Harut Avakian*

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


•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


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!!!


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


Miller/”pretzelosity”

Spin densities from Lattice (QCDSF and UKQCD Collaborations)

Proton spin quark spin

GPD-E GPD-ET


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)


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


Unpolarized quarks

TMDs and spin-orbit correlations

Pretzelosity

Transversely polarized quarks

QCD large-x limit, Brodsky & Yuan (2006) (perturbative limit)

-


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


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


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


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)


Sivers SSA

•Transverse asymmetries measured at HERMES and COMPASS•Effects are large at large x

proton

deuteron


Sivers from HERMES

Need precision measurements of PT-dependences on proton and deuteron

Disagreement in shape and magnitude of PT-dependences


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)


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


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


Pretzelosity @ EIC

•EIC measurement combined with CLAS12 will provide a complete kinematic range for pretzelosity measurements

5x50 eXpositivity bound

-

+


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.


Support slides….


Hard Scattering Processes: Kinematics Coverage

Study of high x domain requires high luminosity, low x higher energies

e p5 GeV 50 GeV


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)


Pretzelosity @ EIC

•EIC measurement combined with CLAS12 will provide a complete kinematic range for pretzelosity measurements

5x50 e+Xpositivity bound


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


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


Sivers effect: PT-dependence

Model calculationsYuan & Vogelsang,Schweizer & Efremov

PT-dependence at large PT crucial (not accessible at Hall-A/C).


Acceptance corrections for AUT

Esimated acceptance corrections for CLAS using HERMES analysis chain (GMCtrans)


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)



First calculations of “pretzelosity”

F.Yuan, Bag model P.Schweitzer, diquark model


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)


SIDIS transverse SSA

Documents

Harut Avakian*