Generalized parton distributions and double distributions for q q-bar pions

Abstract

We consider two simple covariant models for pions (one with scalar and the other with spin-1/2 constituents). Pion generalized parton distributions are derived by integration over the light-cone energy. The model distributions are consistent with all known properties of generalized parton distributions, including positivity. We also construct the corresponding double distributions by appealing to Lorentz invariance. These ostensibly constructed double distributions lead to different generalized parton distributions that need not respect the positivity constraints. This inconsistency arises from the ambiguity inherent in defining double distributions in a one-component formalism (even in the absence of the Polyakov-Weiss term). We demonstrate that the correct model double distributions can be calculated from non-diagonal matrix elements of twist-two operators.

10 pages, 7 figures, RevTex4, reference added, typos corrected

References in corpus (4)

• Integral representations for nonperturbative GPDs in terms of perturbative diagrams
• Generalized parton distributions for $q\bar{q}$ pions
• Current in the light-front Bethe-Salpeter formalism II: Applications
• Current in the light-front Bethe-Salpeter formalism I: Replacement of non-wave function vertices

Cited by in corpus (33)

• Generalized Parton Distributions
• Unraveling hadron structure with generalized parton distributions
• GPD phenomenology and DVCS fitting - Entering the high-precision era
• Generalized parton distributions of the pion in chiral quark models and their QCD evolution
• Pion Generalized Parton Distributions with covariant and Light-front constituent quark models
• Generalized parton distributions of the pion in a Bethe-Salpeter approach
• Sketching the pion's valence-quark generalised parton distribution
• Gravitational and higher-order form factors of the pion in chiral quark models
• From Bethe-Salpeter Wave Functions to Generalised Parton Distributions
• The dual parameterization of the proton generalized parton distribution functions H and E and description of the DVCS cross sections and asymmetries
• The transverse structure of the pion in momentum space inspired by the AdS/QCD correspondence
• Deeply virtual Compton scattering on a virtual pion target
• Dual parameterization of generalized parton distributions and description of DVCS data
• Double distributions: Loose ends
• Estimates for Pion-Photon Transition Distributions
• An introductory lecture on Generalised Parton Distributions
• Virtual Compton scattering in the generalized Bjorken region and positivity bounds on generalized parton distributions
• Double distributions for the proton
• The Relation Between Equal-Time and Light-Front Wave Functions
• Complex conjugate poles and parton distributions
• Neutron contribution to nuclear DVCS asymmetries
• Towards a Pion Generalized Parton Distribution Model from Dyson-Schwinger Equations
• Relativity and constituent quark structure in model calculations of parton distributions
• A note on the QCD evolution of generalized form factors
• Inequalities for nucleon generalized parton distributions with helicity flip
• QCD Sum Rules and Models for Generalized Parton Distributions
• DSE inspired model for the pion's valence dressed-quark GPD
• Generalized Parton Distributions -- theoretical review --
• Violation of Positivity Bounds in Models of Generalized Parton Distributions
• Generalized Parton Distributions of Pions. Spin Structure of Hadrons
• Generalized vector form factors of the pion in a chiral quark model
• Pion's valence-quark GPD and its extension beyond DGLAP region
• Generalised Parton Distributions: A Dyson-Schwinger approach for the pion