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

Introduction Basic questions

Introduction Basic questions

Parton distributions ?

Introduction Basic questions

Quark-gluon interactions ?

Parton distributions ?

Introduction Basic questions

Proton spin decomposition ?

Quark-gluon interactions ?

Parton distributions ?

Introduction Basic questions

Proton spin decomposition ?

Spin-orbit correlations ?

Quark-gluon interactions ?

Parton distributions ?

Angular momentum Spin and OAM

Orbital angular momentum

Angular momentum Spin and OAM

Orbital angular momentum

Angular momentum

Angular momentum Spin and OAM

Orbital angular momentum

Angular momentum

Spin

Angular momentum Polarizations

Relativity couples spin and OAM

Angular momentum Polarizations

Rest frame

Relativity couples spin and OAM

Angular momentum Polarizations

Rest frame

Relativity couples spin and OAM

Moving frame

Canonical spin

Angular momentum Polarizations

Rest frame

Relativity couples spin and OAM

Moving frame

Canonical spin

Helicity

Angular momentum Polarizations

Rest frame

Relativity couples spin and OAM

Moving frame

Canonical spin

Helicity

Light-front helicity

Angular momentum Polarizations

Rest frame

Relativity couples spin and OAM

Moving frame

Canonical spin

Helicity

Light-front helicity Light-front dominance

Dark spin

Quark spin ?

~ 30 %

Sum rule

Proton spin puzzle

Dark spin

Quark spin ?

~ 30 %

Proton spin puzzle

Sum rule

• 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)]

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

Probing the proton structure

Inelastic scattering

2

~ Im

Coherent scattering

Extremely hard to describe with QCD !

Factorization

Incoherent scattering

Probing the proton structure

Deep inelastic scattering

PDFs

2

~ Im pQCD

universal

Factorization

Incoherent scattering

Probing the proton structure

Deep inelastic scattering

PDFs

2

~ Im pQCD

universal

DGLAP

In practice

DIS

Parton Distribution Functions

Probing the proton structure

Quark polarization

Nu

cle

on

po

lari

za

tio

n

0+1D Picture

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

+ +

± ±

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

+ +

± ±

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

+ -

+ -

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)]

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)]

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)]

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)]

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)]

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

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

Generalized PDFs

Probing the proton structure

2+1D Picture

Quark polarization

Nu

cle

on

po

lari

za

tio

n

DVCS

[Burkardt (2000,2003)]

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)]

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

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)]

Parton distribution zoo

Complete set

GTMDs

TMDs

[C.L., Pasquini, Vanderhaeghen (2011)]

Charges

PDFs

GPDs

FFs TMCs

TMFFs

Momentum

Fock expansion of the proton state

Fock states Simultaneous 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,b Fock state

Normalization

Overlap representation

gauge

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

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

Emerging picture

Longitudinal

[C.L., Pasquini (2011)]

Transverse

[Burkardt (2005)] [Barone et al. (2008)]

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 !