1

Probing the Light Quark Sea Flavor Asymmetry and Measuring the Neutron Transversity in Semi-

inclusive Charged Meson Electroproduction

Xin Qian

Duke University

2

Outline Nucleon Structure and Electron Scattering

FlavorFlavor structure: Probing light quark sea flavor asymmetry

Spin structure: Measuring neutron transversity

Summary

3

Nucleon Structure Nucleon anomalous magnetic

moment (Stern, Nobel Prize 1943)

Electromagnetic form factor from electron scattering (Hofstadter, Nobel Prize 1961)

Deep-in-elastic scattering, quark underlying structure of the nucleon (Freedman, Kendell, Feldman, Nobel Prize 1990)

Understanding the underlying nucleon structure (Spin, flavor, charge, current distribution)from quantum chromodynamics (confinement region) is essential.

4

Electronuclear Scattering

------ A powerful tool to study nuclear structure

Inclusive: (the main tool)

detecting electron only Semi-inclusive: (providing additional information)

detecting electron and one of the hadrons coincidently

Charge distribution:Spectrum:

Energy

5

Cross Section

( ) 2 21 2~ ( , ), ( , )sW F x Q F x Q

( ) 2 21 2~ ( , ), ( , )AW g x Q g x Q

Structure Functions:

21 1

, , , , ,

1( ) ( )

2 i Li

i u u d d s s

g x e g x

21 1

, , , , ,

1( ) ( )

2 i Ti

i u u d d s s

h x e h x

21 1

, , , , ,

1( ) ( )

2 i i

i u u d d s s

F x e f x

Transversity Distributions:

Polarized and Unpolarized inclusive DIS

γ*

Relations to Form Factor:Charge distribution:

Magnetic moment distribution:

2

1 224E

qG F F

M

1 2MG F F

Hadronic Part:

6

Semi-Inclusive DIS A DIS reaction in which a hadron h, produced in the

current fragmentation region is detected coincidently with scattered electron.

SIDIS

Parton distribution Function (PDF)

Fragmentationfunction (FF)

Semi-inclusive

DXs~PDFFF

Current frag.

Target frag.

7

Outline Nucleon structure and electron scattering

Flavor structure: Probing light quark sea flavor asymmetry

Spin structure: Measuring neutron transversity

Summary

8

Flavor Asymmetry in the light nucleon sea

Gottfried sum rule:

A flavor-symmetric nucleon sea and isospin symmetry would lead

New Muon Collaboration result determined

The Drell-Yan measurement also supports the flavor asymmetry.

12 2

2 2

0

1 12 2 2 2

0 0

[ ( , ) ( , )]

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

3 3

p nG

v v

dxI F x Q F x Q

x

u x Q d x Q dx u x Q d x Q dx

1

3GI

0.82 2

2 2

0.004

( ( , ) ( , ) 0.221 0.021)p n dxF x Q F x Q

x

9

Semi-inclusive Pion production from proton and deuteron target

The Pion yield in unpolarized SIDIS can be expressed as:

The flavor asymmetry can be determined by four yields:

2( , ) [ ( ) ( ) ( )]i ii i q i q

i

Y x z e q x D z q D z

( ) ( )

( ) ( )

d x u x

u x d x

( ) ( ( ) ( )) ( ( ) ( ))

( ) ( ( ) ( )) ( ( ) ( ))

d x d x u x d x u x

u x d x u x d x u x

will introduce systematic error.

