Abstract
A systematic approach for the model building of Generalized Parton Distributions (GPDs), based on their overlap representation within the DGLAP kinematic region and a further covariant extension to the ERBL one, is applied to the valence-quark pion's case, using light-front wave functions inspired by the Nakanishi representation of the pion Bethe–Salpeter amplitudes (BSA). This simple but fruitful pion GPD model illustrates the general model building technique and, in addition, allows for the ambiguities related to the covariant extension, grounded on the Double Distribution (DD) representation, to be constrained by requiring a soft-pion theorem to be properly observed.
Highlights
Generalized Parton Distributions (GPDs) provide a three-dimensional picture of hadrons [1], unifying both Parton Distributions Functions (PDFs) and Form Factors into a single nonperturbative object which yields information about the distributions of partons within the light front
We deal here with the ambiguities related to the covariant extension to the ERBL region, by using a soft-pion theorem [29] for their constraining, and produce a full sketch of the pion valence-quark GPD based on the Bethe– Salpeter light-front wave functions (LFWFs)
Since the PDA is completely described by the two-body LFWF, one can wonder whether there is some genuine information in the 4-body LFWF interplaying with the 2-body one via overlap to produce a GPD fulfilling the soft pion theorem in our lowest-Fock-states approach
Summary
GPDs provide a three-dimensional picture of hadrons [1], unifying both Parton Distributions Functions (PDFs) and Form Factors into a single nonperturbative object which yields information about the distributions of partons within the light front After their introduction 20 years ago [2,3,4], GPDs became a hot topic in hadron physics which many experimental and theoretical efforts have been since devoted to The technique was developed only for a specific algebraic model of light-front wave functions (LFWFs) We generalized it recently in a model-independent way based on the Radon inverse transform in Ref. We deal here with the ambiguities related to the covariant extension to the ERBL region, by using a soft-pion theorem [29] for their constraining, and produce a full sketch of the pion valence-quark GPD based on the Bethe– Salpeter LFWFs
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