The six-photon amplitude
C. Bernicot
TL;DR
The paper investigates six-photon one-loop amplitudes as a rigorous testbed for multi-leg quantum corrections, leveraging the absence of tree-level contributions and rational terms to study Landau singularities associated with double parton scattering. It delivers compact analytic expressions for all helicity amplitudes across QED, scalar QED, and $ extrm{QED}^{ extrm{N}=1}$, expressed as linear combinations of $n+2$-dimensional four-point and $n$-dimensional three-external-mass scalar integrals, and analyzes kinematic configurations (Nagy–Soper) where dual-photon scattering reveals a DPS-like Landau structure. By introducing a regulator and examining the NMHV amplitudes as a function of the rotation angle, the work shows that the apparent singularity is regularized: the amplitude remains finite because the numerator vanishes at the Landau point. Overall, the study demonstrates the utility of six-photon amplitudes for exploring loop analyticity and the behavior of Landau singularities, with implications for unitarity-based NLO methods and DPS phenomena in high-energy processes.
Abstract
Thanks to the absence of tree order, the six-photon processes is a good laboratory to study multi-leg one-loop diagrams. Particularly, there are enough on-shell external legs to observe a special Landau singularity: the double parton scattering.