•introduction •exclusive processes •semi-inclusive...
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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.