Single Target Spin Asymmetries and GPDs

Jian-ping Chen, Jefferson Lab, Virginia, USA SSA Workshop, BNL, June 1-3, 2005

• Nucleon structure and GPDs

• DVCS and Wide Angle Compton Scattering

• Target SSA with 2 exchange to probe GPDs

• JLab E05-015: neutron SSA with vertically polarized 3He

• Summary

Nucleon Structure

• Elastic scattering nucleon has finite size

Dirac Form Factor, F1(Q2) - charge distribution

Pauli Form Factor, F2(Q2) – current distribution

• DIS parton distribution functions (PDFs)

q(x) – quark longitudinal momentum distribution

q(x) – quark longitudinal spin distribution

quark flavors, g(x), …

• Connection?

Beyond charge and quark distributions – Generalized Parton Distributions (GPDs)

Elastic: transverse charge & current densities

DIS: quark longitudinalmomentum & helicity distributions

X. Ji, D. Mueller, A. Radyushkin (1994-1997), …

Correlated distributions in transverse space - GPDs

M. Burkardt, A. Belitsky (2000) …

GPDs and ‘Handbag’ Diagram

A Unified Description of Hadron Structure

Parton momentumdistributions

Elastic form factors

Real Comptonscattering at high t

Parton spin distributions

Deeply Virtual Compton Scattering

GPDs

Quark angular Momentum

Link to DIS and Elastic Form Factors

),,(~ ,~ , , txEHEH

JG = 1

1

)0,,q()0,,q(21

21 xE xHxdxJq

Quark angular momentum (Ji’s sum rule)

X. Ji, Phy.Rev.Lett.78,610(1997)

DIS at =t=0

)(),()0,0,(~)(),()0,0,(

xqxqxH

xqxqxH

Form factors (sum rules)

)(),,(~ , )(),,(~

) Dirac f.f.(),,(

,

1

1,

1

1

1

tGtxEdxtGtxHdx

tF1txHdx

qPqA

) Pauli f.f.(),,(1

tF2txEdx

Access GPDs

Accessed by cross sections

Accessed by beam/target spin asymmetry

t=0

Quark distribution q(x)

-q(-x)

DIS measures at =0

Program to access/determine GPD’s

• Direct access:

-Deep Inelastic Scattering (DIS)

-Deep Virtual Compton Scattering (DVCS)

-Deep Virtual Meson Production (DVMP)

-Doubly Deep Virtual Compton Scattering (DDVCS)

• Form Factors: Moments of GPDs:

-Elastic Scattering

-Wide Angle Compton Scattering

-Single Target Spin Asymmetry through 2- exchange

SSA in DVCS to probe GPD

Accessing GPDs through DVCS

d4dQ2dxBdtd ~ |DVCS + BH|2

BH : given by elastic form factorsDVCS: determined by GPDs

LU ~ BH Im(DVCS)sin + higher twist.

~ |DVCS|2 + |BH|2 + BH*Im(DVCS)

DVCS

BH

GPDs FF

e-’

p

e- *

plane

ee’* plane

*p

ep ep

Separating GPDs through polarization

LU~ sin{F1H + (F1+F2)H +kF2E}d~Polarized beam, unpolarized target:

Unpolarized beam, longitudinal target:

UL~ sin{F1H+(F1+F2)(H + … }d~

Unpolarized beam, transverse target:

UT~ sin{k(F2H – F1E) + …. }d

= xB/(2-xB)

k = t/4M2

H, H, E

Kinematically suppressed

H, H~

H, E

A =

=

~

First observation of DVCS/BH beam asymmetry

GPD analysis of CLAS/HERMES/HERA data in LO/ NLO shows results consistent with handbag mechanism and lowest order pQCDA. Freund, PRD 68,096006 (2003), A. Belitsky, et al. (2003)

sin + sin2

<< 1 twist-3 << twist-2

e+p e+X e-p e-pX

CLAS4.3 GeV

2001

0

HERMES27 GeV

-180 180(deg)

Q2=2.5 GeV2 Q2=1.5 GeV2

[rad]

CLAS preliminary

5.75 GeV

<Q2> = 2.0GeV2

<x> = 0.3<-t> = 0.3GeV2

e p ep

<Q2> = 2.0GeV2

<x> = 0.2<-t> = 0.25GeV2

CLAS preliminary

E=5.75 GeV

AUL

Longitudinally polarized target

AUL~sin{F1H+(F1+F2)H...}d~

DVCS/BH target asymmetry

Asymmetry observed at about the expected magnitude. Much higher statistics, and broad kinematical coverage are needed.

HERMES data on deuterium target

First Dedicated DVCS Experiments at JLab

Azimuthal and Q2 dependence of Im(DVCS) at fixed .Test Bjorken scaling.

=> Full reconstruction of all final state particles e, p, => High luminosity 1037

Data taking completed

, t, Q2 - dependence of Im(DVCS) in wide kinematics. Constrain GPD models.

