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We study low-energy nucleon Compton scattering in the framework of baryonchiral 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 areall "predictive" powers in the sense that no unknown low-energy constants enteruntil at least one order higher (i.e, $p^4$). Estimating the theoreticaluncertainty on the basis of natural size for $p^4$ effects, we find thatuncertainty of such a NNLO result is comparable to the uncertainty of thepresent experimental data for low-energy Compton scattering. We find anexcellent agreement with the experimental cross section data up to at least thepion-production threshold. Nevertheless, for the proton's magneticpolarizability we obtain a value of $(4.0\pm 0.7)\times 10^{-4}$ fm$^3$, insignificant disagreement with the current PDG value. Unlike the previous$\chi$PT studies of Compton scattering, we perform the calculations in amanifestly Lorentz-covariant fashion, refraining from the heavy-baryon (HB)expansion. The difference between the lowest order HB$\chi$PT and B$\chi$PTresults for polarizabilities is found to be appreciable. We discuss the chiralbehavior of proton polarizabilities in both HB$\chi$PT and B$\chi$PT with thehope to confront it with lattice QCD calculations in a near future. In studyingsome of the polarized observables, we identify the regime where their naivelow-energy expansion begins to break down, thus addressing the forthcomingprecision measurements at the HIGS facility.

Predictive powers of chiral perturbation theory in Compton scattering off protons