New superconvergence relations for spin and tensor structure functions of $\gamma\gamma$ fusion

The Burkhardt--Cottingham sum rule is an exact superconvergence relation for a spin-structure function, derived from general principles of light absorption and scattering, and valid at any momentum transfer $Q^2$. I illustrate how a class of such relations emerges from the Siegert point, an unphysical kinematical point where both the probe and the target are at rest. From light-by-light scattering, new sum rules for $\gamma^\ast \gamma^\ast$ fusion are emerging, valid for arbitrary photon virtualities. Regarding the convergence of these relations, there is a simple argument for the suppression of longitudinal photon polarizations at high energy. Among its consequences is the prediction of $\sigma_L/ \sigma_T \to 0$ at high energy, for the ratio of unpolarized nucleon photoabsorption cross sections.