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

TL;DR

This paper establishes all-order factorization for virtual Compton scattering at next-to-leading power using SCET, clarifying the conditions under which collinear factorization holds in different virtual photon polarization cases.

Contribution

It demonstrates collinear factorization at NLP for virtual Compton scattering in both double- and single-deeply-virtual regimes, connecting SCET with traditional approaches and analyzing polarization effects.

Findings

Collinear factorization holds in double-virtual case at NLP.

Non-target collinear contributions affect transversely polarized DVCS at NLP.

Longitudinally polarized virtual photon DVCS amplitude is free of non-target collinear contributions.

Abstract

We discuss all-order factorization for the virtual Compton process at next-to-leading power (NLP) in the $\Lambda_{\rm QCD}/Q$ and $\sqrt{-t}/Q$ 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 $\alpha_s^0$, 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 (ultra)soft interactions between the photon-collinear and target-collinear modes. However, such contributions appear only for the transversely polarized virtual photon at the NLP accuracy and in fact it is the only NLP $\sim (\Lambda_{\rm QCD}/Q)^1 \sim (\sqrt{-t}/Q)^1$ contribution in that case. We therefore conclude that the DVCS amplitude for a longitudinally polarized virtual photon, where the leading power $\sim (\Lambda_{\rm QCD}/Q)^0 \sim (\sqrt{-t}/Q)^0$ contribution vanishes, is free of non-target collinear contributions and the collinear factorization in terms of twist-3 GPDs holds in that case as well.