Note on low-energy proton Compton scattering

The unpolarized differential cross section for spin-1/2 Compton scattering is shown to be completely specified up to terms of the sixth power of the photon frequency by the mass, charge, anomalous magnetic moment, and dynamic electromagnetic polarizabilities of the target and four other sturcture dependent constants. The two polarizabilities and the four new constants are expressed in terms of the threshold values and threshold derivatives of the invariant amplitudes of the process. Their parts which can be expected to satisfy fixed-$t=0\mathrm{}$ unsubtracted dispersion relations are evaluated in terms of single-pion photoproduction data. The extraction of the proton polarizabilities from low-energy elastic $\gamma$-proton scattering is discussed in the light of the results obtained.