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H. Avakian, Argonne, April 81
Harut Avakian (JLab)Harut Avakian (JLab)
Modification of transverse momentum distributions in nucleiModification of transverse momentum distributions in nuclei
Workshop on Nuclear Chromo-Dynamic Studies with a Future Electron Ion Collider
Argonne National Laboratory, April 7 - 9, 2010
•TMDs and spin-orbit correlations•kT-distributions•Higher twists in SIDIS
•MC-simulations•Projections for observables•Conclusions
H. Avakian, Argonne, April 82
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
d2 r T
PDFs f1u(x), .. h1
u(x)
quark polarization
H. Avakian, Argonne, April 83
kT and FSI
l l’
x,kT
proton
spectator system
•The difference is coming from final state interactions (different remnant)
Tang,Wang & Zhou
Phys.Rev.D77:125010,2008
lT
l l’
x,k’T l’T
spectator systemnucleus
total transverse momentum broadening squaredBHS 2002
Collins 2002Ji,Yuan 2002
soft gluon exchanges included in the distribution function (gauge link)
H. Avakian, Argonne, April 844
SIDIS: partonic cross sections
kT
PT = p┴ +z kT
p┴
Ji,Ma,Yuan Phys.Rev.D71:034005,2005
Is the info on x-kT correlations accessible in kT integrated observables?
H. Avakian, Argonne, April 855
Quark distributions at large kQuark distributions at large kTT: models: models
Effect of the orbital motion on
the q- may be most significant
JMR model
q
DqMR , R=s,a
u/u
(dipole formfactor), J.Ellis, D-S.Hwang, A.Kotzinian
Higher probability to find a quark anti-aligned with proton spin at large kT
(H.A.,S.Brodsky, A.Deur,F.Yuan 2007)
H. Avakian, Argonne, April 866
Quark distributions at large kQuark distributions at large kTT: lattice: lattice
Higher probability to find a d-quark at large kT
Higher probability to find a quark anti-aligned with proton spin at large kT
B.Musch arXiv:0907.2381
Understanding the transverse structure is crucial!
H. Avakian, Argonne, April 87
A1
A1 PT-dependence
CLAS data suggests that width of g1 is less than the width of f1
AnselminoCollins
Lattice
New CLAS data would allow multidimensional binning to study kT-dependence for fixed x
PT
PT
arXiv:1003.4549
H. Avakian, Argonne, April 88
H. Avakian, Argonne, April 899
Quark distributions at large kQuark distributions at large kTT
Higher probability to find a hadron at large PT in nuclei
kT-distributions may be wider in nuclei?
PT = p┴ +z kT
bigger effect at large z
H. Avakian, Argonne, April 81010
Jet limit: Higher Twist azimuthal asymmetriesJet limit: Higher Twist azimuthal asymmetries
No leading twist, provide access to quark-gluon correlations
T-odd
H.A.,A.Efremov,P.Schweitzer,F.Yuan arXiv:1001.5467
“interaction dependent”
Twist-2
Twist-3
H. Avakian, Argonne, April 811
Modification of Cahn effect
•Large cosn moments observed at COMPASS
Bag model
arXiv:1001.3146 Gao, Liang & Wang
•Nuclear modification of Cahn may provide info on kT broadening and proton TMDs
H. Avakian, Argonne, April 81212
s
x
h
PT
Fragmenting quark polarization
C
C
y
x
S h
PTS = +h
HT function related to force on the quark. M.Burkardt (2008)
Collins mechanism for SSACollins mechanism for SSAfragmentation of transversely polarized quarks into unpolarized hadrons
x
PT
h
S=y
x
PT
h
S=y
H. Avakian, Argonne, April 813
Electroproduction kinematics: JLab12→EIC
JLab 0.1<xB<0.7 JLab@12GeV
Study of high x domain requires high luminosity, low x higher energies
EIC
JLab12
Q2
EIC
collider experiments
H1, ZEUS 10-4<xB<0.02
EIC 10-4<xB<0.3gluons (and quarks)
fixed target experiments
COMPASS 0.006<xB<0.3
HERMES 0.02<xB<0.3
gluons/valence and sea quarks
valence quarks
EIC (4x60):
H. Avakian, Argonne, April 814
LEPTO/PEPSI: quark distributions
Need to model TMDs in LUND MC
•Implemented in PEPSI modification to LEPTO done by A. Kotzinian •Add different widths for q+ and q-
z>0.1
z>0.3
MC with Cahn
Event Generator with polarized electron and nucleon: PEPSI,….
