Cédric Lorcé IPN Orsay - LPT Orsay Orbital Angular Momentum in QCD June 27 2013, Dipartimento di Fisica, Universita’ di Pavia, Italy
Cédric Lorcé
Feb 22, 2016
Orbital Angular Momentum in QCD. Cédric Lorcé. IPN Orsay - LPT Orsay. June 27 2013, Dipartimento di Fisica , Universita ’ di Pavia , Italy. The outline. Basic question. Quark spin. ?. ~ 30 %. Dark spin. The decompositions in a nutshell - PowerPoint PPT Presentation
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Cédric LorcéIPN Orsay - LPT Orsay
Orbital Angular Momentum in QCD
June 27 2013, Dipartimento di Fisica, Universita’ di Pavia, Italy
The outline
Dark spin
Quark spin?
~ 30 %
• The decompositions in a nutshell• Canonical formalism and Chen et al. approach• Geometrical interpretation of gauge symmetry• Path-dependence and measurability• Conclusions
Basic question
Jaffe-Manohar (1990)
The decompositions in a nutshell
Sq
SgLg
Lq
Noether’s theorem
Ji (1997)Jaffe-Manohar (1990)
The decompositions in a nutshell
Sq
SgLg
Lq Sq
Jg
Lq
Noether’s theorem
Ji (1997)Jaffe-Manohar (1990)
Chen et al. (2008)
The decompositions in a nutshell
Sq
SgLg
Lq
Sq
SgLg
Lq
Sq
Jg
Lq
Gauge-invariant extension (GIE)
Noether’s theorem
Wakamatsu (2010)
Ji (1997)Jaffe-Manohar (1990)
Chen et al. (2008)
The decompositions in a nutshell
Sq
SgLg
Lq
Sq
SgLg
Lq Sq
SgLg
Lq
Sq
Jg
Lq
Gauge-invariant extension (GIE)
Noether’s theorem
Wakamatsu (2010)
Ji (1997)Jaffe-Manohar (1990)
Chen et al. (2008)
Canonical Kinetic
The decompositions in a nutshell
Sq
SgLg
Lq
Sq
SgLg
Lq Sq
SgLg
Lq
Sq
Jg
Lq
Gauge-invariant extension (GIE)
Noether’s theorem
Wakamatsu (2010)
Ji (1997)Jaffe-Manohar (1990)
Chen et al. (2008)
Canonical Kinetic
The decompositions in a nutshell
Sq
SgLg
Lq
Sq
SgLg
Lq Sq
SgLg
Lq
Sq
Jg
Lq
Gauge-invariant extension (GIE)
Noether’s theorem
The Chen et al. approach[Chen et al. (2008,2009)] [Wakamatsu (2010,2011)]
The Chen et al. approach
Gauge transformation (assumed)
[Chen et al. (2008,2009)] [Wakamatsu (2010,2011)]
The Chen et al. approach
Gauge transformation (assumed)
Pure-gauge covariant derivatives
[Chen et al. (2008,2009)] [Wakamatsu (2010,2011)]
The Chen et al. approach
Gauge transformation (assumed)
Field strength
Pure-gauge covariant derivatives
[Chen et al. (2008,2009)] [Wakamatsu (2010,2011)]
The canonical formalism
Textbook
Dynamical variables
Lagrangian
[C.L. (2013)]
The canonical formalism
Textbook
Gauge covariant
Dynamical variables
Lagrangian
[C.L. (2013)]
The canonical formalism
Textbook
Gauge covariant
Gauge invariant
Dynamical variables
Lagrangian
Dirac variables
Dressing field Gauge transformation
[Dirac (1955)][Mandelstam
(1962)]
[C.L. (2013)]
The analogy with General Relativity[C.L. (2012,2013)]
Dual role
Pure gauge
Physical polarizations
The analogy with General Relativity
Degrees of freedom
[C.L. (2012,2013)]
Dual role
Pure gauge
Physical polarizations
The analogy with General Relativity
Geometrical interpretationParallelism Curvature
Degrees of freedom
[C.L. (2012,2013)]
Dual role
Pure gauge
Physical polarizations
Analogy with General
Relativity
The analogy with General Relativity
Geometrical interpretationParallelism Curvature
Inertial forces
Gravitational forces
Degrees of freedom
[C.L. (2012,2013)]
Dual role
[Wakamatsu (2010)][Chen et al. (2008)]
The Stueckelberg symmetry
Ambiguous!
[Stoilov (2010)][C.L. (2013)]
Sq
SgLg
Lq Sq
SgLg
Lq
Coulomb GIE
[Hatta (2011)][C.L. (2013)]
Sq
SgLg
Lq
Light-front GIE
Lpot
LpotSq
Sg
Lg
Lq
Infinitely many possibilities!
Gauge
GIE1
GIE2
Gauge-variant operator
« Natural » gauges
Lorentz-invariant extensions~
RestCenter-of-mass
Infinite momentum
« Natural » frames
The gauge-invariant extension (GIE)
The geometrical interpretation[Hatta (2012)]
[C.L. (2012)]Parallel transport
The geometrical interpretation[Hatta (2012)]
[C.L. (2012)]Parallel transport
The geometrical interpretation[Hatta (2012)]
[C.L. (2012)]Parallel transport
Non-local !
