Low and moderate $x$ gluon contribution to exclusive Compton scattering processes

TL;DR

This paper refines the semi-classical approach to exclusive scattering processes like DVCS and TCS by explicitly incorporating Feynman $x$ dependence, deriving a compact formula, and analyzing the small $x$ behavior.

Contribution

It introduces a modified shock wave approximation and a partial twist expansion to explicitly include Feynman $x$ dependence in the analysis of exclusive processes.

Findings

Derived a compact factorized master formula for exclusive processes.

Recovered the full one-loop collinear limit for gluon exchange.

Discussed the interplay of collinear and small $x$ limits.

Abstract

We revisit the high energy semi-classical description of the exclusive processes DVCS, TCS, and Double DVCS by explicitly keeping track of the Feynman $x$ dependence in both the hard and the hadronic matrix elements. This is achieved by a modification of the standard shock wave approximation to derive the effective Feynman rules, which leads to a generic expression on which we then perform a partial twist expansion to get rid of quantities suppressed by the proper physical scales. We obtain a compact factorized master formula that can be used to investigate the Bjorken limit at leading twist. In particular, we recover the full one-loop result in the collinear limit for pure gluon exchange with the target. Finally, we discuss the subtleties in taking the simultaneous collinear and small $x$ limit.