wigner distributions and quark orbital angular momentum
DESCRIPTION
Wigner distributions and quark orbital angular momentum. Cédric Lorcé. and. May 14 2012, JLab, Newport News, VA, USA. Outline. Parton distribution zoo PDFs, FFs, GPDs, TMDs, GTMDs Partonic interpretation Proton spin puzzle Decompositions Relations with observables Model results - PowerPoint PPT PresentationTRANSCRIPT
Wigner distributions and quark orbital
angular momentum
Cédric Lorcé
and
May 14 2012, JLab, Newport News, VA, USA
Outline Parton distribution zoo
PDFs, FFs, GPDs, TMDs, GTMDs Partonic interpretation
Proton spin puzzle Decompositions Relations with observables
Model results Overlap representation Wigner distributions
Outline Parton distribution zoo
PDFs, FFs, GPDs, TMDs, GTMDs Partonic interpretation
Proton spin puzzle Decompositions Relations with observables
Model results Overlap representation Wigner distributions
Parton distribution zooCharges
Charges
Partonic interpretation (twist-2)
Vector
Tensor
Axial
0D Picture
Parton distribution zoo
Partonic interpretation (twist-2)
DIS
Parton Distribution Functions
Charges
PDFs
1D Picture
Parton distribution zoo
Partonic interpretation (twist-2)
ES
Form Factors
PDFs
Charges
FFs
2D Picture
Impact parameter
Transverse center of
momentum
DVCS
Parton distribution zoo
Partonic interpretation (twist-2)
Generalized PDFs
GPDs
Charges
PDFs FFs
3D Picture
[Soper (1977)][Burkardt (2000,2003)]
[Diehl, Hägler (2005)]
Parton distribution zoo
Partonic interpretation (twist-2)
SIDIS
Transverse-Momentum dependent PDFs
No direct connection
TMDs
Position space
Momentum space
Mean momentu
m
Displacement
Mean position
Momentum
transfer
gauge Charges
PDFs FFs
GPDs
3D Picture
Parton distribution zoo
Partonic interpretation (twist-2)
Generalized TMDs
GTMDs
TMDs
[Wigner (1932)][Belitsky , Ji, Yuan (2004)]
[C.L., Pasquini (2011)]
Quasi-probabilistic interpretation
??????
Charges
PDFs
GPDs
FFs
5D Picture
Parton distribution zooComplete set
GTMDs
TMDs[C.L., Pasquini, Vanderhaeghen
(2011)]
Charges
PDFs
GPDs
FFsTMCs
TMFFs
TMFFs
TMFFs
TMCs
TMCs
4D Picture 2D Picture
Partonic interpretation (twist-2)
Twist-2 structureGPDs TMDs
Nu
cle
on
pola
riza
tion
Quark polarization Quark polarization
Nu
cle
on
pola
riza
tion
Monopole Dipole Quadrupole
Naive T-odd
-odd
Twist-2 structureGTMDs
Nu
cle
on
pola
riza
tion
Quark polarization
Monopole Dipole Quadrupole
Naive OAM
[Meißner, Metz, Schlegel (2009)]
Twist-3 structureGPDs TMDs
Nu
cle
on
pola
riza
tion
Quark polarization Quark polarization
Nu
cle
on
pola
riza
tion
Naive T-odd
-odd
Monopole Dipole Quadrupole
Outline Parton distribution zoo
PDFs, FFs, GPDs, TMDs, GTMDs Partonic interpretation
Proton spin puzzle Decompositions Relations with observables
Model results Overlap representation Wigner distributions
• Does not satisfy canonical relations• Incomplete decomposition
Proton spin puzzleJi Jaffe-Manohar
[Ji (1997)] [Jaffe, Manohar (1990)]
• Gauge-invariant decomposition• Accessible in DIS and DVCS
Kinetic Canonical
Pros:
Cons:
Pros:
Cons:
• Satisfies canonical relations• Complete decomposition
• Gauge-variant decomposition• Missing observables for the OAM
Improvements:
[Wakamatsu (2009,2010)]• Complete decomposition
Improvements:
[Chen et al. (2008)]
• Gauge-invariant extension
• OAM accessible via Wigner distributions [C.L., Pasquini (2011)]
[C.L., Pasquini, Xiong, Yuan(2011)]
[Hatta (2011)]
Quark spin and OAMGPDs TMDs GTMDs
Quark spin
Quark kinetic OAM
ALL
AUU+AU
T
[Penttinen et al. (2000)]
Pure twist-3!
[Ji (1997)]
AUL
ALL ALLQuark spin Quark spin
Quark canonical OAM
Quark canonical OAMATT
• Model-dependent• Not intrinsic!
