  Using the helicity amplitudes formalism, we study deeply virtual exclusive
electron photo-production off an unpolarized nucleon target, $ep \rightarrow e'
p' \gamma$, through a range of kinematics both in the fixed target setting with
initial electron energies of 6 GeV, 11 GeV and 24 GeV, and for an electron ion
collider. We reformulate the cross section bringing to the forefront the
defining features of the $ep \rightarrow e'p'\gamma$ process, where the
observables are expressed as bilinear products of the independent helicity
amplitudes which completely describe it in terms of the electric, magnetic and
axial currents of the nucleon. %This structure is reflected in different ways
in the Deeply virtual Compton scattering and Bethe-Heitler parts of the cross
section. % These contributions are checked against the Fourier harmonics-based
formalism which has provided so far the underlying mathematical framework to
study Deeply virtual Compton scattering and related experiments. Using
theoretical model calculations of the twist-two generalized parton
distributions, $ H$, $E$, $\widetilde{H}$ and $\widetilde{E}$, we uncover large
discrepancies between the harmonic series and our proposed framework. Most
importantly, these numerical differences appear in the intermediate $Q^2$ range
which represents a sweet spot for extracting generalized parton distributions
from data. % We provide a framework that is ideal, on one side, to study and
compare the different conventions that can be used to describe the leading
order contribution to DVCS in QCD, while on the other, it facilitates a
quantitative extraction of physically meaningful information from experiment
through traceable and controllable approximations in the intermediate $Q^2$
region.
