Consistent Calculation of the Nucleon Electromagnetic Polarizabilities in Chiral Perturbation Theory Beyond Next-to-Leading Order

We calculate the nucleons’ electromagnetic polarizabilities in heavy baryon chiral perturbation theory including all terms to order $\mathcal{O}(q^4)$. The chiral prediction of the electric polarizabilities for the neutron and the proton are in good agreement with the data. In the case of the magnetic polarizabilities the big positive contribution from the $\mathrm{\Delta }(1232)$ resonance is largely cancelled by a non–analytic loop contribution of the $\ln M_\pi$ type. This novel effect helps to understand the rather small empirical value of the nucleons’ magnetic polarizability.