The geometrical interpretation[Hatta (2012)]
[C.L. (2012)]Parallel transport
Path dependent !
Stueckelberg symmetry
Non-local !
The path dependence[Ji, Xiong, Yuan (2012)]
[Hatta (2012)][C.L. (2013)]Canonical quark OAM operator
FSIISI
SIDISDrell-Yan
The path dependence[Ji, Xiong, Yuan (2012)]
[Hatta (2012)][C.L. (2013)]
Naive T-even
Canonical quark OAM operator
Light-frontLq
FSIISI
SIDISDrell-Yan
The path dependence[Ji, Xiong, Yuan (2012)]
[Hatta (2012)][C.L. (2013)]
Coincides locally with kinetic quark OAM
Naive T-even
Canonical quark OAM operator
x-based Fock-SchwingerLight-frontLq
Lq
The gauge symmetry
Quantum electrodynamics« Physical »
[C.L. (in preparation)]
« Background »
The gauge symmetry
Quantum electrodynamics
Passive
« Physical »
[C.L. (in preparation)]
« Background »
The gauge symmetry
Quantum electrodynamics
Passive Active
« Physical »
[C.L. (in preparation)]
« Background »
The gauge symmetry
Quantum electrodynamics
Passive Active
« Physical »
[C.L. (in preparation)]
« Background »
Active x (Passive)-1
The gauge symmetry
Quantum electrodynamics
Passive Active
« Physical »
[C.L. (in preparation)]
« Background »
Active x (Passive)-1
Stueckelberg
The semantic ambiguity
« measurable »Quid ? « physical »
« gauge invariant »
The semantic ambiguity
Observables
« measurable »Quid ? « physical »
« gauge invariant »
Measurable, physical, gauge invariant (active and passive)E.g. cross-sections
The semantic ambiguity
PathStueckelbergBackground
Observables
« measurable »Quid ? « physical »
« gauge invariant »
Measurable, physical, gauge invariant (active and passive)
Expansion scheme
E.g. cross-sections
dependentE.g. collinear factorization
The semantic ambiguity
PathStueckelbergBackground
Observables
Quasi-observables
« measurable »Quid ? « physical »
« gauge invariant »
Measurable, physical, gauge invariant (active and passive)
« Measurable », « physical », « gauge invariant » (only passive)
Expansion scheme
E.g. cross-sections
E.g. parton distributions
dependentE.g. collinear factorization
Canonical Kinetic
The observability
Sq
SgLg
Lq
Sq
SgLg
Lq Sq
SgLg
Lq
Sq
Jg
Lq
Not observableObservable Quasi-observable
[Wakamatsu (2010)]
[Ji (1997)][Jaffe-Manohar (1990)]
[Chen et al. (2008)]
The gluon spin
[Jaffe-Manohar (1990)] [Hatta (2011)]
Light-front GIE Light-front gauge
Gluon helicity distribution
Local fixed-gauge interpretation
Non-local gauge-invariant interpretation
« Measurable », gauge invariant but non-local
The kinetic and canonical OAM
Quark naive canonical OAM (Jaffe-Manohar)
[Burkardt (2007)][Efremov et al.
(2008,2010)][She, Zhu, Ma (2009)][Avakian et al. (2010)][C.L., Pasquini (2011)]
Model-dependent !
Kinetic OAM (Ji)
[Ji (1997)]
[Penttinen et al. (2000)][Kiptily, Polyakov (2004)]
[Hatta (2012)]
but
No gluons and not QCD EOM!
[C.L., Pasquini (2011)]
Pure twist-3
Canonical OAM (Jaffe-Manohar) [C.L., Pasquini (2011)][C.L., Pasquini, Xiong, Yuan (2012)]
[Hatta (2012)]
Wakamatsu (2010)
Ji (1997)Jaffe-Manohar (1990)
Chen et al. (2008)
Canonical Kinetic
The conclusion
Sq
SgLg
Lq
Sq
SgLg
Lq Sq
SgLg
Lq
Sq
Jg
Lq
Not observable Observable
Quasi-observableQuasi-observable
Backup slides
[PRD79 (2009) 014507] [Nucl. Phys. A825 (2009) 115]
[PRL104 (2010) 112001][PRD79 (2009) 113011]
GTMDs
TMDs
Charges
PDFs
GPDs
FFsTMCs
TMFFs[PRD84 (2011) 034039]
[PLB710 (2012) 486]
[PRD84 (2011) 014015][PRD85 (2012) 114006]
[JHEP1105 (2011) 041]
[PRD74 (2006) 054019][PRD78 (2008) 034001]
[PRD79 (2009) 074027]
Phase-space densities
The parton distributions
« Vorticity »
The twist-2 OAM
Quark Wigner operator
[C.L., Pasquini (2011)][C.L., Pasquini, Xiong, Yuan (2012)]
[Hatta (2012)]
Quark OAM operator
Exact relation
The spin-spin-orbit correlations[C.L., Pasquini (2011)]
Overlap representation
Momentum Polarization
[PRD74 (2006) 054019][PRD78 (2008) 034001][PRD79 (2009) 074027]
Light-front quark models Wigner rotation
The light-front wave functions
OAM
Canonical (naive)
Kinetic
Canonical GTMDs
TMDs
GPDs
Phenomenological comparison
but
The orbital angular momentum
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