Predictive powers of chiral perturbation theory in Compton scattering off protons

We study low-energy nucleon Compton scattering in the framework of baryon chiral perturbation theory (B$\chi$PT) with pion, nucleon, and $\Delta$(1232) degrees of freedom, up to and including the next-to-next-to-leading order (NNLO). We include the effects of order $p^2$, $p^3$ and $p^4/\varDelta$, with $\varDelta\approx 300$ MeV the $\Delta$-resonance excitation energy. These are all "predictive" powers in the sense that no unknown low-energy constants enter until at least one order higher (i.e, $p^4$). Estimating the theoretical uncertainty on the basis of natural size for $p^4$ effects, we find that uncertainty of such a NNLO result is comparable to the uncertainty of the present experimental data for low-energy Compton scattering. We find an excellent agreement with the experimental cross section data up to at least the pion-production threshold. Nevertheless, for the proton's magnetic polarizability we obtain a value of $(4.0\pm 0.7)\times 10^{-4}$ fm$^3$, in significant disagreement with the current PDG value. Unlike the previous $\chi$PT studies of Compton scattering, we perform the calculations in a manifestly Lorentz-covariant fashion, refraining from the heavy-baryon (HB) expansion. The difference between the lowest order HB$\chi$PT and B$\chi$PT results for polarizabilities is found to be appreciable. We discuss the chiral behavior of proton polarizabilities in both HB$\chi$PT and B$\chi$PT with the hope to confront it with lattice QCD calculations in a near future. In studying some of the polarized observables, we identify the regime where their naive low-energy expansion begins to break down, thus addressing the forthcoming precision measurements at the HIGS facility.Comment: 24 pages, 9 figures, RevTeX4, revised version published in EPJ