spin theory: a short taste
TRANSCRIPT
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Spin theory: A short taste
Cédric Lorcé
Institut de Physique Nucléaire d’Orsay and
Laboratoire de Physique Théorique
February 11, 2013, ECT*, Trento, Italy
Physics at A Fixed Target ExpeRiment (AFTER)
using the LHC beams
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Introduction Basic questions
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Introduction Basic questions
Parton distributions ?
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Introduction Basic questions
Quark-gluon interactions ?
Parton distributions ?
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Introduction Basic questions
Proton spin decomposition ?
Quark-gluon interactions ?
Parton distributions ?
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Introduction Basic questions
Proton spin decomposition ?
Spin-orbit correlations ?
Quark-gluon interactions ?
Parton distributions ?
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Angular momentum Spin and OAM
Orbital angular momentum
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Angular momentum Spin and OAM
Orbital angular momentum
Angular momentum
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Angular momentum Spin and OAM
Orbital angular momentum
Angular momentum
Spin
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Angular momentum Polarizations
Relativity couples spin and OAM
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Angular momentum Polarizations
Rest frame
Relativity couples spin and OAM
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Angular momentum Polarizations
Rest frame
Relativity couples spin and OAM
Moving frame
Canonical spin
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Angular momentum Polarizations
Rest frame
Relativity couples spin and OAM
Moving frame
Canonical spin
Helicity
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Angular momentum Polarizations
Rest frame
Relativity couples spin and OAM
Moving frame
Canonical spin
Helicity
Light-front helicity
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Angular momentum Polarizations
Rest frame
Relativity couples spin and OAM
Moving frame
Canonical spin
Helicity
Light-front helicity Light-front dominance
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Dark spin
Quark spin ?
~ 30 %
Sum rule
Proton spin puzzle
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Dark spin
Quark spin ?
~ 30 %
Proton spin puzzle
Sum rule
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• Does not satisfy canonical relations • Incomplete decomposition
Proton spin puzzle
Ji 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
News: [Wakamatsu (2009,2010)]
• Complete decomposition News: [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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News:
• Does not satisfy canonical relations • Incomplete decomposition
Proton spin puzzle
Ji 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
News: [Wakamatsu (2009,2010)]
• Complete decomposition
[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-gluon interaction Twist-3 effect
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Probing the proton structure
Inelastic scattering
2
~ Im
Coherent scattering
Extremely hard to describe with QCD !
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Factorization
Incoherent scattering
Probing the proton structure
Deep inelastic scattering
PDFs
2
~ Im pQCD
universal
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Factorization
Incoherent scattering
Probing the proton structure
Deep inelastic scattering
PDFs
2
~ Im pQCD
universal
DGLAP
In practice
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DIS
Parton Distribution Functions
Probing the proton structure
Quark polarization
Nu
cle
on
po
lari
za
tio
n
0+1D Picture
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DIS
Parton Distribution Functions
Probing the proton structure
Quark polarization
Nu
cle
on
po
lari
za
tio
n
Vector
Spin-spin correlations
0+1D Picture
+ +
± ±
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DIS
Parton Distribution Functions
0+1D Picture
Probing the proton structure
Quark polarization
Nu
cle
on
po
lari
za
tio
n
Vector
Axial
Spin-spin correlations
+ +
± ±
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Not accessible in DIS !
DIS
Parton Distribution Functions
Probing the proton structure
Quark polarization
Nu
cle
on
po
lari
za
tio
n
Vector
Tensor
Axial
Spin-spin correlations
0+1D Picture
+ -
+ -
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SIDIS
Transverse-Momentum dependent PDFs
Probing the proton structure
0+3D Picture
Quark polarization
Nu
cle
on
po
lari
za
tio
n
[Kotzinian (1995)] [Boer, Mulders (1998)]
[Bacchetta et al. (2007)] [Anselmino et al. (2011)]
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SIDIS
Transverse-Momentum dependent PDFs
Probing the proton structure
0+3D Picture
Quark polarization
Nu
cle
on
po
lari
za
tio
n
Monopole
[Kotzinian (1995)] [Boer, Mulders (1998)]
[Bacchetta et al. (2007)] [Anselmino et al. (2011)]
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Monopole
SIDIS
Transverse-Momentum dependent PDFs
Probing the proton structure
0+3D Picture
Quark polarization
Nu
cle
on
po
lari
za
tio
n
Dipole
[Kotzinian (1995)] [Boer, Mulders (1998)]
[Bacchetta et al. (2007)] [Anselmino et al. (2011)]
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SIDIS
Transverse-Momentum dependent PDFs
Probing the proton structure
0+3D Picture
Quark polarization
Nu
cle
on
po
lari
za
tio
n
Monopole
Dipole
Quadrupole
[Kotzinian (1995)] [Boer, Mulders (1998)]
[Bacchetta et al. (2007)] [Anselmino et al. (2011)]
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SIDIS
Transverse-Momentum dependent PDFs
Probing the proton structure
0+3D Picture
Quark polarization
Nu
cle
on
po
lari
za
tio
n
Monopole
Dipole
Quadrupole
?
