Low-energy Compton scattering on the nucleon and sum rules

Abstract

The Gerasimov-Drell-Hearn and Baldin-Lapidus sum rules are evaluated in the dressed K-matrix model for photon-induced reactions on the nucleon. For the first time the sum $α+β$ of the electric and magnetic polarisabilities and the forward spin polarisability $γ_0$ are explicitly calculated in two alternative ways -- from the sum rules and from the low-energy expansion of the real Compton scattering amplitude -- within the {\em same} framework. The two methods yield compatible values for $α+β$ but differ somewhat for $γ_0$. Consistency between the two ways of determining the polarisabilities is a measure of the extent to which basic symmetries of the model are obeyed.