H. Avakian, Hampton, May 21 1
Harut Avakian*Harut Avakian*
Spin-orbit correlation studies with EICSpin-orbit correlation studies with EIC
The 4th Electron Ion Collider Workshop
A New Experimental Quest to Study QCD, Hadron Structure, and Nuclear Matter
Dates: May 19-23, 2008 Location: Hampton University
*) In collaboration with A. Bruell
H. Avakian, Hampton, May 21 2
•Physics motivation–TMD parton distributions and spin-orbit correlations–Accessing TMDs in semi-inclusive DIS
•Projections for transverse SSAs at EIC and comparison with other experiments
–Boer-Mulders TMD–Sivers TMD–Pretzelosity TMD
•Summary
OutlineOutline
H. Avakian, Hampton, May 21 3
The Spin Structure of the Nucleon
Describe the complex nucleon structure in terms of partonic degrees of freedom of QCD
EMC at CERN (85): ~20% from Deep Inelastic Scattering (DIS)
~0.6 from QCD-sum rule“spin crisis”
Proton’s spin
J q
RHIC Spin & SIDIS
Understanding of the orbital motion of quarks crucial and requires understanding of spin-orbit correlations!!!
H. Avakian, Hampton, May 21 4
Structure of the Nucleon
GPDs/IPDs
d2kT
d2kT
TMD PDFs f1
u(x,kT), .. h1u(x,kT)
Gauge invariant definition (Belitsky,Ji,Yuan 2003)Universality of kT-dependent PDFs (Collins,Metz 2003)Factorization for small kT. (Ji,Ma,Yuan 2005)
Wpu(k,rT) “Mother” Wigner distributions
d2r T
PDFs f1u(x), .. h1
u(x)
quark polarization
H. Avakian, Hampton, May 21 5
Miller/”pretzelosity”
Spin densities from Lattice (QCDSF and UKQCD Collaborations)
Proton spin quark spin
GPD-E GPD-ET
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TMDs in SIDIS at leading twist
Correlation between the transverse momentum and transverse spin of quarks
-
-
Correlation between the quark transverse momentum and transverse spin of the proton
Meissner, Metz & Goeke (2007)
Collins (2002)
H. Avakian, Hampton, May 21 7
SIDIS kinematical plane and observables
Beam polarizationTarget polarization
U unpolarizedL long.polarizedT trans.polarized
sin(Smoment of the cross section for unpolarized beam and transverse target
PT
H. Avakian, Hampton, May 21 8
Unpolarized quarks
TMDs and spin-orbit correlations
Pretzelosity
Transversely polarized quarks
QCD large-x limit, Brodsky & Yuan (2006) (perturbative limit)
-
H. Avakian, Hampton, May 21 9
PretzelosityTransversely polarized quarks in
transversely polarized proton
•The difference between transversity and helicity distributions is measure of relativistic effects!
positivity conditions
Large Nc
P. SchweitzerF. Yuan
H. Avakian, Hampton, May 21 10
Hard Scattering Processes: Kinematics Coverage
Study of high x domain requires high luminosity, low x higher energies
27 G
eV
com
pass
herm
es JLab (upgraded)
JLab@6GeV
Q2
EIC
collider experiments H1, ZEUS (EIC)10-4<xB<0.02 (0.3): gluons (and quarks) in the proton
fixed target experiments COMPASS, HERMES 0.006/0.02<xB<0.3 : gluons/valence and sea quarks JLab/JLab@12GeV 0.1<xB<0.7 : valence quarks
HERA
H. Avakian, Hampton, May 21 11
EIC: Kinematics Coverage
Major part of current particles at large angles in Lab frame (PID at large angles crucial).
e p5 GeV 50 GeV
e’+X all
xF>0
z>0.3
EIC-MC (PYTHIA based)
xF>0 (CFR)
xF<0 ( TFR)
EIC-MC 100 days,L=1033cm-2s-1
H. Avakian, Hampton, May 21 12
Boer-Mulders Asymmetry with CLAS12 & EIC
CLAS12 and ELIC studies of transition from non-perturbative to perturbative regime will provide complementary info on spin-orbit correlations and test unified theory (Ji et al)
Nonperturbative TMDPerturbative region
Transversely polarized quarks in the unpolarized nucleon-
CLAS12
EIC
e p5-GeV 50 GeV
sin(C) =cos(2h)
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Sivers SSA
•Transverse asymmetries measured at HERMES and COMPASS•Effects are large at large x
proton
deuteron
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Sivers from HERMES
Need precision measurements of PT-dependences on proton and deuteron
Disagreement in shape and magnitude of PT-dependences
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Sivers effect: pion electroproduction
•EIC measurements at small x will pin down sea contributions to Sivers function
S. Arnold et al arXiv:0805.2137
M. Anselmino et al arXiv:0805.2677
GRV98, Kretzer FF (4par)
GRV98, DSS FF (8par)
H. Avakian, Hampton, May 21 16
Sivers effect: Kaon electroproduction
•At small x of EIC Kaon relative rates higher, making it ideal place to study the Sivers asymmetry in Kaon production (in particular K-). •Combination with CLAS12 data will provide almost complete x-range.
