Cédric Lorcé

IPN Orsay - IFPA Liège

Quark spin-orbit correlations

May 14th 2014, Santa Fe, New Mexico, USA

[C.L., arXiv:1401.7784]

[C.L., Pasquini (in preparation)]

Based on :

Outline

• Energy-momentum tensor

• Quark spin-orbit correlations

• Phase-space transverse modes

• Conclusions

Energy-momentum tensor

A lot of interesting physics is contained in the EM tensor

Energy density

Momentum density

Energy flux

Momentum flux

Shear stress

Normal stress (pressure)

E.g.

[Polyakov, Shuvaev (2002)]

[Polyakov (2003)]

[Goeke et al. (2007)]

[Cebulla et al. (2007)]

Energy-momentum tensor

Momentum-space expression

General parametrization

Non-conservation

Asymmetry

[Ji (1997)]

[Shore, White (2000)]

Angular momentum

Link with GPDs

« Trick »

Local Non-local

GPD operator

[Penttinen et al. (2000)]

[Kiptily, Polyakov (2004)]

[Hatta, Yoshida (2012)]

Twist-2

Twist-3

[Ji (1997)]

Proton spin structure

« Quark spin »

« Quark OAM »

Quark spin-orbit correlation

[C.L., Pasquini (2011)] [C.L. (2014)]

Not involved in proton spin sum rule !

Proton spin structure

« Quark spin »

« Quark OAM »

Quark spin-orbit correlation

[C.L., Pasquini (2011)] [C.L. (2014)]

Quark number

UU

LL

LU

UL

Spin OAM

P-odd energy-momentum tensor

Chiral decomposition

General parametrization

Twist-2

Twist-3

[C.L. (2014)]

Some figures

[C.L. (2014)]

Valence number

Spin and kinetic OAM of valence quarks are anti-correlated !

Phase-space transverse modes

Parametrization of a correlator is not unique Natural modes ?

[C.L., Pasquini (in preparation)]

Phase-space transverse modes

Parametrization of a correlator is not unique Natural modes ?

[C.L., Pasquini (in preparation)]

Phase-space transverse modes

Properties under

parity and time-reversal

Parametrization of a correlator is not unique Natural modes ?

[C.L., Pasquini (in preparation)]

Phase-space transverse modes

Unpolarized quark in unpolarized target

[C.L., Pasquini (in preparation)]

UU

Phase-space transverse modes

Unpolarized quark in longitudinally polarized target

[C.L., Pasquini (in preparation)]

LU

Phase-space transverse modes

Unpolarized quark in transversely polarized target (1)

[C.L., Pasquini (in preparation)]

TU

Phase-space transverse modes

Unpolarized quark in transversely polarized target (2)

[C.L., Pasquini (in preparation)]

TU

Phase-space transverse modes

Unpolarized quark in transversely polarized target (1+2)

[C.L., Pasquini (in preparation)]

TU

Conclusions

• Complete characterization of spin structure requires spin-orbit correlation

• Like quark OAM, quark spin-orbit correlation is given by moments of measurable parton distributions

• Natural phase-space transverse modes help to understand the physics contained in parton distributions

Backup slides

Energy-momentum tensor

In presence of spin density

In rest frame

No « spin » contribution !

Belinfante « improvement »

Spin density gradient Four-momentum circulation

Light-front quark models Wigner rotation

Light-front overlap representation

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

GTMDs ~

Momentum Polarization