Acceptance checkDesign parameters
Smearing/resolution routinesUse GEANT as input
Physics analysis using the “reconstructed” event sample
H. Avakian, Argonne, April 815
(p) = 0.05 + 0.06*p [GeV] %
EIC 4x60 (Lumi 1033,cm-2sec-1 , ~1 hour)
K*s can be studied with EIC
<x>=0.1, <Q2>=4
H. Avakian, Argonne, April 816
Nonperturbative TMD Perturbative region
sinLU~FLU~ 1/Q (Twist-3)
In the perturbative limit 1/PT behavior expected
Study for SSA transition from non-perturbative to perturbative regime.
EIC will significantly increase the PT range.
PT-dependence of beam SSA
4x60 100 days, L=1033cm-2s-1
H. Avakian, Argonne, April 817
Boer-Mulders Asymmetry with CLAS12 & EIC
CLAS12 and EIC 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)
Perturbative limit calculations available for :
J.Zhou, F.Yuan, Z Liang: arXiv:0909.2238
H. Avakian, Argonne, April 818
Summary
Studies of spin and azimuthal asymmetries in semi-inclusive processes at EIC :
•Measure nuclear modification of transverse momentum distributions and spin-orbit correlations of partons at small x, in a wide range of Q•Study quark-gluon correlations (HT) in nucleon and nucleus•Provide information on correlations of longitudinal and transverse degrees of freedom
EIC: Studies of nuclear modifications of spin orbit and quark-gluon correlations combined with JLab12 data will help construct a more complete picture about the structure of the nucleon and nuclei.
H. Avakian, Argonne, April 819
Support slides….
H. Avakian, Argonne, April 820
High energy quarks at small angles
Struck quark kinematics (EIC 4x60)
q
H. Avakian, Argonne, April 821
SIDIS (*p->X) x-section at leading twist
•Measure Boer-Mulders distribution functions and probe the polarized fragmentation function•Measurements from different experiments consistent
TMD PDFs
H. Avakian, Argonne, April 822
kT and FSI
l l’
x,kT
proton
spectator system
•The difference is coming from final state interactions (different remnant)
Tang,Wang & Zhou
Phys.Rev.D77:125010,2008
lT
l l’
x,k’T l’T
spectator systemnucleus
total transverse momentum broadening squaredBHS 2002
Collins 2002Ji,Yuan 2002
H. Avakian, Argonne, April 82323
Transverse force on the polarized quarks
Interpreting HT (quark-gluon-quark correlations) as force on the quarks (Burkardt hep-ph:0810.3589)
Quark polarized in the x-direction with kT in the y-direction
Force on the active quark right after scattering (t=0)
H. Avakian, Argonne, April 824
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
xF>0 (CFR)
xF<0 ( TFR)
EIC-MC
H. Avakian, Argonne, April 825
sinLU(UL) ~FLU(UL)~ 1/Q (Twist-3)
1/Q behavior expected (fixed x bin)
Study for Q2 dependence of beam SSA allows to check the higher twist nature and access quark-gluon correlations.
