Manifestly-covariant chiral PT calculation of nucleon Compton scattering

Abstract

We compute the Compton scattering off the nucleons in the framework of manifestly covariant baryon chiral perturbation theory (B$χ$PT). The results for observables differ substantially from the corresponding calculations in heavy-baryon chiral perturbation theory (HB$χ$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 $Δ$(1232) resonance at order $p^4/\varDelta$, with $\varDelta\approx 300$ MeV, the resonance excitation energy. We find that the substantial effect of the $Δ$-excitation on the nucleon polarizabilities can naturally be accommodated in the manifestly covariant calculation.

6 pages, 4 figures, REVTeX; Major revision, the effect of Delta is computed entirely to order p^4 over the Delta-nulceon mass difference