We study low-energy nucleon Compton scattering in the framework of baryon chiral perturbation theory (BχPT) with pion, nucleon, and ∆(1232) degrees of freedom, up to and including the nextto-next-to-leading order (NNLO). We include the effects of order p 2 , p 3 and p 4 /∆, with ∆ ≈ 300 MeV the ∆-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 ± 0.7) × 10 −4 fm 3 , in significant disagreement with the current PDG value. Unlike the previous χPT 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 HBχPT and BχPT results for polarizabilities is found to be appreciable. We discuss the chiral behavior of proton polarizabilities in both HBχPT and BχPT 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.

We obtain leading-and next-to-leading order predictions of chiral perturbation theory for several prominent moments of nucleon structure functions. These free-parameter free results turn out to be in overall agreement with the available empirical information on nearly all of the considered moments, in the region of low-momentum transfer (Q 2 < 0.3 GeV 2 ). Especially surprising is the situation for the spin polarizability δ LT , which thus far was not reproducible in chiral perturbation theory for proton and neutron simultaneously. This problem, known as the "δ LT puzzle," is not seen in the present calculation.

We update the predictions of the SU(2) baryon chiral perturbation theory for the dipole polarisabilities of the proton, {α E1 , β M 1 } p = {11.2(0.7), 3.9(0.7)} × 10 −4 fm 3 , and obtain the corresponding predictions for the quadrupole, dispersive, and spin polarisabilities:The results for the scalar polarisabilities are in significant disagreement with semiempirical analyses based on dispersion relations, however the results for the spin polarisabilities agree remarkably well. Results for proton Compton-scattering multipoles and polarised observables up to the Delta(1232) resonance region are presented too. The asymmetries Σ 3 and Σ 2x reproduce the experimental data from LEGS and MAMI. Results for Σ 2z agree with a recent sum rule evaluation in the forward kinematics. The asymmetry Σ 1z near the pion production threshold shows a large sensitivity to chiral dynamics, but no data is available for this observable. We also provide the predictions for the polarisabilities of the neutron, the numerical values being {α E1 , β M 1 } n = {13.7(3.1), 4.6(2.7)} × 10 −4 fm 3 , {α E2 , β M 2 } n = {16.2(3.7), −15.8(3.6)} × 10 −4 fm 5 , {α E1ν , β M 1ν } n = {0.1(1.0), 7.2(2.5)} × 10 −4 fm 5 , and {γ E1E1 , γ M 1M 1 , γ E1M 2 , γ M 1E2 } n = {−4.7(1.1), 2.9(1.5), 0.2(0.2), 1.6(0.4)}×10 −4 fm 4 . The neutron dynamical polarisabilities and multipoles are examined too. We also discuss subtleties related to matching dynamical and static polarisabilities.