Transcript The Transverse Momentum Distribution Program Status and Prospects Harut Avakian (JLab) June 9, 2010 H.

The Transverse Momentum Distribution Program
Status and Prospects
Harut Avakian (JLab)
June 9, 2010
H. Avakian, Users Meeting, 2010
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Outline
• Introduction
–3D parton distributions in hard processes
• Final State Interactions and Spin Azimuthal
Asymmetries
• Higher Twist effects
• TMD measurements
• Future studies
• Summary
H. Avakian, Users Meeting, 2010
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Parton Distribution Functions
• The Proton:
• Distribution of quarks, antiquarks and gluons (PDFs)
– QCD evolution tells us how distribution evolves, but
not original distributions
q(x) - Probability to find a quark with a
fraction x of proton momentum P
q(x)
Quarks interact
Quarks have spin, which can be aligned
or anti aligned with proton spin
BBS-1995, Power counting at large x
Quarks have transverse momentum, kT
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Some questions to address
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What is the shape of kT-distributions?
Can kT-distributions be flavor dependent?
Are kT-distributions the same for different spin orientations?
How spin-orbit correlations change the momentum
distributions?
How gluons and sea are distributed in kT
How nuclear medium changes kT-distributions?
What is the fraction of kT-generated in FSI?
How big are quark-gluon correlations?
How spin-orbit correlations are related to the
longitudinal structure and nuclear effects?
H. Avakian, Users Meeting, 2010
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Structure of the Nucleon
Wpu(k,rT) “Mother” Wigner distributions
d2 k T
In nuclear env. TMDs
and GPDs modify
d2 r T
rT
TMD PDFs
q(x,kT), Dq(x,kT)…
GPD/IPDs
H(x,rT), H~(x,rT)…
d2 k T
d2 r T
PDFs q(x), Dq(x)…
dx
Form Factors
x-kT and x-rT
correlations define the
final x-distributions
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Transverse Momentum Dependent PDFs
Off diagonal PDFs related to interference
between light-cone wave functions with L=0,1,2.
Gauge invariant definition (Belitsky,Ji,Yuan 2003)
Universality of kT-dependent PDFs (Collins,Metz 2003)
Factorization for small kT. (Ji,Ma,Yuan 2005)
Observation of Sivers and Collins Asymmetries at HERMES (2005)
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Tang,Wang & Zhou
Phys.Rev.D77:125010,2008
kT and FSI
l’
l
l’
l
total transverse momentum
broadening squared
BHS 2002
Collins 2002
Ji,Yuan 2002
lT “dynamic”
x,kT
x,k’T
l’T
“static”
proton
spectator
system
soft gluon exchanges included in the
distribution function (gauge link)
nucleus
spectator
system
•The difference is coming from final
state interactions (different remnant)
Understanding of partonic final state interactions is crucial
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SIDIS: partonic cross sections
p┴
PT = p┴ +z kT
Ji,Ma,Yuan Phys.Rev.D71:034005,2005
Is the info on x-kT correlations accessible in kT integrated observables?
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Polarized DIS
Polarized
deep
inelastic
scattering
Poke a quark with a high energy electron
Parallel electron
& quark spins
Anti-parallel electron
& quark spins
The momentum transferred,
Q2 defines the scale
Most u-quarks are aligned with proton spin (Du>0)
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Quark distributions at large kT: models
q
JMR model
Orbital motion affects the
x-dependence of PDFs (mostly
Dq
q- )
(H.A.,S.Brodsky, A.Deur,F.Yuan 2007)
kT
Higher probability to find
a quark anti-aligned with
proton spin at large kT
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Quark distributions at large kT: lattice
B.Musch arXiv:0907.2381
Higher probability to find a quark antialigned with proton spin at large kT
Higher probability to find a
d-quark at large kT
H. Mkrtchyan et al. Phys.Lett.B665:20-25,2008.
Understanding the transverse
structure is crucial!
