Studies of OAM at JLAB

•Introduction•Exclusive processes•Semi-Inclusive processes•Summary

HarutHarut AvakianAvakianJefferson LabJefferson Lab

UNM/RBRC Workshop on Parton Angular Momentum , NM, Feb 2005

* In collaboration with V.Burkert and L.Elouadrhiri

Parton picture: Longitudinal and transverse variables

“long before”

[ ]∫−

ξ+ξ− J G = =1

1

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

21

xExHxdxJ q

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

Quark Angular Momentum Sum Rule

GPDs Hu, Hd, Eu, Ed provide access to total quark contribution to proton angular momentum.

½ = ½ (Δu+Δd+Δs) + Lq + Jg

J q

Proton’s spin

Large x contributions important.

PDFs fpu(x,kT), g1, h1 FFs F1pu(t),F2p

u(t)..

d2k

T

ξ=0,

t=0 dx

Measure momentum transfer to quark

Measure momentum transfer to target

Analysis of SIDIS and DVMP are complementary

TMD PDFs fpu(x,kT), GPDs Hpu(x,ξ,t)..

3D Parton Distributions

Form Factor Studies

n

GE(t)=F1(t)+t/4M2*F2(t)GM(t)=F1(t)+F2(t)

~9 0%Sachs Form Factors

More data expected in 2006/2007

Form Factor StudiesUse various parameterizations for GPDs to fit the existing form factor data

A.Afanasev hep-ph/9910565Diehl et al, Eur.Phys.J c39 (2005)M.Guidal et al PRD (2005)

Different parameterizations yield different contributions for quarks to the OAM

A)Large Ld and small LuB)Sum of Lu and Ld small

More observables needed for detailed studies of GPDs and the OAM (RCS,DVCS,DVMP)

Issues: different realistic fits to FFs produce different values for Lqfits done at high t, need to be extrapolated to t→0

DVCSDVCS DVMPDVMP

Hard Exclusive Processes and GPDs

hard vertices

hard gluon

DVCS – for different polarizations of beam and target provide access to different combinations of GPDs H, H, E

long. only

DVMP for different mesons is sensitive to flavor contributions (ρ0/ρ+ select H, E, for u/d flavors, π, η, K select H, E)

Study the asymptotic regime and guide theory in describing HT.

~

Deeply Virtual Compton Scattering ep->e’p’γ

•Different GPD combinations accessible as azimuthal momentsof the total cross section.

10-5

10-4

10-3

10-2

10-1

1

0 0.5 1

6 GeV

dσ/d

t (nb

/GeV

4 )

0 0.5 1-t(GeV2)

27 GeV

0 0.5 1

200 GeV

DVCS

BH

ΔσLU ~ sinφIm{F1H + ξ(F1+F2)H +kF2E}~

Polarized beam, unpolarized target:

Unpolarized beam, longitudinal target:

ΔσUL ~ sinφIm{F1H+ξ(F1+F2)(H +.. }~

ξ = xB/(2-xB ),k = t/4M2

Kinematically suppressed

Kinematically suppressed

d4σdQ2dxBdtdφ ~ |TDVCS + TBH|2DVCS BH

TBH : given by elastic form factorsTDVCS: determined by GPDs

GPD

ΔσUT ~ sinφIm{k1(F2H-F1E ) +.. }

Unpolarized beam, transverse target:

Kinematically suppressed

Deeply Virtual Compton Scattering ep→e’p’γ

Interference responsible for SSA, contain the same lepton propagator P1(φ) as BH

( )[ ]ΕFH~FFHFIm)y(KysMx

xIB

B2421211 2

228 Δ− −++−= λ

BH

IB

cs

yx

LUA0

1≈ Way to access to GPDS

GPD combinations accessible as azimuthal moments of the total cross section.

φ-dependent amplitude

Strong dependence on kinematics of prefactor φ-dependence, at y=ycol P1(φ)=0 Fraction of pure DVCS increases with t and φ

φ=0

φ=45

φ=90

BH

DVCS

xMEQxMEQQtcol )2(

)2(2

22

−−

=yxtQtQy col =

−−

= 2

2

x=0.25

5.7 GeV

DVCSExperiments

Α(φ) = αsinφ + βsin2φ

S. Stepanyan et al. Phys. Rev. Lett. 87 (2001)

CLAS at 4.3 GeV HERMES 27 GeV

A. Airapetian et al. Phys. Rev. Lett. 87 (2001)

•Define relation between ALU and s2I

•effect of other non-0 moments ~5-10%•effect of finite bins ~10%

•Define background corrections•pion contamination ~10%•radiative background•ADVCS <3% at CLAS

