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

Abstract

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 ( χ PT ). Here we focus on the unpolarized VVCS amplitudes T 1 ( ν , Q 2 ) and T 2 ( ν , 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 χ PT ) and heavy-baryon ( HB χ PT ) frameworks.