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We consider two simple covariant models for pions (one with scalar and theother with spin-1/2 constituents). Pion generalized parton distributions arederived by integration over the light-cone energy. The model distributions areconsistent with all known properties of generalized parton distributions,including positivity. We also construct the corresponding double distributionsby appealing to Lorentz invariance. These ostensibly constructed doubledistributions lead to different generalized parton distributions that need notrespect the positivity constraints. This inconsistency arises from theambiguity inherent in defining double distributions in a one-componentformalism (even in the absence of the Polyakov-Weiss term). We demonstrate thatthe correct model double distributions can be calculated from non-diagonalmatrix elements of twist-two operators.Comment: 10 pages, 7 figures, RevTex4, reference added, typos correcte

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

Generalized parton distributions and double distributions for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>q</mml:mi><mml:mrow><mml:mrow><mml:mover><mml:mrow><mml:mi>q</mml:mi></mml:mrow><mml:mrow><mml:mi>¯</mml:mi></mml:mrow></mml:mover></mml:mrow></mml:mrow></mml:math>pions

Generalized parton distributions and double distributions forqq¯pions