The two-loop coefficient functions for double deeply virtual Compton scattering

TL;DR

This paper computes the two-loop coefficient functions for double deeply virtual Compton scattering using conformal symmetry in large-$n_f$ QCD, providing essential corrections for high-precision theoretical predictions.

Contribution

It presents the first calculation of two-loop coefficient functions in this context, advancing the accuracy of theoretical descriptions of double deeply virtual Compton scattering.

Findings

Calculated large two-loop corrections significantly affect Compton form factors.

Analytic expressions provided in momentum fraction space in the $ar{MS}$ scheme.

Corrections are substantial for experimental kinematics.

Abstract

Making use of conformal symmetry of large-$n_f$ QCD in $d=4-2\epsilon$ dimensions at the Wilson-Fischer fixed point, we calculate the two-loop coefficient functions in the operator product expansion of two electromagnetic currents in general kinematics with two different photon virtualities. This result is necessary for the description of the double deeply virtual Compton scattering to the next-to-next-to-leading order accuracy, but is also interesting for a range of other two-photon processes. We present analytic expression for the coefficient function in momentum fraction space in the $\overline{\text{MS}}$ scheme and study its numerical impact on the Compton form factors for a simple model of the generalized parton distributions. The calculated corrections turn out to be large and are significant for the kinematics of proposed experiments.