GPDs from ep->e’p’γ

Requirements for precision (<15%) measurements of s2

I

and GPDs from DVCS SSA:

More relevant when proton is not detected

DVCS event samples 3 event samples(after data quality cuts)1) ep 0 photons (~2M events)

tight cuts on PID,missing mass MX2) epγ 1 photon in Calorimeter (~150000 events)

cut on the direction θγX<0.015, 3) epγγ 2 photon(π0) in Calorimeter (~70000 events)

cut on the direction θπX<0.02,

Kinematic coverage of 5.75 GeV(red) and 5.48(blue) CLAS data sets

Angular cut most efficient in separating π0

epγ(DVCS)

epγ(π0)

π0 MC vs Data

•Exclusive pi0 production simulated using a realistic MC•Kinematic distributions in x,Q2,t tuned to describe the CLAS data

π0 beam SSA cross section Main unknown in corrections of photon SSAare the π0 contamination and its beam SSA.

Contamination from π0 photons increasing at large t and x and also at large f.Significant SSA measured for exclusive π0s also should be accounted

Use epγγ to estimate the contribution of π0 in the ep and epγ samples

1.6<Q2<2.6, 0.22<x<0.32

CLAS 5.7 GeV

PRELIMINARY

BH cosφ moment

BH cosφ moment can generate ~3% sin2φ in the ALU

BH

BHBHII

BHBHBH

I

LU cccss

cccsA

0

0122

010

2 2sin)2/(sin)cos/1(

sin φλφλφ

φλ −≈

+∝

DVCS SSA kinematic dependences at 5.7 GeV

ALU for ep->ep[γ] sample with -t<0.5 GeV2

Fine binning allows to observe the x and Q2 dependence

Preliminary data for fully exclusive epγ is consistent with the ep data and consistent with GPD base predictions

PRELIMINARY

JLab/CLASCalorimeter and superconducting

magnet within CLAS torus

Plastic scintillator array

LH2 targete

Beam

Electromagneticcalorimeter

HRS

p

e

γ

ee’p

γ

→ Dedicated detection of 3 particles e, p and γ in final state

→ Firmly establish scaling laws (up to Q2 ~ 5 GeV2), if observed, or deviations thereof understood,

first significant measurement of GPDs.→ Large kinematical coverage in xB and t

JLab/Hall A

424 PbWO4crystals

HRS + PbF2 + Plastic scintillatorH(e,e’γp)D(e,e’γN)N

Dedicated DVCS experiments

dedicated calorimeters

Extraction of GPD H from ALU moment

•Red[blue] points correspond to projected ALU [un]corrected for π0 (bin by bin) •H stands for the ratio of the ALU and prefactor calculated for all events in a bin (averaged over φ) •Curves are for a simple model for CFF H (blue) and H+…(red)

ξ(F1+F2)H +kF2E~20%

~

epγ

2<Q2<2.4 GeV

cLU

ALU

/cLU

Target Spin Asymmetry: t- Dependence

Measurements with polarized target will constrain the polarized GPD and combined with beam SSA measurements would allow precision measurement of unpolarized GPDs.

ΔσUL ~ sinφIm{F1H+ξ(F1+F2)(H +.. }ΔσLL ~ cosφRe{F1H+ξ(F1+F2)(H +.. }~

Unpolarized beam, longitudinal target:

Kinematically suppressed

~

First data available(5 CLAS days), more(60 days) to come at 6 GeV

CLAS (4.2 GeV)

Regge (JML)

C. H

adjid

akis

et a

l., P

LB 6

05

GPD formalism (beyond leading order) describes approximately data

for xB<0.4, Q2 >1.5 GeV2GPD (MG-MVdh)

CLAS (5.75 GeV)

Analysis

in progress

Two-pion invariant mass spectra

Decent description in pQCD framework already at moderate Q2

Exclusive ρ meson production: ep → epρ0

Exclusive π+π− and π+π0

e p e p e pe p ρρπ+ π-

e- p → e- nρ+π+π0

ρ+n

ρ0

Provide access to different combinations of orbital momentum contributions Ju,Jd

ρ0 -> 2Ju + Jd, ρ+ -> Ju - Jd

Exclusive ρ0 production on transverse target

A ~ 2Hu + Hd

B ~ 2Eu + Edρ0

K. Goeke, M.V. Polyakov,M. Vanderhaeghen, 2001

Eu, Ed needed forangular momentum sum rule.