Q2-dependence of beam SSA
H. Avakian, Argonne, April 826
EIC medium energy
• Electron energy: 3-11 GeV
• Proton energy: 20-60 GeV
– More symmetric kinematics provides better resolution and particle id
• Luminosity: ~ 1034 cm-2 s-1
– in range around s ~ 1000 GeV2
• Polarized electrons and light ions
– longitudinal and transverse
• Limited R&D needs
• 3 interaction regions (detectors)
• Potential upgrade with high-energy ring
Main FeaturesMain Features• Electron energy: 4-20 GeV
• Proton energy: 50-250 GeV
– More symmetric kinematics provides better resolution and particle id
• Luminosity: ~ 1033 cm-2 s-1
– in range around s ~ 1000-10000 GeV2
• Polarized electrons and light ions
– longitudinal and transverse
• Limited R&D needs
• ? interaction regions (detectors)
• 90% of hardware can be reused
EIC@JLabEIC@RHIC
Slides are for a “generic” US version of an EIC (5x50 or 4x60):• polarized beams (longitudinal and transverse, > 70%)• luminosities of at least 1033
H. Avakian, Argonne, April 827
JETSET:Single particle production in hard scattering
Lund-MC should be modified to allow checks of sensitivity of measurements to different effects related to the transverse structure
- Before- After quarkTarget remnant
LUND Fragmentation Functions
H. Avakian, Argonne, April 82828
Cross section is a function of scale variables x,y,z
z
SIDIS kinematical plane and observablesSIDIS kinematical plane and observables
U unpolarized
L long.polarized
T trans.polarizedBeam polarizationTarget polarization
sin2moment of the cross section for unpolarized beam and long. polarized target
H. Avakian, Argonne, April 829
Identification using the missing mass may be possible
detected
CLAS12
EIC4x60
FAST-MC
Kaon production in SIDIS
(p) = 0.05 + 0.06*p [GeV] %
H. Avakian, Argonne, April 830
JLab, Nov 2530
Azimuthal moments with unpolarized target
quark polarization
H. Avakian, Argonne, April 831
JLab, Nov 2531
Azimuthal moments with unpolarized target
quark polarization
H. Avakian, Argonne, April 832
JLab, Nov 2532
SSA with unpolarized target
quark polarization
H. Avakian, Argonne, April 833
JLab, Nov 2533
SSA with unpolarized target
quark polarization
H. Avakian, Argonne, April 834
SSA with long. polarized target
quark polarization
H. Avakian, Argonne, April 835
SSA with long. polarized target
quark polarization
H. Avakian, Argonne, April 836
SSA with unpolarized target
quark polarization
H. Avakian, Argonne, April 837
SSA with unpolarized target
quark polarization
H. Avakian, Argonne, April 83838
Single hadron production in hard scattering
Measurements in different kinematical regions provide complementary information on the complex nucleon structure.
xF - momentum
in the CM frame
xF>0 (current fragmentation)
xF<0 (target fragmentation)
h
h
Target fragmentation Current fragmentation
Fracture Functions
xF
M
0-1 1
h
h
PDF GPD
kT-dependent PDFs Generalized PDFs
hFF
DA DA
exclusivesemi-inclusive semi-exclusive
H. Avakian, Argonne, April 839
production in the target fragmentation
xF - momentum
in the CM frame
Wide kinematical coverage of EIC would allow studies of hadronization in the target fragmentation region (fracture functions)
polarization in TFR provides information on contribution of strange sea to proton spin
Study polarized diquark fracture functions sensitive to the correlations between struck quark transverse momentum and the diquark spin.
x F(
)EIC CLAS12
(ud)-diquark is a spin and isospin singlet s-quark carries whole spin of uds
H. Avakian, Argonne, April 840
Collins effect
Simple string fragmentation for pions (Artru model)
leading pion out of page
production may produce an opposite
sign AUT
Leading opposite to leading (into page)
hep-ph/9606390 Fraction of in eX
% left from eX asm
20%
40%
~75%
~50%
Fraction of direct kaons may be significantly higher than the fraction of direct pions.
LUND-MC
L
z
L
z
H. Avakian, Argonne, April 841
K/K* and separations
Detection of K+ crucial for separation of different final states (,K*)
H. Avakian, Argonne, April 842
Sivers effect in the target fragmentation
A.Kotzinian
High statistics of CLAS12 will allow studies of kinematic dependences of the Sivers effect in target fragmentation region
H. Avakian, Argonne, April 843
27 G
eV
com
pass
herm
es JLab (upgraded)
JLab@6GeV
Q2
EIC
HERA
ENCENC
Hard Scattering Processes: Kinematics Coverage
Study of high x domain requires high luminosity, low x higher energies
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
JLab
12
EIC(4
x60)
ENC(3x1
5)
Q2
H. Avakian, Argonne, April 844
Hard Scattering Processes: Kinematics Coverage
Study of high x domain requires high luminosity, low x higher energies
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
27 G
eV
com
pass
herm
es JLab (upgraded)
JLab@6GeV
Q2
EIC
HERA
ENCENC
JLab12
EIC
ENC
Q2
H. Avakian, Argonne, April 845
hep:arXiv-09092238
H. Avakian, Argonne, April 846
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)
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