Burkhardt-Cottingham sum rule and forward spin polarizabilities in heavy baryon chiral perturbation theory

Abstract

We study spin-dependent sum rules for forward virtual Compton scattering (VVCS) off the nucleon in heavy baryon chiral perturbation theory (HBChPT) at order $\mathcal{O}{(p}^{4}).$ We show how these sum rules can be evaluated from low energy expansions (in the virtual photon energy) of the forward VVCS amplitude. We study in particular the Burkhardt-Cottingham sum rule in HBChPT and the higher terms in the low energy expansion, which can be related to the generalized forward spin polarizabilities of the nucleon. The dependence of these observables on the photon virtuality ${Q}^{2}$ can be accessed, at small and intermediate ${Q}^{2}$ values, from existing and forthcoming data at Jefferson Lab.