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

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 (χPT). Here we focus on the unpolarized VVCS amplitudes T1ðν;Q2Þ and T2ðν;Q2Þ, and the corresponding structure functions F1ðx;Q2Þ and F2ðx;Q2Þ. 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 (BχPT) and heavy-baryon (HBχPT) frameworks.