Compton scattering sum rules for electromagnetic moments of higher-spin targets

In 1965, a sum rule for the anomalous magnetic moment of nucleons in doubly-polarized Compton scattering was derived by Gerasimov and by Drell and Hearn (GDH). It is a fundamental relation in dispersion theory of QCD, based on properties of the amplitude, such as analyticity and crossing symmetry. For the derivation, the low-energy theorem by Low, and Gell-Mann and Goldberger, as well as the optical theorem is applied. For S ≥(1)/(2) particles higher order anomalous moments become relevant. In this work, we focused on massive S=1 particles. Using a generalized decomposition of the polarized forward Compton scattering amplitude for arbitrary spin S, we were able to obtain sum rules for anomalous magnetic and quadrupole moments. The method of derivation of arbitrary spin is discussed, as well as an approach to verifying our result.