Next-to-leading order corrections to timelike, spacelike, and double deeply virtual Compton scattering

Abstract

We calculate the $O({\ensuremath{\alpha}}_{s})$ corrections to the timelike, spacelike, and double deeply virtual Compton scattering amplitudes in the generalized Bjorken scaling region. Special attention is devoted to studies of the difference between the next-to-leading order timelike and spacelike coefficient functions, which plays for this process a role analogous to the large $K$ factor which was much discussed in the analysis of inclusive Drell-Yan cross sections. Also in the present studies the timelike nature of the hard scale gives rise to a new absorptive part of the amplitude and to the presence of characteristic ${\ensuremath{\pi}}^{2}$ terms, which can potentially lead to sizable corrections.