Proof of Factorization for Deeply Virtual Compton Scattering in QCD

TL;DR

The authors prove that the deeply virtual Compton scattering amplitude in QCD factorizes into convolutions of off-forward parton distributions with perturbatively calculable hard-scattering coefficients, up to power-suppressed terms, valid to all orders in the strong coupling.The proof adapts a momentum-space, contour-analytic approach to factorization, establishing leading regions via pinch surfaces, ruling out soft contributions at leading power, and ensuring gauge invariance through Wilson-line constructions.Key contributions include a robust treatment of breakpoints at $x_1=0$ and $x_2=0$, a clear power-counting framework, and a complete all-orders demonstration that the produced photon's virtuality does not affect the factorization theorem.The result solidifies the use of generalized (off-forward) parton distributions in DVCS as a clean probe of nucleon structure, with implications for related exclusive processes.

Abstract

We show that factorization holds for the deeply virtual Compton scattering amplitude in QCD, up to power suppressed terms, to all orders in perturbation theory. Furthermore, we show that the virtuality of the produced photon does not influence the general theorem.

Figures (6)

• Figure 1: a) Reduced graph for DVCS with direct coupling for the out-going photon to hard subgraph. b) The same without a direct like coupling for the out-going photon.
• Figure 2: Those reduced graphs that contribute to the leading regions in DVCS.
• Figure 3: Soft gluon loop attaching to collinear line.
• Figure 4: a) A scalar gluon attaching the collinear subgraph to the hard subgraph $H$ in the unfactorized form. b) Factorized form after application of gauge invariance and Ward-identities. The double line represents the eikonal line to which the scalar gluon attaches.
• Figure 5: Particular example of potentially problematic diagram.