Manifestly-covariant $p^3$ calculation of nucleon Compton scattering

We compute the Compton scattering off the nucleons in the framework of manifestly covariant baryon chiral perturbation theory (B$\chi$PT). The results for observables differ substantially from the corresponding calculations in heavy-baryon chiral perturbation theory (HB$\chi$PT), most appreciably in the forward kinematics. We verify that the covariant $p^3$ result fulfills the forward-Compton-scattering sum rules. We also explore the effect of the $\Delta$(1232) resonance at order $p^4/\Delta$, with $\Delta\approx300$ MeV, the resonance excitation energy. We find that the substantial effect of the $\Delta$-excitation on the nucleon polarizabilities can naturally be accommodated in the manifestly covariant calculation.