Two-loop corrections to Light-by-Light scattering in Supersymmetric QED
T. Binoth, E. W. N. Glover, P. Marquard, J. J. van der Bij
TL;DR
The paper develops an n-dimensional projection framework to compute two-loop light-by-light scattering amplitudes with massless internal particles and applies it to both the Standard Model and SUSY QED. It reduces the tensor structure to three independent coefficients and constructs projection operators to isolate them, enabling a graph-by-graph, regulator-friendly calculation. The results confirm the Standard Model two-loop amplitudes and reveal systematic supersymmetric cancellations: in N=1, two helicity amplitudes vanish and the remaining one simplifies with higher weight functions; in N=2, the amplitude further simplifies to weight-4 contributions with no scale-ratio dependence. Overall, the method provides an efficient, scalable approach to multi-loop helicity amplitudes and highlights striking SUSY-induced simplifications that may extend to more complex theories.
Abstract
We use an n-dimensional projection method to calculate helicity amplitudes for photon-photon scattering up to the two-loop level, for massless particles inside the loop. We confirm the recent standard model results found by Bern et al using another calculational method. We further apply the method to N=1 and N=2 supersymmetric QED. As predicted by the supersymmetric Ward identity, two of the independent amplitudes vanish. The remaining amplitude simplifies as the number of supersymmetries increases. For N=2 SUSY QED, only contributions of weight 4 remain.