( ) ( )u x d x

( ) ( )u x d x

10

Semi-inclusive Kaon production from proton and deuteron target

Fragmentation Function Ratio (ignored the strange quark contribution):

With

1

1

( ) ( )24

( ) ( )

K K K KK dn n p pd K

K K K K KK Ku p p n n

Y Y r Y YD D

D DD Y Y r Y Y

1

( ) ( )

( ) ( )

d x d xr

u x u x

K K K KK u u s sD D D D D

K K K KK u u s sD D D D D

d K K K KK d dd d

D D D D D

PR-04-114

11

Outline Nucleon structure and electron scattering

Flavor structure: Probing light quark sea flavor asymmetry

Spin structure: Measuring neutron transversity

Summary

12

Leading-Twist Quark Distributions

No K┴ dependence

K┴ - dependent, T-odd

K┴ - dependent, T-even

( Eight parton distributions functions)

Transversity:

13

Eight fragmentation functions

T-odd, quark intrinsic momentum dependent H1

(z, кT’ ): related to Collins effect.

Hadron momentum ~кT’ = -zкT ~ quark momentum

--

14

The kinematics and coordinate

E’ is the energy of scattered electron

θe is the scattering angle

ν=E-E’ is the energy transfer.

k: quark transverse momentum

DIS: Q2 (1/λ) and ν is large, but x is finite.

15

Leading-Twist DXs in SIDIS

4

26 4

Q

sxd

2 21 1

,

21{ [1 (1 ) ] ( ) (

2, )q q

q hq q

e f x D z Py

2

2

2

2

2 (1) 21 1

,

2 21

,

21

21

,

(1)1

(1 ) cos(2 )4

| | (1 ) sin(2 )

( ) ( , )

(

sin

4

| | (

, )

( , )(1 ( ) ))

( )

lhh

N h

l

l lh

q qq h

q q

qq h

h

q q

qq h

q

L hN h

hT

h q

qS

qL

e h x H z P

e H z P

e

Py

z M M

PS

H z P

yz M M

PS y

zh x

M

h x

2 (1) 2

1 1,

2 (

2

3

32) 2

1 1,

2 21 1

,

2

1| | (1 )

2

| | (1 ) sin(3

sin( ) ( ) ( , )

( ) ()6

1| | (1 )

2

1| | (1 ) cos( )

, )

( ) ( )

2

,

hT

N

l lhT h S

N h

e L

l lhe T h S

q qq T h

q q

q qq T h

q q

q qq h

q

l l

q

N

h S e f x D z P

e h

PS y y

zM

PS y

z M M

S

x H z P

e g x D z P

e

y y

PS y y

zM

2 (1) 2

1 1,

( ) ( , )}q qq T h

q q

g x D z P

Unpolarized

Polarized target

Polarized beam and

target

SL and ST: Target Polarizations; λe: Beam Polarization

Sivers

Collins

DXs ~ PDFFF

Transversity

16

Characteristics of Transversity Some characteristics of transversity:

h1T = g1L for non-relativistic quarks In non-relativistic case, boosts and rotations commute. ΛQCD=200 MeV, mu and md ~ 5 MeV, quark are relativistic.

Important inequalities: |h1Tq| ≤ f1

q ; |h1T

q| ≤ (f1q + g1L

q )/2.

h1T and gluons do not mixGluon can not be included in transversity for

nucleon.

Q2-evolution for h1T

and g1L are different N

q q

N

Helicity state

17

Characteristics of Transversity Chiral-odd → not accessible in inclusive DIS

In calculating the hadronic part in inclusive DIS, the gluon contribution cancel the quark mass term which contains the transversity distribution.

Decoupling mass term will turn off transversity distribution

- +

18

Characteristics of Transversity It takes two Chiral-

odd objects to measure transversity Drell-Yan (Doubly

transversely polarized p-p collision)

Semi-inclusive DISChiral-odd distributions

function (transversity)

Chiral-odd fragmentation function (Collins function)

Chiral-quark soliton model

-

19

Asymmetry in Semi-Inclusive DIS with polarized target

4

26 4

Q

sxd

2 2 21 1

,

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

2q q

q hq q

y e f x D z P

22 (1) 2

1 12,

22 (1) 2

1 12,

2 21 1

,

(1 ) cos(2 ) ( ) ( , )4

| | (1 ) sin(2 ) ( ) ( , )4

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

l q qhh q h

q qN h

l q qhL h q L h

q qN h

q qhT q h

q qh

l lh S

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 21 1

,

1| | (1 ) ( ) ( , )

2

| | (1 ) sin(3 ) ( ) ( , )6

1| | (1 ) ( ) ( , )

sin

2

1| | (1 ) cos( )

2

( ) q qhT q T h

q qN

l l q qhT h S q T h

q qN h

q qe L q h

q q

l lhe T h S

N

l lh 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 qq 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

20

Asymmetry in Semi-Inclusive DIS with polarized target ----- Collins effect Access to transversity

Artru model Based on LUND

fragmentation

picture.

