Forward doubly-virtual Compton scattering off the nucleon in chiral perturbation theory. II. Spin polarizabilities and moments of polarized structure functions
J. M. Alarcón, Franziska Hagelstein, Vadim Lensky, Vladimir Pascalutsa
Abstract
We examine the polarized doubly-virtual Compton scattering (VVCS) off the nucleon using chiral perturbation theory ($\ensuremath{\chi}\mathrm{PT}$). 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 calculation of the polarized VVCS amplitudes ${S}_{1}(\ensuremath{\nu},{Q}^{2})$ and ${S}_{2}(\ensuremath{\nu},{Q}^{2})$, 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 $\ensuremath{\chi}\mathrm{PT}$ and heavy-baryon frameworks.