Dispersion relations of deeply virtual Compton scattering: investigating twist-4 kinematic power corrections

In this paper we include kinematic power corrections up to twist-four to the deeply virtual Compton scattering dispersion relation. We demonstrate that, both for (pseudo-)scalar and spin-$1/2$ targets, the formal expression of the n-subtracted leading-twist dispersion relations is preserved. However, the expression of the subtracted constants is modified by the kinematic powers. Importantly, the minimal-subtracted dispersion relation for the helicity-conserving amplitude, previously thought to depend only on the Polyakov-Weiss D-term, now also depends on the double distributions F and K. These results are consistent with the ones obtained previously in the literature. Such a mixing may be critical for the Jefferson Lab kinematic range, as it is not suppressed for typical values of t and Q² in the valence region. We therefore expect a strong impact on attempts to extract pressure forces from DVCS data.