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A1
A1 PT-dependence
arXiv:1003.4549
Lattice
Anselmino
Collins
PT
PT
CLAS data suggests that width of g1 is less than the width of f1
New CLAS data would allow multidimensional binning to study kT-dependence for fixed x
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Sivers mechanisms for SSA
FS
fS
PT
-
Correlation between quark transverse
momentum and the proton spin
fkT
Proton
polarization
x
T-odd f1T┴, requires final state
interactions + interference between
different helicity states
(Brodsky et al., Collins, Ji et al. 2002)
SIDIS
P
M.Burkardt (2000)
Drell-Yan
•Correlation between the quark
transverse momentum and transverse
spin of the proton
•L/R SSA generated in distribution
•All hadrons from struck quark have
the same sign SSA
•Opposite effect in target fragmentation
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Jet limit: Higher Twist azimuthal asymmetries
Twist-2
Twist-3
T-odd
“interaction dependent”
No leading twist,
provide access to quarkgluon correlations
H.A.,A.Efremov,P.Schweitzer,F.Yuan
Phys.Rev.D81:074035,2010
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Collins mechanism for SSA
FC
fs
PT
fragmentation of transversely polarized
quarks into unpolarized hadrons
fh
FC
Fragmenting
quark polarization
x
fS = p/2+fh
y
PT
fS
fS = -fh
fh
fS
x
PT
PT
fh
fh
fh
x
y
fS=p/2
x
y
fS=p
x
HT function related to force on
the quark. M.Burkardt (2008)
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Kotzinian-Mulders Asymmetries
HERMES
CLAS (5 days)
Worm gear TMDs are unique (no analog in GPDs)
H. Avakian, Users Meeting, 2010
B.Musch arXiv:0907.2381
B.Pasquini et al, arXiv:0910.1677
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Sivers Asymmetries with transversely polarized target
HERMES
FSI in distribution are significant
E06-010
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Collins Asymmetries with transversely polarized target
HERMES
FSI in fragmentation are significant
PRELIMINARY
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Measurement of Sivers function and GPD-E
(DVCS)
CLAS E08-015
(SIDIS)
GPD-E=0
DVCS Transverse asymmetry
(function of momentum transfer to
proton) is large and has strong
sensitivity to GPD-E
CLAS will provide a measurements of
Sivers asymmetry at large x, where the
effect is large and models unconstrained
by previous measurements.
Meissner, Metz & Goeke (2007)
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Future Studies of 3D PDFs
JPARC
FNAL
BNL
SIDIS/DER
Drell-Yan
H. Avakian, Users Meeting, 2010
e–e+ to pions
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SIDIS @ JLab12
LTCC
PCAL
Wide detector and physics acceptance
(current/target fragmentation)
Lumi = 1035cm-2s-1
High beam polarization 80%
High target polarization 85%
NH3 (30 days) ND3 (50 days)
HTCC
FTOF
EC
Solenoid Spectrometer for SIDIS@Hall-A
CLAS12
Replace LTCC with a RICH detector to
identify Kaons approved by JLab PAC34
High luminosity study of current
fragmentation region
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EIC medium energy
EIC@JLab
EIC@RHIC
•
Electron energy:
•
Proton energy:
–
•
50-250 GeV
Electron energy:
•
Proton energy:
–
•
•
20-60 GeV
More symmetric kinematics provides better
resolution and particle id
in range around s ~ 1000 GeV2
Polarized electrons and light ions
–
longitudinal and transverse
3-11 GeV
Luminosity: ~ 1034 cm-2 s-1
–
in range around s ~ 1000-10000 GeV2
Polarized electrons and light ions
–
•
More symmetric kinematics provides better
resolution and particle id
Luminosity: ~ 1033 cm-2 s-1
–
•
Main Features
4-20 GeV
longitudinal and transverse
•
Limited R&D needs
•
Limited R&D needs
•
? interaction regions (detectors)
•
3 interaction regions (detectors)
•
90% of hardware can be reused
•
Potential upgrade with high-energy ring
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Electroproduction kinematics: JLab12→EIC
Q2
collider experiments
EIC (4x60):
H1, ZEUS 10-4<xB<0.02
gluons (and quarks)
EIC 10-4<xB<0.3
EIC
ENC (3x15):
fixed target experiments
COMPASS 0.006<xB<0.3
EIC
HERMES 0.02<xB<0.3
ENC
gluons/valence and sea quarks
JLab12
JLab
 0.1<xB<0.7
JLab@12GeV
valence quarks
Study of high x domain requires high
luminosity, low x higher energies
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A1 PT-dependence in SIDIS
M.Anselmino et al
hep-ph/0608048
m02=0.25GeV2
mD2=0.2GeV2
Perturbative limit calculations
available for
:
J.Zhou, F.Yuan, Z Liang: arXiv:0909.2238
•ALL (p) sensitive to difference in kT distributions for f1 and g1
•Wide range in PT allows studies of transition from TMD to perturbative approach
H. Avakian, Users Meeting, 2010
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Boer-Mulders Asymmetry with CLAS12 & EIC
5-GeV
-
e
p
50 GeV
Transversely polarized quarks in
the unpolarized nucleon
sin(fC) =cos(2fh)
CLAS12
EIC
Perturbative limit calculations
available for
Nonperturbative TMD
Perturbative region
:
J.Zhou, F.Yuan, Z Liang:
arXiv:0909.2238
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)
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Q2-dependence of beam SSA
ssinfLU(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.