EIC
CLAS12
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Sivers effect: sea contributions
•Negative Kaons most sensitive to sea contributions. •Biggest uncertainty in experimental measurements (K- suppressed at large x).
GRV98, DSS FF
S. Arnold et al arXiv:0805.2137
M. Anselmino et al arXiv:0805.2677
GRV98, Kretzer FF
H. Avakian, Hampton, May 21 18
Pretzelosity @ EIC
•EIC measurement combined with CLAS12 will provide a complete kinematic range for pretzelosity measurements
5x50 eXpositivity bound
-
+
H. Avakian, Hampton, May 21 19
Summary•Correlations of spin and transverse momentum of partons are crucial in understanding of the nucleon structure in terms of partonic degrees of freedom of QCD.
Welcome to the exciting world of 3D parton distributions!!!
EIC: Measurements related to the spin, spin orbit correlations and orbital angular momentum of the quarks combined with JLab12 HERMES,COMPASS, RHIC,BELLE,J-PARC,GSI data will help construct a more complete picture about the spin structure of the nucleon beyond the collinear approximation.
H. Avakian, Hampton, May 21 20
Support slides….
H. Avakian, Hampton, May 21 21
Hard Scattering Processes: Kinematics Coverage
Study of high x domain requires high luminosity, low x higher energies
e p5 GeV 50 GeV
H. Avakian, Hampton, May 21 22
TMDs: QCD based predictions
Large-Nc limit (Pobilitsa)
Brodsky & Yuan (2006) Burkardt (2007)
Large-x limit
Do not change sign (isoscalar)
All others change sign u→d (isovector)
H. Avakian, Hampton, May 21 23
Pretzelosity @ EIC
•EIC measurement combined with CLAS12 will provide a complete kinematic range for pretzelosity measurements
5x50 e+Xpositivity bound
H. Avakian, Hampton, May 21 24
Sivers effect on0: extracting the Sivers function
Sivers asymmetry measurements on deuteron and proton target allow model independent extraction of Sivers function for u and d quarks at large x
or AUT for proton doesn’t depend on fragmentation functions
this experiment
up
down
ed→e’0Xep→e’0X
H. Avakian, Hampton, May 21 25
Collins SSA at CLAS @5.7GeV
CLAS with a transversely polarized target will allow simultaneous measurement of SIDIS asymmetries in current and target fragmentation regions and exclusive asymmetries (background)
•L/R SSA generated in fragmentation•Hadrons from struck quark have opposite sign SSA
sin(C)=sin(hS)
L=1
u dd du
Anselmino et al
H. Avakian, Hampton, May 21 26
Sivers effect: PT-dependence
Model calculationsYuan & Vogelsang,Schweizer & Efremov
PT-dependence at large PT crucial (not accessible at Hall-A/C).
H. Avakian, Hampton, May 21 27
Acceptance corrections for AUT
Esimated acceptance corrections for CLAS using HERMES analysis chain (GMCtrans)
H. Avakian, Hampton, May 21 28
Sivers Effect
-Correlation between the quark transverse momentum and transverse spin of the proton + FSI
The shift ~ 0.3 fm related to anomalous magnetic moment of proton (Burkardt 2000)
Unpolarized quarks: Probability to find a quark with longitudinal momentum x and transverse momentum kT
Collins (2002)
Calculation of moments of f1T┴requires knowledge of kT-dependence in a wide range
Meissner, Metz & Goeke (2007)
H. Avakian, Hampton, May 21 29
H. Avakian, Hampton, May 21 30
First calculations of “pretzelosity”
F.Yuan, Bag model P.Schweitzer, diquark model
H. Avakian, Hampton, May 21 32
CLAS12: Kinematical coverage
Large Q2 accessible with CLAS12 are important for separation of HT contributions
Q2>1GeV2
W2>4 GeV2(10)y<0.85MX>2GeV
SIDIS kinematics
eX
x=0.3 → Q2=~2 GeV2 (CLAS), ~5 GeV2 (HERMES) ~15 GeV2 (COMPASS)
H. Avakian, Hampton, May 21 33
SIDIS transverse SSA