All order factorization for virtual Compton scattering at next-to-leading power

We discuss all-order factorization for the virtual Compton process at next-to-leading power (NLP) in the ΛQCD/Q and √-t/Q expansion (twist-3), both in the double-deeply-virtual case and the single-deeply-virtual case. We use the soft-collinear effective theory (SCET) as the main theoretical tool. We conclude that collinear factorization holds in the double-deeply virtual case, where both photons are far off-shell. The agreement is found with the known results for the hard matching coefficients at leading order αₛ⁰, and we can therefore connect the traditional approach with SCET. In the single-deeply-virtual case, commonly called deeply virtual Compton scattering (DVCS), the contribution of non-target collinear regions complicates the factorization. These include momentum modes collinear to the real photon and ultrasoft interactions between the photon-collinear and target-collinear modes. Indeed, we identify a potentially problematic non-perturbative contribution, which might violate the universality of the generalized parton distributions (GPDs) at NLP accuracy.