1 1( ) ( , )T TA h x H z k

Scatteringplane

21

Asymmetry in Semi-Inclusive DIS with polarized target ----- Sivers effect

Sivers effect A new type of PDF, T-odd, depends on intrinsically

quark transverse momentum quark orbital momentum

1 1( ) ( )TA f x D z

Beam direction

Into the page

22

Asymmetry in Semi-Inclusive DIS with polarized target ----- Discussion

Can not separate two effects in the longitudinal case.

In longitudinal case, some higher twist distribution contributes.

Need transversely polarized target in order to separate.

~ ( )

~ ( )

0

collins h S

sivers h S

S

A Sin

A Sin

<ST> ~ 0.15 Hermes kinematics

23

JLab Hall-A E03-004 Experiment

High luminosity 15 μA electron beam on 10-atm 40-cm transversely

polarized 3He target Measure neutron transversity

Sensitive to h1d, complementary to HERMES

Disentangle Collins/Sivers effects

Measurement of Single Target-Spin Asymmetry in Semi-Inclusive Pion Electroproduction on a

Transversely Polarized 3He Target

Argonne, CalState-LA, Duke, E. Kentucky, FIU, UIUC, JLab, Kentucky, Maryland, UMass, MIT, ODU, Rutgers, Temple, UVa, W&M, USTC-China, CIAE-China, Glasgow-UK, INFN-Italy, U. Ljubljana-Slovenia, St. Mary’s-

Canada, Tel Aviv-Israel, St. Petersburg-Russia

Spokespersons: J.-P. Chen (JLab), X. Jiang (Rutgers), J. C. Peng (UIUC)

24

Single Spin Asymmetry

With 100% polarization,

From azimuthal angular distribution, we can separate Collins effect and Sivers effect in this experiment.

Comparison with HERMES projection

25

Experimental Configuration

26

Future plan

JLAB E03-004 will be my thesis experiment.BigBite background simulation.Work on target.Doing the data analysis.

Plan to move to JLAB this summer.

27

Summary Semi-inclusive DIS meson electroproduction can

provide additional information to the inclusive DIS (transversity).

By measurement of SIDIS π+/π- , K+/K- yield ratio on hydrogen and deuterium target, we will independently check the light sea quark flavor asymmetry. The flavor dependent fragmentation function will be studied (flavor structure).

The Hall-A measurement on transversely polarized 3He target should provide new information and powerful constraints on transversity of u-quark and d-quark, when combined with HERMES and COMPASS data (spin structure).

28

Thank you!

29

Supporting slides …..

30

Transversity (Chiral-odd)

31

Semi-inclusive Pion production from proton and deuteron target

The Pion yield in unpolarized DIS can be expressed as:

The flavor asymmetry can be determined as:

in which with and

2( , ) [ ( ) ( ) ( )]i ii i q i q

i

Y x z e q x D z q D z

( ) ( ) ( )[1 ( , )] [1 ( , )]

( ) ( ) ( )[1 ( , )] [1 ( , )]

d x u x J z r x z r x z

u x d x J z r x z r x z

'

'

3 1 ( )( )

5 1 ( )

D zJ z

D z

' ( ) u

u

DD z

D

( , ) ( , )( , )

( , ) ( , )

p n

p n

Y x z Y x zr x z

Y x z Y x z

( ) ( )( ) ( ) ( ( ) ( ))

( ) ( )

d x u xd x u x u x d x

u x d x

( ) ( ( ) ( )) ( ( ) ( ))

( ) ( ( ) ( )) ( ( ) ( ))

d x d x u x d x u x

u x d x u x d x u x

will introduce systematic error.

