Low-energy Compton scattering on the nucleon and sum rules

The Gerasimov-Drell-Hearn and Baldin-Lapidus sum rules are evaluated in a relativistic, unitary, crossing symmetric and gauge-invariant model for photon-induced reactions on the nucleon. The property of analyticity is partially incorporated through a dressing procedure for propagators and vertices. The sum α + β of the electric and magnetic polarisabilities and the forward spin polarisability γ0 are calculated in two alternative ways – from the sum rules and from the low-energy expansion of the real Compton scattering amplitude – within the same framework. The two methods yield compatible values for α + β but differ for γ0. We suggest that dressing the ∆ resonance beyond a one-loop approximation is important to achieve consistency between the sum-rule and low-energy calculations of the spin polarisability. Typeset using REVTEX