Forward doubly-virtual Compton scattering off the nucleon in chiral perturbation theory: II. Spin polarizabilities and moments of polarized structure functions

TL;DR

This paper presents a next-to-leading-order chiral perturbation theory calculation of polarized doubly-virtual Compton scattering off the nucleon, providing insights into the nucleon's spin structure, polarizabilities, and structure function moments relevant for atomic and scattering experiments.

Contribution

It offers a complete NLO calculation of polarized VVCS amplitudes and structure functions within B$ m ext{χ}$PT, comparing results with other theories and experimental data, and analyzing differences with heavy-baryon approaches.

Findings

Agreement with some experimental data and theoretical predictions.

Reproduction of heavy-baryon results in the appropriate limit.

Insights into differences between Lorentz-invariant and heavy-baryon frameworks.

Abstract

We examine the polarized doubly-virtual Compton scattering (VVCS) off the nucleon using chiral perturbation theory ($\chi$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 $S_1(\nu, Q^2)$ and $S_2(\nu, Q^2)$, 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 $\chi$PT (B$\chi$PT) and heavy-baryon (HB$\chi$PT) frameworks.