Rigorous Bounds on Light-by-Light Scattering

TL;DR

This paper establishes rigorous bounds on effective field theory coefficients for light-by-light scattering, using fundamental principles like unitarity and crossing symmetry, and compares these bounds with possible UV completions.

Contribution

It introduces new sum rules and null constraints to derive bounds on higher-derivative operators in photon scattering EFTs, including two-sided bounds on their ratios.

Findings

Some bounds are saturated by known UV completions with massive scalars or axions.

Certain bounds suggest the existence of unknown amplitudes beyond current models.

The work provides a systematic framework for constraining EFT coefficients in photon scattering.

Abstract

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.