### Evaluation of the forward Compton scattering off protons: I. Spin-independent amplitude *[Cross-Listing]*

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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): $\alpha_{E1}+\beta_{M1}=(14.0\pm 0.20)\times 10^{-4}\,\mathrm{fm}^3$. An analogous sum rule involving the quadrupole polarizabilities is evaluated here too. The spin-independent forward amplitude of proton Compton scattering is evaluated in a broad energy range. The results are compared with previous evaluations and the only experimental data point for this amplitude (at 2.2 GeV). We also remark on sum rules for the elastic component of polarizabilities.