and x
EIC and p-A collision will
explore new region
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Measure Meson PDF with Drell-Yan Process
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CEDAR
(CErenkov Differential counter with
Achromatic Ring focus)
Hadron beam at COMPASS
Projected D-Y events in 140 days
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Transverse structures of the nucleons
• Transverse degrees of freedom offer new insights on the nucleon structure
• TMDs provide stringent tests for various nucleon models
• The progress of lattice QCD calculations allow direct comparison with the experiments
• Novel parton distributions are accessible by experiments using lepton as well as hadron beams
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Why is it interesting?
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Three parton distributions describing
transverse momentum and/or transverse spin
1) Transversity
2) Sivers function
3) Boer-Mulders function
Correlation between and q Ns S
Correlation between and q qs k
Correlation between and N qS k
Three transverse quantities:
1) Nucleon transverse spin
2) Quark transverse spin
3) Quark transverse
momentum
Three different correlations
N
q
q
S
s
k
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4
26 4
Q
sxd
•
),()(])1(1{[ 2
11
,
22
h
q PzDxfey
22 (1) 2
1 12,
22 (1) 2
1 12,
2 2
1 1
,
cos(2 )
sin(2 )
(1 ) ( ) ( , )4
| |
s
(1 ) ( ) ( , )4
| | (1 ) ( ) (in( )) ,
q qhq h
q qN h
q qhL q L h
q qN h
q
l
h
l
h
l l
h
qhST q h
q qh
Py e h x H z P
z M M
PS y e h x H z P
z M M
PS y e h x H z P
zM
•
2 2 (1) 2
1 1
,
32 (2) 2
1 13 2,
2 2
1 1
,
1| | (1 ) ( ) ( , )
2
| | (1 ) ( ) ( , )6
1| | (1 ) ( ) ( , )
2
1| | (1 )
sin( )
sin(3 )
co ( )2
s
q qhT q T h
q qN
q qhT q T h
q qN h
q q
e L q h
q q
he T
N
l l
h S
l l
h S
l l
h S
PS y y e f x D z P
zM
PS y e h x H z P
z M M
S y y e g x D z P
PS y y e
zM
2 (1) 2
1 1
,
( ) ( , )}q q
q T h
q q
g x D z P
Unpolarized
Polarized
target
Polarzied
beam and
target
SL and ST: Target Polarizations; λe: Beam Polarization
Sivers
Transversity
Boer-Mulders
Transversity and TMD PDFs are probed in
Semi-Inclusive DIS
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Extraction of Transversity and Collins fragmentation
function from SIDIS and Belle data
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Torino group, Anselmino et al., PRD 87, 094019 (2013)
SIDIS
on p
SIDIS
on pSIDIS
on d
Belle
ee
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Extraction of Transversity and Collins fragmentation
function from SIDIS and Belle data
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Torino group, Anselmino et al., PRD 87, 094019 (2013)
Transversity Collins pion FF
quarku
quarkd
Favored
Unfavored
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Extraction of nucleon tensor charge
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Torino group, Anselmino et al., PRD 87, 094019 (2013)
1
1 10[ ( ) ( )]q qq h x h x dx
1 : Extractions from global fits
(using two different Collins FF
parameterizations)
2-10: Predictions from various
models (including LQCD)
u d
0.787 0.319u d
Tensor charges are smaller
than axial charge
Difference between data and theory
could be partly caused by neglecting
sea transversity in the extraction?
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Recent progress in LQCD suggests the possibility to
calculate the x-dependence of parton distributions
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The -dependence of
the quark and antiquark
transversity distributions
can be calculated (not
just their moments)
x
Predicts large sea-quark transversity!
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Transversity at Jlab 12-GeV
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Hall-B
Extensive SIDIS program
with SoliD in Hall-A
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Extraction of Sivers function from SIDIS data
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Torino group, Anselmino et al.,
Eur. Phys. J. A39 (2009) 89
(2013)
and -quark Sivers functions have opposite signs
Sea-quark Sivers functions are non-zero (from data)
u d
K
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• Does Sivers function change sign between DIS and Drell-Yan?
• Sign and magnitude of the sea-quark Sivers functions?
• Q2-evolution of the Sivers function?
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Outstanding questions on Sivers function
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Polarized Drell-Yan with 190 GeV/c pion beam
(Sivers asymmetry)
Polarized target
Expect data-taking in 2014-2015
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Proposal to measure Sivers in polarized
Drell-Yan at Fermilab
• Propose using the existing dimuon spectrometer
• Possibility of polarized target is also being considered 31
Proposal (P-1027) ( Polarized Drell-Yan with polarized proton beam)
Main goals:
2) T
1) Accelerate polarized p
est "sign-change" of T-od
roton b
d Siver
eam at the Main Injector
s function in Drell-Yan
(W. Lorenzon, P. Reimer, et al.)
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Another proposal to measure sea-quark Sivers in
polarized Drell-Yan at Fermilab
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Global interest in polarized Drell-Yan measurements
• Fermilab (proton beam, unpolarized, polarized beam/target possible)
• COMPASS (pion beam, polarized target)
• FAIR (polarized antiproton beam)
• RHIC (polarized proton beam)
• J-PARC (proton beam, polarzied beam possible)
• JINR NICA (proton beam)
Fermilab COMPASS J-PARC NICA RHIC
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Summary
• Significant progress has been made in
measuring and understanding the flavor and
momentum dependencies of parton
distributions in the nucleon.
• Exciting physics opportunities await us with
existing and future electron and hadron
facilities to further advance our knowledge
on hadron structure and QCD.