( ) ( )u x d x( ) ( )u x d x

32

Current & target fragmentation

33

Quark-nucleon helicity amplitude If use the quark-nucleon helicity amplitudes:

Express three leading twist distribution function as amplitudes:

h1T(x)

g1L(x)

f1(x)

* * * *( ) ( ) 2( ) 0a a a a a a a a

34

Kinematics

35

Hermes data and detailed interpretations

36

Makins DNP04 talk

π

37

Observation of Single-Spin Azimuthal Asymmetry

Longitudinally polarized target

ep → e’πx HERMES

hep-ex/0104005

<ST> ~ 0.15• Suggests transversity, δq(x), is sizeable

• Suggests Collins T-odd fragmentation function is sizeable

• Other effects (Sivers effect, higher twist) could also contribute

38

39

Why Collins π- asymmetries so large? DIS on proton target dominates by u-quark scattering.

1 1,

1 1,

~

~

uCol favored

uCol disfavored

A h H

A h H

…expect: positive.

…expect: ~zero.

Data indicate the disfavored fragmentation function is sizable and negative.

40

QCD Q2 evolution

41

Nobel Prize this year!

“ Running” of Coupling Constants with energy scale is a key prediction

14

42

21

43

Probability of parton i going into parton j with momentum fraction z

Calculable in pQCD as expansions in αS

In Leading Order Pij(z) take simple forms

Pqq Pqg Pgq Pgg

Splitting Functions Pij(z)

44

b) Sum i) over q and q separately

Fit to DGLAP equations

c) Define: Valence quark density

Singlet quark density

I) Rewrite DGLAP equations

a) Simplify notation

Nf … number of flavors

i)

ii)

ia)

ib)

← u,u,d

45

II) DGLAP equations govern evolution with Q2

Do not predict x dependence: Parameterize x-dependence at a given Q2 = Q2

0 = 4 – 7 GeV2

d) Rewrite DGLAP equations

Valence quark density decouples from g(x,Q2) Only evolves via gluon emission depending on Pqq

55 parameters

Low x behaviour High x behaviour: valence quarks

46

Proton Structure function F2(x,Q2)

Scaling violation explicitly seen… Beyond the fixed target regime H1 and ZEUS data in agreement.

Further, pQCD predictions at NLO describe data impressively over many decades in x and Q2.

Studies have resulted in the determination of gluon distribution, precise determination of S

Rise in F2 at low x

47

Polarized He3 target

48

Why polarized 3He is an effective neutron target?

S-state about 90% D-state about 8% S’-state about 2%

49

Optical Pumping for Rubidium

37Rb:

Rb vapor in a weak B field is optically pumped

Buffer gas N2 let the electrons decay without emitting photons

)55(1 2/12/1 PSD

1s22s22p63s23p6

4s23d104p65s1

50

Polarized 3He target description

51

NMR Polarimetry

The magnetic moment of a free particle of spin

When placed in an external B-field Transform into a frame rotating

Effective field

I

IM

)(ˆ

BMt

Mz

xBzBBeff ˆˆ)( 10

BMdt

Md

52

NMR - Adiabatic Fast Passage (AFP)

Ramp the holding field from below the resonance to above it

Spin Flip (Twice)

Signal

zB ˆ0

CtBmBtB

BMtS nmrHe

)(

)/)(()( 02

12

0

13

r/

<M> is the fitted amplitude

xBzBBeff ˆˆ)( 10

53

NMR-AFP Condition

The sweep rate is slow enough (Adiabatic)

The sweep rate is fast enough (Fast)

10

1

1B

dt

dB

B

21

0

1

1,

11

TTdt

dB

B

T1 and T2 are the longitudinal and transverse relaxation times