Exclusive Meson Electroproduction: GPDs, Regge and Dispersion Relations

TL;DR

This paper explores the connection between GPDs, Regge theory, and dispersion relations in exclusive pi0 electroproduction, highlighting the challenges in extracting real parts of amplitudes due to unphysical regions in dispersion integrals.

Contribution

It demonstrates the relation between GPDs and Regge exchanges in pi0 electroproduction and analyzes the limitations of dispersion relations in non-forward kinematics.

Findings

GPDs are related to C-odd Regge exchanges with final state interactions.

Dispersion relations face significant unphysical regions at non-zero momentum transfer.

Unphysical regions complicate the extraction of real parts of amplitudes from experimental data.

Abstract

Exclusive pi0 electroproduction from nucleons at large photon virtuality can be described in terms of Generalized Parton Distributions, particularly the chiral odd subset. Chiral odd GPDs are related to transversity and can be accessed experimentally for various special choices of observables. This is accomplished by choosing C-parity odd and chiral odd combinations of t-channel exchange quantum numbers. These GPDs are calculated in a spectator model, and are constrained by boundary functions. Alternatively, the production amplitudes correspond to C-odd Regge exchanges with final state interactions. The helicity structure of the virtual photoproduction amplitudes provides relations between the partonic description via GPDs and the hadronic, Regge description of C-odd processes, all via quark helicity flip. GPDs, in general, are analytic functions of energy variables. Their integrals over unobservable parton momenta thereby satisfy Dispersion Relations (DR). Using DR's could allow the real part of the amplitudes, the integrated GPDs, to be extracted from the more easily measured imaginary parts. However, at non-zero momentum transfer DRs require integration over unphysical regions of the variables. We show that the relevant unphysical region of the non-forward DRs is considerable. This will vitiate the efforts to avoid the actual measurement of the real parts more directly.