Two-photon processes in conformal QCD: Resummation of the descendants of leading-twist operators

TL;DR

This paper derives a comprehensive expression for the contributions of leading twist operators and their descendants to the operator product expansion in QCD, applicable to processes like deeply-virtual Compton scattering, using conformal field theory techniques.

Contribution

It provides a novel closed-form resummation of all twist contributions in the OPE of electromagnetic currents in QCD, including all orders in perturbation theory up to beta-function corrections.

Findings

Matches previous results at twist-four accuracy

Resums contributions of all twists and orders in perturbation theory

Provides a simple OPE representation for scalar currents

Abstract

Using some techniques of conformal field theories, we find a closed expression for the contribution of leading twist operators and their descendants, obtained by adding total derivatives, to the operator product expansion (OPE) of two electromagnetic currents in QCD. Our expression resums contributions of all twists and to all orders in perturbation theory up to corrections proportional to the QCD $\beta$-function. At tree level and to twist-four accuracy, our result agrees with the expression derived earlier by a different method. The results are directly applicable to deeply-virtual Compton scattering and, e.g., $\gamma\gamma^\ast$ annihilation in two mesons. As a byproduct, we derive a simple representation for the OPE of two scalar currents that is convenient for applications.