Dual parametrization of generalized parton distributions in two equivalent representations

Abstract

Abstract:The dual parametrization and the Mellin-Barnes integral approach represent two frameworks for handling the double partial wave expansion of generalized parton distributions (GPDs) in the conformal partial waves and in the t-channel SO(3) partial waves. Within the dual parametrization framework, GPDs are represented as integral convolutions of forward-like functions whose Mellin moments generate the conformal moments of GPDs. The Mellin-Barnes integral approach is based on the analytic continuation of the GPD conformal moments to the complex values of the conformal spin. GPDs are then represented as the Mellin-Barnes-type integrals in the complex conformal spin plane. In this paper we explicitly show the equivalence of these two independently developed GPD representations. Furthermore, we clarify the notions of the J = 0 fixed pole and the D-form factor. We also provide some insight into GPD modeling and map the phenomenologically successful Kumerički-Müller GPD model to the dual parametrization framework by presenting the set of the corresponding forward-like functions. We also build up the reparametrization procedure allowing to recast the double distribution representation of GPDs in the Mellin-Barnes integral framework and present the explicit formula for mapping double distributions into the space of double partial wave amplitudes with complex conformal spin.

J=0fixed pole andD-term form factor in deeply virtual Compton scattering

“…(3.13). The analogous cancelation appears also in the framework of dual parametrization of GPDs [24].…”

“…6.2 of Ref. [24]. In other words, experimental data turn to be directly sensitive only to a possible additional non-universal contribution ∆H ∞ (t|ϑ) into H ∞ (t|ϑ) (c.f.…”

“…[24,27], the analytic properties in j of GPD Gegenbauer/Mellin moments control the validity of the internal duality principle for GPDs (see also discussion in Ref. [28]).…”

“…6.3 of Ref. [24], it is instructive to consider the Froissart-Gribov projection [3,4] of the cross channel SO(3) PWs of the CFF H(ξ, t|ϑ): 11) where, neglecting the threshold corrections…”

“…This representation is known in two versions (the approach based on the Mellin-Barnes integral techniques of Ref. [20], and the so-called dual parametrization approach [21][22][23]) that were recently found to be completely equivalent [24]. Within this approach it was first realized that the problem of universality of J = 0 fixed pole is related to the analytic properties of GPD moments in the complex conformal spin j.…”