Limitations on dispersion relations for Generalized Parton Distributions

TL;DR

This paper examines the application of dispersion relations to Generalized Parton Distributions in scattering processes, revealing significant unphysical regions that challenge the practicality of such methods.

Contribution

It demonstrates that unphysical regions in non-forward dispersion relations are substantial, complicating the extraction of real parts of scattering amplitudes.

Findings

Unphysical regions in non-forward DRs are large at non-zero momentum transfer.

Applying DRs to GPDs involves integration over unphysical regions, limiting their usefulness.

Direct measurement of real parts may be more practical than dispersion relation approaches.

Abstract

Deeply Virtual Compton Scattering and electroproduction of mesons involve amplitudes that are analytic in energy. Analyticity enables Dispersion Relations (DR's) for such amplitudes, relating real and imaginary parts. Lately it has been suggested that DR's be applied to the integrated Generalized Parton Distributions that embody the spin-dependent soft, but factorizable part of the scattering. 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, vitiating efforts to avoid the actual measurement of the real parts more directly.