Rigorous Bounds on Light-by-Light Scattering

Understand

We bound EFT coefficients appearing in $2 \to 2$ photon scattering amplitudes in four dimensions.

• After reviewing unitarity and positivity conditions in this context, we use dispersion relations and crossing symmetry to compute sum rules and null constraints.
• This allows us to derive new rigorous bounds on operators with four, six, and eight derivatives, including two-sided bounds on their ratios.
• Comparing with a number of partial UV completions, we find that some of our bounds are saturated by the amplitudes that arise from integrating out a massive scalar or axion, while others suggest the existence of unknown amplitudes.