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The dual parametrization and the Mellin-Barnes integral approach representtwo frameworks for handling the double partial wave expansion of generalizedparton distributions (GPDs) in the conformal partial waves and in the$t$-channel ${\rm SO}(3)$ partial waves. Within the dual parametrizationframework, GPDs are represented as integral convolutions of forward-likefunctions whose Mellin moments generate the conformal moments of GPDs. TheMellin-Barnes integral approach is based on the analytic continuation of theGPD conformal moments to the complex values of the conformal spin. GPDs arethen represented as the Mellin-Barnes-type integrals in the complex conformalspin plane. In this paper we explicitly show the equivalence of these twoindependently developed GPD representations. Furthermore, we clarify thenotions of the $J=0$ fixed pole and the $D$-form factor. We also provide someinsight into GPD modeling and map the phenomenologically successfulKumeri\v{c}ki-M\"uller GPD model to the dual parametrization framework bypresenting the set of the corresponding forward-like functions. We also buildup the reparametrization procedure allowing to recast the double distributionrepresentation of GPDs in the Mellin-Barnes integral framework and present theexplicit formula for mapping double distributions into the space of doublepartial wave amplitudes with complex conformal spin.

Dual parametrization of generalized parton distributions in two equivalent representations