Dual parametrization of GPDs versus the double distribution Ansatz

TL;DR

This paper links the dual parametrization of GPDs with the double distribution Ansatz, showing how forward-like functions influence the small-x behavior of DVCS amplitudes and fixing the D-form factor through Mellin moments.

Contribution

It establishes a connection between dual parametrization and double distribution Ansatz for GPDs, providing explicit expressions for forward-like functions and their impact on DVCS amplitude behavior.

Findings

Forward-like functions dominate the GPD quintessence function.

Small-x_Bj behavior of DVCS amplitude is independent of PDF asymptotics.

The D-form factor is expressed in terms of GPD quintessence and forward-like functions.

Abstract

We establish a link between the dual parametrization of GPDs and a popular parametrization based on the double distribution Ansatz, which is in prevalent use in phenomenological applications. We compute several first forward-like functions that express the double distribution Ansatz for GPDs in the framework of the dual parametrization and show that these forward-like functions make the dominant contribution into the GPD quintessence function. We also argue that the forward-like functions $Q_{2 \nu}(x)$ with $\nu \ge 1$ contribute to the leading singular small-$x_{Bj}$ behavior of the imaginary part of DVCS amplitude. This makes the small-$x_{Bj}$ behavior of $\im A^{DVCS}$ independent of the asymptotic behavior of PDFs. Assuming analyticity of Mellin moments of GPDs in the Mellin space we are able to fix the value of the $D$-form factor in terms of the GPD quintessence function $N(x,t)$ and the forward-like function $Q_0(x,t)$.