1 / 23

Generalized TMDs of the Proton

Generalized TMDs of the Proton. Barbara Pasquini Pavia U. & INFN, Pavia. i n collaboration with Cédric Lorcé Mainz U. & INFN, Pavia. Outline. Generalized Transverse Momentum Dependent Parton Distributions (GTMDs). FT    b . Wigner Distributions.

baka
Télécharger la présentation

Generalized TMDs of the Proton

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Generalized TMDsof the Proton Barbara Pasquini Pavia U. & INFN, Pavia in collaboration with Cédric Lorcé Mainz U. & INFN, Pavia

  2. Outline Generalized Transverse Momentum Dependent Parton Distributions (GTMDs) FT b Wigner Distributions • Results in light-cone quark models • unpolarized quarks in unpolarized nucleon (generalized transverse charge density)

  3. Generalized TMDs GTMDs • Complete parametrization : 16 GTMDs at twist-2 [Meißner, Metz, Schlegel (2009)] • Fourier Transform : 16 Wigner distributions [Belitsky, Ji, Yuan (2004)] »: fraction of longitudinal momentum transfer x: average fraction of quark longitudinal momentum k?: average quark transverse momentum ¢: nucleon momentum transfer

  4. TMFFs Spin densities GTMDs PDFs TMSDs FFs GPDs TMDs Charges 2D Fourier transform Wigner distribution Transverse charge densities ¢= 0 [ Lorce, BP, Vanderhaeghen, arXiv:1102.4704 ]

  5. Transverse Longitudinal GTMDs GPDs TMDs Wigner Distributions [Wigner (1932)] [Belitsky, Ji, Yuan (04)] [Lorce’, BP: arXiv:1012.0169] QM QFT (Breit frame) QFT (light cone) Heisenberg’s uncertainty relations Quasi-probabilistic Third 3D picture ! No restrictions from Heisenberg’s uncertainty relations

  6. Wigner Distributions • Wigner distributions in QCD: at »=0 ! diagonal in the Fock-space N N N=3 ! overlap of quark light-cone wave-functions • real functions, but in general not-positive definite not probabilistic interpretation correlations of quark momentum and position in the transverse planeas function of quark and nucleon polarizations • no known experiments can directly measure them ! needs phenomenological models

  7. Light-Cone Quark Models LCWF: invariant under boost, independent of P internal variables: [Brodsky, Pauli, Pinsky, ’98] momentum wf spin-flavor wf rotation from canonical spin to light-cone spin Bag Model, ÂQSM, LCQM, Quark-Diquark and Covariant Parton Models Bag Model, ÂQSM, LCQM, Quark-Diquark and Covariant Parton Models Common assumptions : • No gluons • Independent quarks [ Lorce, BP, Vanderhaeghen, arXiv:1102.4704 ]

  8. Transverse Longitudinal k T Example:Unpol. upQuark in Unpol. Proton (1 out of 16) Generalized Transverse Charge Density fixed angle between k? and b? and fixed value of |k?| q b?

  9. Transverse Longitudinal Example:Unpol. upQuark in Unpol. Proton (1 out of 16) fixed = 3Q light-cone model [Lorce’, BP, in preparation]

  10. Transverse Longitudinal Example:Unpol. upQuark in Unpol. Proton (1 out of 16) fixed unfavored = favored 3Q light-cone model [Lorce’, BP, in preparation]

  11. Transverse Longitudinal Example:Unpol. upQuark in Unpol. Proton (1 out of 16) 0.1 GeV² 0.2 GeV² 0.3 GeV² 3Q light-cone model 0.4 GeV² [Lorce’, BP, in preparation]

  12. Summary • GTMDs $ Wigner Distributions - the most complete information on partonic structure of the nucleon • General Formalism for 3-quark contribution to GTMDs - applicable for large class of models: LCQMs, ÂQSM, Bag model • Results for Wigner distributions in the transverse plane - anisotropic distribution in k? for unpolarized quarks in unpolarized nucleon - non-trivial correlations between b? and k? due to orbital angular momentum

  13. Integrating over b ? • Integrating over k ? charge density in the transverse plane b? neutron proton charge distribution in the transverse plane [Miller (2007); Burkardt (2007)]

  14. LC helicity amplitudes nucleon ( ¤’ ¤ ) quark ( ¸’ ¸ ) Independentquarks LC helicity $canonical spin rotation around an axis orthogonal to z and k LC helicity canonical spin

  15. Light-Cone Helicity and Canonical Spin rotation around an axis orthogonal to z and k LC helicity canonical spin Light-Cone CQM Chiral Quark-Soliton Model Bag Model (Melosh rotation)

  16. º! quark polarization ¹! nucleon polarization ( ) 16 GTMDs Active quark : Spectator quarks : Model Independent Spin Structure

  17. Backup

  18. k k k T T T Unpolarized u quark in unpolarized proton µ 0 ¼/2 ¼ 3/2 ¼ k T 0.1 GeV 0.2 GeV 0.3 GeV , q fixed k 0.4 GeV T

  19. k k T T Generalized Transverse Charge Densities = + µ = 0 fixed µ = ¼/2 Unpolarized u quark in unpolarized proton

  20. k T Wigner function for transversely pol. quark in longitudinally pol. nucleon T-odd sx b q µ = ¼/2 µ = 0 k ,µ fixed T

  21. k T Wigner function for transversely pol. quark in longitudinally pol. nucleon fixed sx Dipole Monopole Monopole + Dipole µ = 0 µ = ¼/2

  22. k k k T T T u quark pol. in x direction in longitudinally pol.proton µ 0 ¼/2 ¼ 3/2 ¼ k T 0.1 GeV 0.2 GeV 0.3 GeV , q fixed k 0.4 GeV T

  23. Integrating over k ? density in the transverse plane k?of transversely pol. u and d quark in longitudinally pol nucleon • Integrating over b ? sx up down BP, Cazzaniga, Boffi, PRD78 (2008)Lorce`, BP, in preparation Haegler, Musch, Negele, Schaefer, Europhys. Lett. 88 (2009)

More Related