Sum rules for light-by-light scattering

TL;DR

This paper derives and verifies sum rules for light-by-light scattering, revealing superconvergence properties and potential experimental tests, with implications for understanding meson contributions and low-energy photon interactions.

Contribution

It introduces new sum rules for light-by-light scattering and fusion, verified in QED, with implications for hadronic contributions and experimental measurements.

Findings

Sum rules verified in lowest order QED calculations.

Helicity-difference cross-section exhibits superconvergence.

Potential for experimental tests at polarized colliders.

Abstract

We derive a set of sum rules for the light-by-light scattering and fusion: $\gamma\gamma \to all$, and verify them in lowest order QED calculations. A prominent implication of these sum rules is the superconvergence of the helicity-difference total cross-section for photon fusion, which in the hadron sector reveals an intricate cancellation between the pseudoscalar and tensor mesons. An experimental verification of superconvergence of the polarized photon fusion into hadrons is called for, but will only be possible at $e^+ e^-$ and $\gamma\gamma$ colliders with both beams polarized. We also show how the sum rules can be used to measure various contributions to the low-energy light-by-light scattering.