[Kotzinian (1995)] [Boer, Mulders (1998)]
[Bacchetta et al. (2007)] [Anselmino et al. (2011)]
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Transverse-Momentum dependent PDFs
Probing the proton structure
Quark polarization
Nu
cle
on
po
lari
za
tio
n
Naive T-odd
Transverse single spin asymmetry
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Transverse-Momentum dependent PDFs
Probing the proton structure
Quark polarization
Nu
cle
on
po
lari
za
tio
n
Naive T-odd
FSI ISI
DY SIDIS
Transverse single spin asymmetry
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Generalized PDFs
Probing the proton structure
2+1D Picture
Quark polarization
Nu
cle
on
po
lari
za
tio
n
DVCS
[Burkardt (2000,2003)]
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Generalized PDFs
Probing the proton structure
2+1D Picture
Quark polarization
Nu
cle
on
po
lari
za
tio
n
DVCS
Ji’s sum rule [Ji (1997)]
[Burkardt (2000,2003)]
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Probing the proton structure
Quark polarization
Nu
cle
on
po
lari
za
tio
n
Generalized TMDs
[Wigner (1932)] [Belitsky , Ji, Yuan (2004)]
[C.L., Pasquini (2011)]
Quasi-probabilistic interpretation
??? ???
2+3D Picture
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Probing the proton structure
Quark polarization
Nu
cle
on
po
lari
za
tio
n
Generalized TMDs
OAM [C.L., Pasquini (2011)]
[C.L. et al. (2012)]
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Parton distribution zoo
Complete set
GTMDs
TMDs
[C.L., Pasquini, Vanderhaeghen (2011)]
Charges
PDFs
GPDs
FFs TMCs
TMFFs
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Momentum
Fock expansion of the proton state
Fock states Simultaneous eigenstates of
Light-front helicity
Overlap representation
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Light-front wave functions
Proton state
Eigenstates of parton light-front helicity
Eigenstates of total OAM
Probability associated with the N,b Fock state
Normalization
Overlap representation
gauge
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Flavor contribution
Overlap representation
Pure quark system
Conservation of longitudinal momentum
Conservation of transverse momentum
Anomalous gravitomagnetic
sum rule!
[C.L., Pasquini (2011)]
NB: also valid for N,b Fock states
[Hägler, Mukherjee, Schäfer (2004)] [C.L., Pasquini, Xiong, Yuan (2011)]
[C.L., Pasquini (2011)]
[Brodsky, Hwang, Ma, Schmidt (2001)]
Comparison of different OAM
GTMDs
TMDs
GPDs
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Light-front 3Q models
[C.L., Pasquini (2011)]
Models are not QCD
Truncation of Fock space can spoil Lorentz covariance
In model calculations, one should expect but
[Carbonell, Desplanques, Karmanov, Mathiot (1998)]
Comparison of different OAM
GTMDs
TMDs
GPDs
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Emerging picture
Longitudinal
[C.L., Pasquini (2011)]
Transverse
[Burkardt (2005)] [Barone et al. (2008)]
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Summary
Proton spin decomposition ? • Canonical and kinetic AM
• Accessible in (semi-)inclusive and exclusive processes
Spin-orbit correlations ? • Different types of polarization
• Multipolar structure
Quark-gluon interactions ? • Scale dependence • Twist-3 effects
Parton distributions ? • Factorization theorem • Baryon tomography
Thank you !