1

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?

3

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

4

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

5

/ 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

6

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

7

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

9

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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12

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

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

Nuclear binding

Fermi motion

of the nucleon

Shadowing

Anti-shadowing

Nuclear Modifications of Structure Function F2

Connection with SRC? Flavor-dependent EMC effect?

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

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

4

26 4

Q

sxd

•

),()(])1(1{[ 2

11

,

22

h

qq

qq

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

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

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?

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!

Transversity at Jlab 12-GeV

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Hall-B

Extensive SIDIS program

with SoliD in Hall-A

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

• 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

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

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.