Two-loop QED and QCD corrections to massless fermion-boson scattering

TL;DR

This work delivers NNLO virtual corrections for massless 2→2 scattering processes involving photons, including q q̄ → g γ, q q̄ → γ γ, and e⁻ e⁺ → γ γ, along with crossing-related channels. Using conventional dimensional regularization and MSbar renormalization, the authors verify the infrared pole structure against Catani's predictions and provide finite remainders expressed through real logarithms and polylogarithms, organized by color and flavor. They derive explicit I^(1)(ε) and I^(2)(ε) operators (with H^(2) constants decomposed per external leg) and extract the finite parts of both the 0×2 and 1×1 contributions, enabling precise NNLO predictions for these photon-involving processes. The paper also underscores the broader challenge of achieving full NNLO accuracy by combining these virtual pieces with the required real-emission contributions, paving the way for improved theoretical precision in prompt photon phenomenology. Overall, the work advances the methodological groundwork for NNLO QCD/QED calculations in massless 2→2 scattering with photons.

Abstract

We present the NNLO QCD virtual corrections for qurak-antiquark -> gluon photon, quark-antiquark -> photon photon and the NNLO QED virtual corrections for electron positron -> photon photon and all processes related by crossing symmetry. We perform an explicit evaluation of the two-loop diagrams in conventional dimensional regularisation, and our results are renormalised in the MSbar scheme. The infrared pole structure of the amplitudes is in agreement with the prediction of Catani's general formalism for the singularities of two-loop amplitudes, while expressions for the finite remainder are given for all processes in terms of logarithms and polylogarithms that are real in the physical region.

Figures (1)

• Figure 1: Feynman diagrams representative of (a) "light-by-light" scattering and (b) "abelian gluon" exchange. These graphs contribute to $A_c$ and $B_c$ respectively. Depending on the process, the zigzag lines represent either photons or gluons.