Resumming soft and collinear contributions in deeply virtual Compton scattering

TL;DR

This paper develops an all-order resummation of soft and collinear gluon contributions in deeply virtual Compton scattering, providing a simplified closed-form expression for the dominant double logarithmic terms near the kinematic boundaries.

Contribution

It introduces a novel resummation formula for leading double logarithmic contributions in DVCS, extending known one-loop results to all orders in perturbation theory.

Findings

Derived an all-order resummation formula for DVCS amplitude

Provided a simplified closed-form expression for dominant contributions

Validated the resummation near the kinematic boundaries of x = ± xi

Abstract

We calculate the quark coefficient function Tq(x,xi) that enters the factorized amplitude for deeply virtual Compton scattering (DVCS) at all order in a soft and collinear gluon approximation, focusing on the leading double logarithmic behavior in x +/- xi, where x +/- xi is the light cone momentum fraction of the incoming/outgoing quarks. We show that the dominant part of the known one loop result can be understood in an axial gauge as the result of a semi-eikonal approximation to the box diagram. We then derive an all order result for the leading contribution of the ladder diagrams and deduce a resummation formula valid in the vicinity of the boundaries of the regions defining the energy flows of the incoming/outcoming quarks, i.e. x = +/- xi. The resummed series results in a simple closed expression.