The forward doubly-virtual Compton scattering (VVCS) off the nucleon contains a wealth of information on nucleon structure, relevant to the calculation of the two-photon-exchange effects in atomic spectroscopy and electron scattering. We report on a complete next-to-leading-order (NLO) calculation of low-energy VVCS in chiral perturbation theory ($��$PT). Here we focus on the unpolarized VVCS amplitudes $T_1(��, Q^2)$ and $T_2(��, Q^2)$, and the corresponding structure 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-energy structure quantities, such as nucleon polarizabilities. We find significant disagreements with dispersive evaluations at very low momentum-transfer $Q$; for example, in the slope of polarizabilities at zero momentum-transfer. By expanding the results in powers of the inverse nucleon mass, we reproduce the known "heavy-baryon" expressions. This serves as a check of our calculation, as well as demonstrates the differences between the manifestly Lorentz-invariant (B$��$PT) and heavy-baryon (HB$��$PT) frameworks.

31 pages, 11 figures, 1 table; supplemented material: 1 Mathematica notebook; minor modifications, published version