Evaluation of the forward Compton scattering off protons: I. Spin-independent amplitude

Understand

We evaluate the forward Compton scattering off the proton, based on Kramers-Kronig kind of relations which express the Compton amplitudes in terms of integrals of total photoabsorption cross sections.

• We obtain two distinct fits to the world data on the unpolarized total photoabsorption cross section, and evaluate the various spin-independent sum rules using these fits.
• For the sum of proton electric and magnetic dipole polarizabilities, governed by the Baldin sum rule, we obtain the following average (between the two fits): $\alpha_{E1}+\beta_{M1}=14.0(2)\times 10^{-4}\,\mathrm{fm}^3$.
• An analogous sum rule involving the quadrupole polarizabilities of the proton is evaluated too.