Cédric Lorcé SLAC & IFPA Liège Transversity and orbital angular momentum January 23, 2015, JLab, Newport News, USA.

Cédric LorcéSLAC & IFPA Liège

Transversity and orbital angular momentum

January 23, 2015, JLab, Newport News, USA

Outline

• Angular momentum and Relativity • Longitudinal and transverse polarizations• Transversity and orbital angular momentum

Back to basics

Two crucial commutators

RelativisticNon-relativistic

Spin orientation andrelativistic center-of-

mass are frame dependent

Wigner rotation

Special relativity introduces intricate spin-orbit coupling !

Back to basics

Single particle at rest

Total angular

Spin is well-defined and unique

Only upper component matters

Back to basics

Single particle in motion

Total angular

« Spin » is ambiguous and not unique

p-waves are involved

Even for a plane-wave !

Spin vs. Polarization

I will always refer to « spin » as Dirac spin

Dirac states are eigenstates of momentum and polarization operators

but not of spin operator

Pauli-Lubanski four-vector

Polarization four-vector

Spin vs. Polarization

Polarization along z

Total angular momentum is conserved

Spin vs. Polarization

Standard Lorentz transformation defines polarization basis in any frame

Conventional !

Generic Lorentz transformation generates a Wigner rotation of polarization

Changing standard Lorentz transformation results in a Melosh rotation

[Polyzou et al. (2012)]

Popular polarization choices

« Canonical spin »

Advantage : rotations are simple

[Polyzou et al. (2012)]

is a rotationless pure boost

« Light-front helicity » is made of LF boosts

Advantage : LF boosts are simple

Polarization four-vector

Polarization four-vector

Longitudinal vs. Transverse

Longitudinal polarization Helicity !

Reminder

Aka longitudinal spin

Transverse polarization

Transversity !

Helicity vs. Transversity

Chiral odd

Helicity Transversity

Charge odd

Chiral even

Charge even

Many-body system

Axial and tensor charges

Target rest frame quark rest frame

OAM encoded in both WF and spinors

Instant-form and LF wave functions

3Q model of the nucleon

Generalized Melosh rotation

Transfers OAM from spinor to

WF

In many quark models

pure s-wave s-, p- and d-waves

Spherical symmetry !

Not independent !

No gluons, no sea !

Quasi-independent particles in a spherically symmetric potential

Spherical symmetry in quark models

OAM is a pure effect of Generalized Melosh rotation

TMD relations

[Avakian et al. (2010)][C.L., Pasquini (2011)]

[Müller, Hwang (2014)]

[Burkardt (2007)][Efremov et al.

(2008,2010)][She, Zhu, Ma (2009)][Avakian et al. (2010)][C.L., Pasquini (2012)]

[Ma, Schmidt (1998)]

Naive canonical OAM (Jaffe-Manohar)

Transverse spin sum rules

BLT sum rule [Bakker et al. (2004)]

Ambiguous matrix elementsNot related to known

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

Ji-Leader sum rule

[Leader (2012)][Ji (1997)]

[Ji et al. (2012)][Leader (2013)]

[Harindranath et al. (2013)]

Transverse Pauli-Lubanski sum rule

Spin-orbit correlations

Transverse AM and transversely polarized quark [Burkardt (2006)]

[C.L. (2014)]Longitudinal OAM and longitudinally polarized quark

Summary

• Distinction between « spin » and « polarization » is important

• Helicity and transversity contain complementary information about boosts

• Transversity appears in several sum rules but has no model-independent relation with OAM