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Polarized Light Ions: Angular Momentum in QCD

This paper explores the polarized light ions' impact on angular momentum in Quantum Chromodynamics (QCD), focusing on various distribution frames and their contributions to the nucleon spin. It discusses the relativistic nature of the system, quark polarization, and the relationships between different 3D and 2D distributions. The study also highlights the potential applications and opportunities provided by polarized light ions, such as flavor separation, nuclear OAM vs. hadronic OAM, controlled OAM states, nuclear medium modification, and higher spin studies.

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Polarized Light Ions: Angular Momentum in QCD

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  1. Polarized light ion physics with EIC OAM in QCD CPHT Based on [C.L., Mantovani, Pasquini (2018)] Cédric Lorcé February 8, Ghent U., Belgium

  2. Outline Angular momentum in QFT Energy-momentum tensor 3D distributions in Breit frame 2D distributions in elastic frame Results in scalar diquark model

  3. Orbital angular momentum Large contribution to nucleon spin relativistic nature of the system cQCD collaboration [Deka et al. (2015)] Responsible for most of spin asymmetries fine structure and spin-orbit correlation Quark polarization FFs, GPDs, TMDs, GTMDs, … Nucleon polarization PDFs [C.L., Pasquini (2016)]

  4. Angular momentum Quantum mechanics Quantum field theory Poincaré covariance Absent in GR

  5. Canonical, kinetic or Belinfante? Canonical (Jaffe-Manohar) Kinetic (Ji) Belinfante superpotential

  6. Energy-momentum tensor Matrix elements Non-conservation Intrinsic spin Mass-shell conditions Timelike « frame » Spacelike « position »

  7. Energy-momentum form factors Mellin moment of twist-2 vector GPDs [Ji (1996)] Poincaré covariance [C.L., Mantovani, Pasquini (2018)] No contribution to AM from !

  8. 3D distribution in Breit frame Lorentz factors Initial Final Breit frame 3D distribution of OAM

  9. 3D distribution in Breit frame Kinetic OAM Spin Belinfante total AM But !!!!

  10. 3D distribution in Breit frame Kinetic OAM Spin Belinfante total AM Superpotential

  11. Link with other 3D distributions Naive distribution Polyakov’s distribution [Polyakov (2003)] [Goeke et al. (2007)] Discarded without justification

  12. 2D distribution in elastic frame Initial Final Elastic frame 2D distribution of longitudinal OAM

  13. 2D distribution in elastic frame Kinetic OAM Spin Belinfante total AM Superpotential -independent ! Light-front distribution Breit frame Infinite momentum frame

  14. Scalar diquark model Light-front wave functions Diquark Quark Nucleon

  15. Scalar diquark model Kinetic Canonical First analytic proof!

  16. Scalar diquark model Missing in [Adhikari, Burkardt (2016)]

  17. Scalar diquark model Missing in [Adhikari, Burkardt (2016)]

  18. Scalar diquark model Missing in [Adhikari, Burkardt (2016)]

  19. Polarized light ions Our results are valid for any spin-1/2 target ! Opportunities with light ions: • Flavor separation • Nuclear OAM vs hadronic OAM • Controlled OAM state ? • Nuclear medium modification • Higher spin

  20. Summary • Because of spin, the EMT is asymmetric • AM can be defined at the distribution level • Pay attention to contributions with vanishing integral • Longitudinal AM does not depend on target momentum • Scalar diquark model shows large OAM contribution • Polarized light ions offer many interesting opportunities!

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