PbWO4

Electromagneticcalorimeter

s.c.solenoid

CLAS

Currently taking data

Hall A (p and n)

LD2

Deeply Virtual Exclusive Processes - Kinematics Coverage of 12 GeV Upgrade

JLab Upgrade

unique to JLabHigh xB only reachablewith high luminosity H1, ZEUS

Wide Compton Scattering to probe GPD

Wide Angle Compton Scattering• WACS access GPD moments Compton Form Factors: JLab Hall A E99-114

nucl-ex/0410001),()(

1

1

2 txHx

dxetR q

qqV

),()(1

1

2 txEx

dxetR q

qqT

),(~

)(1

1

2 txHx

dxetR q

qqA

Data:

GPD:

V

ALL R

RK

V

T

LL

LS

R

R

K

K

Recoil polarization components:

04.0078.0114.0 LSK

04.0083.0678.0 LLK

02.010.0 LSK

15.057.0 LLK P. Kroll, hep-ph/0412169

Target SSA with 2 exchange to probe GPD

JLab E05-015: vertically polarized n (3He)

GPD moment with target SSA with 2effect JLab E05-015: Spokespersons: T. Averett, J.P. Chen, X. Jiang

Summary on target SSA with 2

• 2-exchange provides a new tool to probe nucleon dynamics

• Non-zero Ay is a clear signature of 2-exchange

• E05-015 goals:

Unambiguously establish a non-zero Ay

First experiment to use 2 Ay to study GPDs

• Ayn sensitive to one GPD moment, cleaner interpretation

Constraints on E GPD• Technically straight-forward measurement, no new equipment needed

• ~ 1 month beam time to test GPD prediction for Ay at 15% level.

Summary

• GPD provides a unified framework

• DVCS SSA direct access GDPs

• Results from JLab, HERMES and other labs

• Dedicated experiments and JLab upgrade

• Wide Angle Compton Scatting access GPD moments

• Recent results on KLL and KLS.

• New way to measure GPD moments: STSA with 2• JLab E05-015: neutron one moment of GPD

constraints on E GPD.

Precision measurement of g2n

Higher twist effects:quark-gluon correlations

Quark-Gluon Correlations

• In simple partonic picture g2(x)=0

• Wandzura and Wilczek have shown that g2 can be written in two parts: – twist-2 contributions given by g1 – the other originating from quark-gluon correlations (twist-3)

g2 (x,Q2) g2WW (x,Q2) g 2(x,Q2)

g2WW(x,Q2 ) g1(x,Q2) g1(y,Q2)

x

1

dy

y

d2n(Q2 ) x2 2g1

n (x,Q2 ) 3g2n (x,Q2) dx

0

1

d2 2 B E / 3

Jefferson Lab Hall A Experiment E97-103Precision Measurement of the Neutron Spin Structure Function g2

n(x,Q2):A Search for Higher Twist Effects

T. Averett, W. Korsch (spokespersons) K. Kramer (Ph.D. student)

• Precision g2n, 0.57 < Q2 < 1.34 GeV2, W > 2 GeV, at x ~ 0.2.

• Direct comparison to twist-2 g2ww prediction using world g1

n data.

• Quantitative measurement of higher twist effects provides information on nucleon structure beyond simple parton model (e.g. quark-gluon correlations).

E97-103 Results: g2n vs. x

Improved precision of g2n by an order of magnitude

E97-103 results: g2n vs. Q2

• Measured g2n consistently higher than g2

ww

E97-103 results: g1n

• Agree with NLO fit to world data, evolved to our Q2

JLab E99-117 Precision Measurement of A1

n at Large xSpokespersons: J. P. Chen, Z. -E. Meziani, P. Souder, PhD Student: X. Zheng

• Precision A1n data at high x

2.7GeV2 < Q2 < 4.8 GeV2, W > 2 GeV• Extracting valence quark spin

distributions• Test our fundamental understanding

of valence quark picture• SU(6) symmetry• Valence quark models• pQCD (with HHC) predictions• Other models: Statistical Model, Chiral

Soliton Model, PDF fits, ….

• Crucial input for pQCD fit to PDF

• A2n at high x, by-product, d2

n

A2n results

• By-product

• Precision better than the world best results

• Also g1n and g2

n results

• Improved d2n precision

by a factor of 2:

d2n=0.0062 ± 0.0028

• PRC 70, 065207 (2004)

Summary on g2n and d2

n results

• Precision measurement of g2n at low Q2

• An order of magnitude improvement in precision

• g2n consistently higher than g2

WW

• Higher twist effects: quark-gluon correlations

• Precision spin structure data at high x from JLab Valence quark neutron spin structure

A1n at high x, an order of magnitude improvement:

A2n at high x, by-product

d2n: a factor of 2 improvement, can compare with

LQCD