ρ0

A ~ Hu - Hd

B ~ Eu - Edρ+

Asymmetry is a more appropriate observable for GPD studies at JLabenergies as possible corrections to the cross section are expected to cancel

2Δ ┴(Im(AB*))/π

|Α|2(1−ξ2) − |Β|2(ξ2+t/4m2) - Re(ΑΒ∗)2ξ2

ΑUT = −

TMD measurements in SIDIS (γ*p→πX)

TMD PDFs related to interference between L=0 and L=1 light-cone wave functions.

f1T┴ ep → eπX D1 sin(φh−φS)

h1┴ ep → eπX H1

┴ sin(φh−φS’)

h1L┴ ep → eπX H1

┴ sin(φh−φS’)

fL┴ ep → eπX D1 sinφh

g┴ ep → eπX D1 sinφh

hL ep → eπX H1┴ sinφh

Significant beam and target SSA were observed in all listed channels, more data under way

Process MomentTMD FF

ST(q×PT)

φS’=π/2-φh

φS’=π-φh

Survive in jet limit

E06-010 and E06-011

Sivers Effect studies with Transversely polarized target

Proposal approved, to study the Sivers function at JLab (Hall-A)

Sivers SSA at CLAS @5.7GeVExpected precision of the AUTwith transversely polarized target

AUT ~Sivers

Measurement of π0 AUT at CLAS would allow model independent extraction of the Sivers function

Simultaneous measurement of SIDIS, exclusive ρ,ρ+,ω and DVCS asymmetries with a transversely polarized target.

π+

Polarized target SSA using CLAS at 6 GeV

•Provide measurement of SSA for all 3 pions, extract the Mulders TMD and study Collins fragmentation with longitudinally polarized target•Allows also measurements of 2-pion asymmetries

Hunf=-1.2Hfav

Hunf=-5Hfav

Hunf=0

curves, χQSMfrom Efremov et al

∑∑ ⊥⊥

=

q

qqq

qqL

ULUL zDxf

zHxhDA

)()(

)()(

11

112sin φ 60 days of CLAS+IC

(L=1.5.1034cm-2s-1)

• Significant SSA measured for pions with longitudinally polarized target• Complete azimuthal coverage crucial for separation of sinφ, sin2φ moments

Target SSA measurements at CLAS

p1sinφ+p2sin2φ

0.12<x<0.48

Q2>1.1 GeV2

PT<1 GeV

ep→e’πXW2>4 GeV2

0.4<z<0.7MX>1.4 GeV

y<0.85

CLAS PRELIMINARY

p1= 0.059±0.010p2=-0.041±0.010

p1=-0.042±0.015p2=-0.052±0.016

p1=0.082±0.018p2=0.012±0.019

)()(1 12

,

sin zDxxfeyyQMS qq

Lqqq

LUL⊥

−Σ−∝φσ

ALU x-dependence: CLAS @ 5.7 GeV

π+,0.5<z<0.8

Parton distribution g┴(x) is calculated within the same dynamical model ofAfanasev, Carlson

•Assume kT is small•Assume NLO corrections small

Beam SSA for π0 may provide a FF independent access to g┴

Measuring the Q2 dependence of SSA

σsinφLU(UL) ~FLU(UL)~ 1/Q (Twist-3)

Wide kinematic coverage and higher statistics will allow to check the higher twist nature of beam and longitudinal target SSAs

For fixed x, 1/Q behavior expected

CLAS12 High luminosity polarized

(~80%) CW beamWide physics acceptance

(exclusive, semi-inclusive current and target fragmentation)

Wide geometric acceptance

12GeV significantly increase the kinematic acceptance and

accessible luminosity

Provides new insight into - quark orbital angular momentum contributions - to the nucleon spin- 3D structure of the nucleon’s interior and correlations- quark flavor polarization

SummaryCurrent JLab data are consistent with a partonic picture, and can be described by a variety of theoretical models.

High luminosity, polarized CW beam, wide kinematic and geometric acceptance allow studies of exclusive and semi-inclusive processes, providing data needed to constrain relevant 3D distribution functions (TMDs,GPDs)

Experimental investigation of properties of 3D PDFs at JLab, complementary to planed studies at HERMES, COMPASS, RHIC, BELLE, GSI, would serve as an important check of our understanding of nucleon structure in terms of quark and gluon properties.

CLAS12 Full acceptance, general purpose detector for high luminosity electron scattering experiments, is essential for high precision measurements of GPDs and TMDs in the valence region.