Limitations on dispersion relations for Generalized Parton Distributions

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.