Eur. Phys. J. C (2010) 65: 195-209
https://doi.org/10.1140/epjc/s10052-009-1183-z

Regular Article - Theoretical Physics

Predictive powers of chiral perturbation theory in Compton scattering off protons

¹ European Centre for Theoretical Studies in Nuclear Physics and Related Areas (ECT*), Villa Tambosi, Villazzano (Trento), 38050, TN, Italy
² Institut für Kernphysik, Johannes Gutenberg Universität, Mainz, 55099, Germany

^* e-mail: lensky@ect.it

Received: 5 July 2009
Revised: 16 September 2009
Published online: 11 November 2009

Abstract

We study low-energy nucleon Compton scattering in the framework of baryon chiral perturbation theory (BχPT) with pion, nucleon, and Δ(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/Δ, with Δ≈300 MeV the Δ-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 fm³, 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.