[C.L., Pasquini (2011)][Hatta (2011)]
[C.L. et al. (2012)]
[Burkardt (2007)][Efremov et al.
(2008,2010)][She, Zhu, Ma (2009)][Avakian et al. (2010)][C.L., Pasquini (2011)]
AULTwist-2
Twist-3
OAM and origin dependenceRelative IntrinsicNaive
Transverse center of
momentumPhysical interpretation ?
Depends on proton
position
Equivalence
Intrinsic RelativeNaive
Momentum conservation
Outline Parton distribution zoo
PDFs, FFs, GPDs, TMDs, GTMDs Partonic interpretation
Proton spin puzzle Decompositions Relations with observables
Model results Overlap representation Wigner distributions
Momentum
Fock expansion of the proton state
Fock statesSimultaneous eigenstates
of
Light-front helicity
Overlap representation
Light-front wave functions
Proton state
Eigenstates of parton light-front helicity
Eigenstates of total OAM
Probability associated with the N, Fock state
Normalization
Overlap representation
gauge
Fock-state contributions
Overlap representation
[C.L., Pasquini (2011)]
[C.L. et al. (2012)]
GTMDs
TMDs
GPDsKinetic OAM
Naive canonical OAM
Canonical OAM
Model calculationsLight-front 3Q
models[C.L., Pasquini
(2011)]
Models are not QCD
Truncation of Fock space spoils Lorentz covariance
In model calculations, one would expect but
[Carbonell, Desplanques, Karmanov, Mathiot (1998)]
GTMDs
TMDs
GPDs
Model calculationsUnpold quark in unpold
nucleon [C.L., Pasquini (2011)]
favored
disfavored
Left-right symmetry No net quark OAM
Model calculationsUnpold quark in longitudinally pold
nucleon
Proton spin
u-quark OAM
d-quark OAM
[C.L., Pasquini (2011)]
Model calculations
Proton spin
u-quark OAM
d-quark OAM
[C.L. et al. (2012)]Unpold quark in longitudinally pold
nucleon
Quark spin
u-quark OAM
d-quark OAM
Model calculationsLongitudinally pold quark in unpold
nucleon [C.L., Pasquini (2011)]
Proton spin
u-quark spin
d-quark spin
Model calculationsLongitudinally pold quark in longitudinally pold
nucleon [C.L., Pasquini (2011)]
Emerging pictureLongitudinal
[C.L., Pasquini (2011)]
Transverse
[Burkardt (2005)][Barone et al.
(2008)]
Summary Parton distribution zoo
PDFs, FFs, GPDs, TMDs, GTMDs Partonic interpretation
Twist-2 phase-space distributions
Proton spin puzzle Decompositions
Kinetic versus canonical
Relations with observables
Model results Overlap representation Wigner distributions
Consistent emerging picture
Incoherent scatteringDVCS vs. SIDIS
DVCS SIDIS
GPDs TMDs
FFs
Factorization
Compton form factor
Cross section • process dependent• perturbative
• « universal »• non-perturbative
hard soft
GPDs vs. TMDsGPDs TMDs
Correlator
Correlator
Dirac matrix
Wilson line
Off-forward! Forward!
FSIISI
e.g. SIDISe.g. DY
LC helicity and canonical spin
LC helicity Canonical spin
Nu
cleon
pola
riza
tion
Quark polarization Quark polarization
Nu
cleon
pola
riza
tion
[C.L., Pasquini (2011)]
Interesting relationsModel
relations
* **
***
Flavor-dependent
Flavor-independent
Linear relations Quadratic relation
BagLFQSMLFCQM
S DiquarkAV DiquarkCov. Parton
Quark Target
[Jaffe, Ji (1991), Signal (1997), Barone & al. (2002), Avakian & al. (2008-2010)][C.L., Pasquini, Vanderhaeghen (2011)][Pasquini & al. (2005-2008)][Ma & al. (1996-2009), Jakob & al. (1997), Bacchetta & al. (2008)][Ma & al. (1996-2009), Jakob & al. (1997)] [Bacchetta & al. (2008)][Efremov & al. (2009)][Meißner & al. (2007)]
*=SU(6)
*
*
*
*
*
*
Geometrical explanationPreliminaries
Quasi-free quarks Spherical symmetry
[C.L., Pasquini (2011)]
Conditions:
Light-front helicity
Canonical spin
Wigner rotation
(reduces to Melosh rotation in case of FREE
quarks)
Geometrical explanationAxial symmetry about
z
Geometrical explanationAxial symmetry about
z