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Kaon Sivers effect: CLAS12→EIC
EIC
CLAS12
•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.
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Pretzelosity: from CLAS12→ EIC
epX
CLAS12
5x50
positivity bound
p+
phelicity-transversity=pretzelosity
In models (bag, diquark)
pretzelosity defines the OAM
•EIC measurement combined with CLAS12 will provide a complete
kinematic range for pretzelosity measurements
H. Avakian, Users Meeting, 2010
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Modification of TMDs in nuclei
Bag model
Gao, Liang & Wang
arXiv:1001.3146
•Large cosnf
•Nuclear
modification
moments
ofobserved
Cahn mayatprovide
COMPASS
info on kT broadening and proton TMDs
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Summary
Studies of spin and azimuthal asymmetries in semi-inclusive
processes in a wide range of x, Q2 and PT:
•Measure transverse momentum distributions of partons
•Provide detailed info on partonic spin-orbit correlations
•Study quark-gluon correlations (HT)
•Study correlations between transverse and longitudinal
degrees of freedom
Masurements related to the spin, spin orbit and quark-gluon
correlations at JLab12 (valence region) and EIC (sea & gluons)
combined with HERMES,COMPASS, RHIC,BELLE,BABAR,Fermilab,JPARC,FAIR data will help construct a complete picture about
the structure of the nucleon and nuclei.
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Support slides….
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PT-dependences in H and D (Hall-C)
H. Mkrtchyan et al. Phys.Lett.B665:20-25,2008.
Data is consistent
with wider d vs u
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Single hadron production in hard scattering
xF>0 (current fragmentation)
h
xF<0 (target fragmentation)
xF - momentum
in the CM frame
Target fragmentation
Current fragmentation
semi-inclusive
semi-exclusive
FF h
-1
Fracture Functions
h
h
DA
DA
h
M
exclusive
PDF
0
kT-dependent PDFs
PDF
GPD
1
xF
Generalized PDFs
Measurements in different kinematical regions for nucleon and nucleus
provide complementary information on the complex nucleon structure.
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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, Users Meeting, 2010
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L production in the target fragmentation
L polarization in TFR provides information on
contribution of strange sea to proton spin
(ud)-diquark is a spin and
isospin singlet s-quark carries
whole spin of L L  uds
xF - momentum
xF(L)
in the CM frame
Sivers-2009
Study polarized diquark fracture
functions sensitive to the correlations
between struck quark transverse
momentum and the diquark spin.
EIC
CLAS12
Combination of CLAS12 and EIC would allow studies of hadronization in
the target fragmentation region (fracture functions) in a wide range of x
H. Avakian, Users Meeting, 2010
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Transverse momentum distributions of hadrons
Gauss
CLAS slightly lower, but
may have bigger
Anselmino et al from EMC
data →
= 0.25
Wider
at smaller beam energies?
H. Avakian, Users Meeting, 2010
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SIDIS (g*p->pX) x-section at leading twist
TMD PDFs
•Measure Boer-Mulders distribution functions and probe the polarized fragmentation function
•Measurements from different experiments consistent
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Collins effect
Simple string fragmentation (Artru model)
p+
z
Leading pion out of
page (
- direction )
L
L
p-
kicked in the opposite
to the leading pion(into
the page)
Sub-leading pion opposite
to leading (double kick
into the page)
Collins analyzing power may be indeed
much bigger for unfavored fragmentation
H. Avakian, Users Meeting, 2010
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Collins effect
p+
Simple string fragmentation
for pions (Artru model)
z
leading pion out of
page
L
r production may
produce an opposite
sign AUT
Fraction of r in
epX
% left from epX
asm
20%
40%
~75%
~50%
L
r
z
Leading r opposite to
leading p(into page)
hep-ph/9606390
Fraction of direct kaons may
be significantly higher than
the fraction of direct pions.
