Analytic Properties of Hard Exclusive Amplitudes

TL;DR

This paper explores the analytic properties of Generalized Parton Distributions (GPDs) and their extensions, Generalized Distribution Amplitudes (GDAs), highlighting their role in understanding exclusive processes and exotic states in particle physics.

Contribution

It introduces the analytic continuation of GPDs via GDAs and discusses the holographic property of GPDs, linking various hard processes through one-dimensional sections.

Findings

GDA's can access four-quark exotic states.

Polynomiality (Cavalieri conditions) underpins GPD analyticity.

Analyticity aids in describing double diffractive production processes.

Abstract

Analytic properties of hard exclusive processes described by Generalized Parton Distributions (GPD's) are considered. The analytic continuation of GPD is provided by Generalized Distribution Amplitudes (GDA). The GDA's for the production of two $\rho-$mesons may give an access to four-quark exotic states. The crucial role in the proof of analyticity is played by the Cavalieri conditions (polynomiality), resulting in the "holographic" property of GPD, when the full information about various hard processes is contained in the one dimensional sections ($x=\pm \xi$)of GPD. The applicability of analyticity for description of the double diffractive production of dileptons and Higgs bosons is discussed.