Cédric Lorcé

SLAC & IFPA Liège

Exploring the proton spin structure

December 11, 2014, IIT Guwahati, Guwahati, India

XXI DAE-BRNS High Energy Physics Symposium 2014

8-12 DECEMBER 2014, IIT GUWAHATI

Outline

• What is it all about ?

• Why is there a controversy ?

• How can we measure AM ?

Outline

• What is it all about ?

• Why is there a controversy ?

• How can we measure AM ?

Structure of nucleons

Our picture/understanding of the nucleon evolves !

But many questions remain unanswered …

• Where does the proton spin come from ?

• How are quarks and gluons distributed inside the nucleon ?

• What is the proton size ?

• Why are quarks and gluons confined ?

• How are constituent quarks related to QCD ?

• …

Why is spin interesting ?

Fundamental, quantum, discrete degree of freedom

Weak interactions are sensitive to spin (V-A coupling)

Large spin asymmetries in QCD

21 cm

Polarized 60Co nuclei ensemble

B

s=(20 GeV)² 7<PT<20 GeV

Why is spin interesting ?

Light polarization has fundamental impact on cosmology

New physics (BSM, Quantum gravity, …) also likely sensitive to spin

Muon g-2 puzzle Space-time with torsion

Angular momentum decomposition

Sq

Sg Lg

Lq Sq

Sg Lg

Lq

Sq

Jg

Lq

Many questions/issues : • Frame dependence ?

• Gauge invariance ?

• Uniqueness ?

• Measurability ?

• …

Reviews:

Dark spin

Quark spin ?

~ 30 %

?

?

?

[Leader, C.L. (2014)] [Wakamatsu (2014)]

~ 20 %

[de Florian et al. (2014)]

Outline

• What is it all about ?

• Why is there a controversy ?

• How can we measure AM ?

In short …

Noether’s theorem :

Continuous symmetry

Translation invariance

Rotation invariance

Conserved quantity

Total (linear) momentum

Total angular momentum

We all agree on the total quantities

BUT …

We disagree on their decomposition

In short …

3 viewpoints :

• Meaningless, unphysical discussions

No unique definition ill-defined problem

• There is a unique «physical» decomposition

Missing fundamental principle in standard approach

• Matter of convention and convenience

Measured quantities are unique BUT physical interpretation is not unique

Spin decompositions in a nutshell

[Jaffe, Manohar (1990)] [Ji (1997)]

Sq

Sg Lg

Lq Sq

Lq

Jg

Canonical Kinetic

Gauge non-invariant ! « Incomplete »

Gluon spin

Gluon helicity distribution

[de Florian et al. (2014)]

« Measurable », gauge invariant but complicated

Gluon spin

[Jaffe-Manohar (1990)]

Light-front gauge

Gluon helicity distribution

Simple fixed-gauge interpretation

« Measurable », gauge invariant but complicated

Chen et al. approach

Gauge transformation (assumed)

Field strength

Pure-gauge covariant derivatives

[Chen et al. (2008,2009)]

[Wakamatsu (2010,2011)]

Spin decompositions in a nutshell

[Jaffe, Manohar (1990)] [Ji (1997)]

Sq

Sg Lg

Lq Sq

Lq

Jg

Canonical Kinetic

Gauge non-invariant ! « Incomplete »

Spin decompositions in a nutshell

[Chen et al. (2008)] [Wakamatsu (2010)]

Sq

Sg Lg

Lq Sq

Lq

Lg

Canonical Kinetic

Sg

Gauge-invariant extension (GIE)

Spin decompositions in a nutshell

[Chen et al. (2008)] [Wakamatsu (2010)]

Sq

Sg Lg

Lq Sq

Lq

Canonical Kinetic

Sg

Gauge-invariant extension (GIE)

Lg

[Wakamatsu (2010)] [Chen et al. (2008)]

Stueckelberg symmetry

Ambiguous !

[Stoilov (2010)]

[C.L. (2013)]

Sq

Sg Lg

Lq Sq

Sg Lg

Lq

Coulomb GIE

[Hatta (2011)]

[C.L. (2013)]

Sq

Sg Lg

Lq

Light-front GIE

Lpot

Lpot Sq

Sg

Lg

Lq

Infinitely many possibilities !

