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The forward doubly-virtual Compton scattering (VVCS) off the nucleon containsa wealth of information on nucleon structure, relevant to the calculation ofthe two-photon-exchange effects in atomic spectroscopy and electron scattering.We report on a complete next-to-leading-order (NLO) calculation of low-energyVVCS in chiral perturbation theory ($\chi$PT). Here we focus on the unpolarizedVVCS amplitudes $T_1(\nu, Q^2)$ and $T_2(\nu, Q^2)$, and the correspondingstructure functions $F_1(x, Q^2)$ and $F_2(x,Q^2)$. Our results are confronted,where possible, with "data-driven" dispersive evaluations of low-energystructure quantities, such as nucleon polarizabilities. We find significantdisagreements with dispersive evaluations at very low momentum-transfer $Q$;for example, in the slope of polarizabilities at zero momentum-transfer. Byexpanding the results in powers of the inverse nucleon mass, we reproduce theknown "heavy-baryon" expressions. This serves as a check of our calculation, aswell as demonstrates the differences between the manifestly Lorentz-invariant(B$\chi$PT) and heavy-baryon (HB$\chi$PT) frameworks.

physical review. d/physical review. d.

Forward doubly-virtual Compton scattering off the nucleon in chiral  perturbation theory: the subtraction function and moments of unpolarized  structure functions