We examine the polarized doubly-virtual Compton scattering (VVCS) off the nucleon using chiral perturbation theory ($��$PT). The polarized VVCS contains a wealth of information on the spin structure of the nucleon which is 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 the polarized VVCS amplitudes $S_1(��, Q^2)$ and $S_2(��, Q^2)$, and the corresponding polarized spin structure functions $g_1(x, Q^2)$ and $g_2(x,Q^2)$. Our results for the moments of polarized structure functions, partially related to different spin polarizabilities, are compared to other theoretical predictions and "data-driven" evaluations, as well as to the recent Jefferson Lab measurements. 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 baryon $��$PT (B$��$PT) and heavy-baryon (HB$��$PT) frameworks.

47 pages, 11 figures, 2 tables. Includes Mathematica notebook with the spin polarizabilities and moments of polarized structure functions as supplemental material. Replaced to match the published version