Nucleon tomography through exclusive and semi-inclusive processes
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Transcript of Nucleon tomography through exclusive and semi-inclusive processes
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Nucleon tomography through exclusive and
semi-inclusive processes
Cédric Lorcé
and
17 Apr 2012, LIP, Lisbon, Portugal
International Workshop on Hadron Structure and Spectroscopy
Lisbon, 16-18 April 2012
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Outline Exclusive vs. Semi-inclusive
DVCS vs. SIDIS GPDs vs. TMDs
Partonic interpretation 3D imaging Twist-2 and Twist-3
Hadron structure Angular momentum decompositions Quark spin and OAM Interesting relations
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Incoherent scatteringDVCS vs. SIDIS
DVCS SIDIS
GPDs TMDs
FFs
Factorization
Compton form factor
Cross section • process dependent• perturbative
• « universal »• non-perturbative
hard soft
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GPDs vs. TMDsGPDs TMDs
Correlator
Correlator
Dirac matrix
Wilson line
Off-forward! Forward!
FSIISI
e.g. SIDISe.g. DY
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Impact parameter
Partonic interpretationGPDs TMDs
Twist-2 ~ LO in
U L T
Interpretation in gauge
3D imaging 3D imaging
[Soper (1977)][Burkardt (2000,2003)]
[Diehl, Hägler (2005)]
Transverse center of
momentum
IPDs
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Complete pictureGTMDs and Wigner
distributions
PDFs FFs
TMDs
Charges
GTMDs
GPDs
TMSDs
TMFFs
[C.L., Pasquini, Vanderhaeghen (2011)]
[C.L., Pasquini (2011)]
5D imaging
Wigner distribution
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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
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Twist-3 structureGPDs TMDs
Nu
cle
on
pola
riza
tion
Quark polarization Quark polarization
Nu
cle
on
pola
riza
tion
Naive T-odd
-odd
[Meißner, Metz, Schlegel (2009)]Parametrization
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• Does not satisfy canonical relations• Incomplete decomposition
Angular momentum decompositionsJi Jaffe-Manohar
[Ji (1997)] [Jaffe, Manohar (1990)]
• Gauge-invariant decomposition• Accessible in DIS and DVCS
Kinematic 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)]
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Quark spin and OAMGPDs TMDs
Quark spin Quark spin
Ji sum rule
Twist-3
PPSS sum rule
[Ji (1997)]
[Penttinen, Polyakov, Shuvaev, Strikman (2000)]
Genuine sum rule
Pretzelosity
[Burkardt (2007)][Efremov, Schweitzer, Teryaev, Zavada
(2008,2010)][She, Zhu, Ma (2009)]
[Avakian, Efremov, Schweitzer, Yuan (2010)][C.L., Pasquini (2011)]
• Model-dependent• Not intrinsic OAM
TMDs
GTMDs
Pure twist-3!
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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)
*
*
*
*
*
*
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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)
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Geometrical explanationAxial symmetry about
z
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Geometrical explanationAxial symmetry about
z
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Summary Exclusive vs. Semi-inclusive
DVCS vs. SIDIS Factorization approach
GPDs vs. TMDs Quark-quark correlator
Partonic interpretation 3D imaging
Probabilistic interpretation Twist-2 and Twist-3
Helicity structure
Hadron structure Angular momentum decompositions
Short overview Quark spin and OAM
• Relation with observables Interesting relations
Spherical symmetry in quark models
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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)]