H. Avakian, Users Meeting, 2010
LUND-MC
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kT-dependent PDFs and FFs: “new testament”
Baccetta, Diehl, Goeke, Metz, Mulders, Schlegel EPJ-2007
No analog in twist-2
appear in sinf moment
of ALU and AUL
quark-gluon-quark correlations
responsible for azimuthal
moments in the cross section
H. Avakian, Users Meeting, 2010
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EIC 4x60 (Lumi 1033,cm-2sec-1 , ~1 hour)
<x>=0.1, <Q2>=4
s(p) = 0.05 + 0.06*p [GeV] %
K*s can be studied with CLAS12/EIC
H. Avakian, Users Meeting, 2010
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Quark distributions at small bT: models
S.Liuti (in progress)
Strong correlation between bT and x
Replacing H&H~ with H+/H- may
change GPD parameterizations
H. Avakian, Users Meeting, 2010
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Quark distributions at large kT
bigger effect at large z
PT = p┴ +z kT
Higher probability to find a
hadron at large PT in nuclei
kT-distributions may be
wider in nuclei?
Understanding of modification of kT widths in nuclei is important also for nucleon TMDs
H. Avakian, Users Meeting, 2010
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PT-dependence of beam SSA
ssinfLU~FLU~ 1/Q (Twist-3)
In the
perturbative limit
1/PT behavior
expected
4x60 100 days,
L=1033cm-2s-1
Nonperturbative TMD
Perturbative region
Study for SSA transition from non-perturbative to perturbative regime.
EIC will significantly increase the PT range.
H. Avakian, Users Meeting, 2010
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Tang,Wang & Zhou
Phys.Rev.D77:125010,2008
kT and FSI
l’
l
BHS 2002
Collins 2002
Ji,Yuan 2002
x,kT
proton
l’
l
total transverse momentum
broadening squared
x,k’T
lT
spectator
system
nucleus
l’T
spectator
system
soft gluon exchanges included in
the distribution function (gauge link)
~4 n, with ~4-6 MeV
guts of nucleus
•The difference is coming from final state interactions (different remnant)
•Studies of DIS and SIDIS with nuclear targets provide info on kT
H. Avakian, Users Meeting, 2010
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Power counting at large-x
q+»
Spin-0
• Eight propagators (1-x)8,
(1-x)-4 from the
scattering, (1-x)-1 from
the phase space integral
– (1-x)3
• Spectator two quarks
with spin-1 configuration
will be suppressed by (1x)2 relative to spin-0
q-»
Spin-1
– q-» (1-x)2q+
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LEPTO/PEPSI: quark distributions
Event Generator with polarized electron
and nucleon: PEPSI/GMC_Trans
MC with Cahn
Acceptance check
Design parameters
Smearing/resolution routines
Use GEANT as input
z>0.1
Physics analysis using the
“reconstructed” event sample
z>0.3
• Implemented in PEPSI Cahn effect
• Implemented radiative effects (radgen)
• Add different widths for q+ and q• Implement GMC_Trans (HERMES)
H.Avakian/A.Kotzinian/D.Hasch
Need to model TMDs in CLAS12 and EIC MC
H. Avakian, Users Meeting, 2010
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Quark helicity distributions: simple model
Quarks have spin, which can be aligned or anti aligned with proton spin
•Leading-order diagram contributing to parton distribution at large x
On-shell quarks with
longitudinal momentum
1-x
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Transverse force on the polarized quarks
Quark polarized in the x-direction with
kT in the y-direction
Force on the active quark right after scattering (t=0)
Interpreting HT (quark-gluon-quark correlations) as force on
the quarks (Burkardt hep-ph:0810.3589)
H. Avakian, Users Meeting, 2010
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Collins effect
p+
Simple string fragmentation
for pions (Artru model)
z
leading pion out of
page
L
r production may
produce an opposite
sign AUT
Fraction of r in
epX
% left from epX
asm
20%
40%
~75%
~50%
L
r
z
Leading r opposite to
leading p(into page)
hep-ph/9606390
Fraction of direct kaons may
be significantly higher than
the fraction of direct pions.
H. Avakian, Users Meeting, 2010
LUND-MC
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K/K* and L/S separations
Detection of K+ crucial for separation of different final states (L,S,K*)
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TMDs: QCD based predictions
Large-x limit
Burkardt (2007)
Brodsky & Yuan (2006)
Large-Nc limit (Pobilitsa)
Do not change sign (isoscalar)
All others change sign
u→d (isovector)
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