Gauge fixing

Stueckelberg symmetry

Gauge non-invariant operator

[C.L. (2013)]

Gauge fixing

GIE1

« Natural » gauges

Stueckelberg symmetry

Gauge non-invariant operator

[C.L. (2013)]

Gauge fixing

GIE1

GIE2

« Natural » gauges

Stueckelberg symmetry

Gauge non-invariant operator

Stueckelberg fixing

[C.L. (2013)]

Gauge fixing

GIE1

GIE2

« Natural » gauges

Lorentz-invariant extensions ~

Rest

Center-of-mass

Infinite momentum

« Natural » frames

Stueckelberg symmetry

Gauge non-invariant operator

Stueckelberg fixing

[C.L. (2013)]

Two different approaches

Lagrangian Hamiltonian

Time

Space

Lorentz covariance

Physical interpretation

Manifest Not manifest

Complicated Simple

Two different approaches

Stueckelberg invariant

Stueckelberg fixed

Physical dofs

Gauge dof

Gauge invariance

Physical interpretation

Local Non-local

Complicated Simple

Outline

• What is it all about ?

• Why is there a controversy ?

• How can we measure AM ?

Photon spin and OAM

Textbooks claim that no gauge-invariant decomposition of photon AM exists

But formally the following decomposition is gauge invariant

No actual contradiction because textbooks implicitly refer to local expressions !

Photon spin and OAM

Should we be happy with ?

Well… for a circularly polarized plane wave travelling along z

Two descriptions related by a non-zero surface term

!

Photon spin and OAM

Should we be happy with ?

[Ghai et al. (2009)]

Single-slit experiment

Photon spin and OAM

Should we be happy with ?

[O’Neil et al. (2002)]

[Garcés-Chavéz et al. (2003)]

Optically trapped microscopic particle

Asymmetries in QCD

Example : SIDIS

[Mulders, Tangermann (1996)] [Boer, Mulders (1998)]

[Bacchetta et al. (2004)] [Bacchetta et al. (2007)] [Anselmino et al. (2011)]

Angular modulations of the cross section are sensitive to AM

Parton distribution zoo

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

TMDs

FFs PDFs

Charges

GPDs

Parton distribution zoo

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

GTMDs

TMDs

FFs PDFs

Charges

GPDs

«P

hysic

al»

ob

jects

T

he

ore

tica

l to

ols

LFWFs

Parton distribution zoo

2+1D

2+0D

0+3D

0+1D

2+3D

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

GTMDs

TMDs

FFs PDFs

Charges

GPDs

«P

hysic

al»

ob

jects

T

he

ore

tica

l to

ols

Phase-space (Wigner) distribution

[C.L., Pasquini (2011)] [C.L. et al. (2012)]

[Hatta (2012)]

Example : canonical OAM

« Vorticity »

Spatial distribution of average transverse momentum

Kinetic vs canonical OAM

Quark naive canonical OAM (Jaffe-Manohar)

Model-dependent !

Kinetic OAM (Ji)

but

No gluons and not QCD EOM !

Pure twist-3

Canonical OAM (Jaffe-Manohar) [C.L., Pasquini (2011)]

[C.L. et al. (2012)]

[Kanazawa et al. (2014)]

[Mukherjee et al. (2014)]

[Ji (1997)]

[Penttinen et al. (2000)]

[Burkardt (2007)] [Efremov et al. (2008,2010)]

[She, Zhu, Ma (2009)] [Avakian et al. (2010)] [C.L., Pasquini (2011)]

Summary

• We all agree on total angular momentum

• but we disagree on its decomposition (matter of convention ?)

• Observables are gauge invariant

but physical interpretation need not

• Information about AM is encoded in

• polarized parton distributions

Reviews: [Leader, C.L. (2014)] [Wakamatsu (2014)]

Summary

Nucleon

FFs PDFs TMDs GPDs

LFWFs

DPDs

Backup slides

Light-front quark model results

[C.L., Pasquini (2011)]

Stueckelberg symmetry

Geometrical interpretation Fixed reference point

Non-local ! Path dependent !

[Hatta (2012)]

[C.L. (2013)]

Fixed by experimental conditions !

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

Parton correlators

Gauge invariant but path dependent

2+3D

Longitudinal momentum

Transverse momentum

Transverse position

[Ji (2003)] [Belitsky, Ji, Yuan (2004)]

[C.L., Pasquini (2011)]

Phase-space «density»

Lattice results

CI DI

[Deka et al. (2013)]

Semantic ambiguity

Path Stueckelberg Background

Observables

Quasi-observables

« measurable »

Quid ?

« physical »

« gauge invariant »

Measurable, physical, gauge invariant and local

« Measurable », « physical », gauge invariant and non-local

Expansion scheme

E.g. cross-sections

E.g. parton distributions

-dependent

E.g. collinear factorization