2025/07/24 by Vladimir Pascalutsa, Pascalutsa, Vladimir
Mathematics · #Advanced Topics in Algebra #Holomorphic and Operator Theory #Algebraic and Geometric Analysis
paper · pdf · doi:10.48550/arxiv.2507.18234
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 Q2. 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 γ^∗ γ^∗ 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 σL/ σT → 0 at high energy, for the ratio of unpolarized nucleon photoabsorption cross sections.