Predictive powers of chiral perturbation theory in Compton scattering off protons
Abstract
We study low-energy nucleon Compton scattering in the framework of baryon chiral perturbation theory (B) with pion, nucleon, and (1232) degrees of freedom, up to and including the next-to-next-to-leading order (NNLO). We include the effects of order p2, p3 and p4/, 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, p4). Estimating the theoretical uncertainty on the basis of natural size for p4 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 fm3, in significant disagreement with the current PDG value. Unlike the previous 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 and B results for polarizabilities is found to be appreciable. We discuss the chiral behavior of proton polarizabilities in both HB and B 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.