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

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.

arXiv comment47 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

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Cited by in corpus (11)

• The Present and Future of QCD
• Dispersion relation analysis of the radiative corrections to $g_A$ in the neutron $\beta$-decay
• Measurement of the proton spin structure at long distances
• Radiative corrections to semileptonic beta decays: Progress and challenges
• The Standard Model theory of neutron beta decay
• Measurement of the generalized spin polarizabilities of the neutron in the low $Q^2$ region
• Nucleon polarizabilities in covariant baryon chiral perturbation theory with explicit $\Delta$ degrees of freedom
• Single-pion contribution to the Gerasimov--Drell--Hearn sum rule and related integrals
• Measurement of the nucleon spin structure functions for 0.01<$Q^2$<1 GeV${}^2$ using CLAS
• Laser excitation of the 1s-hyperfine transition in muonic hydrogen
• Coupled-channel contributions to the GDH sum rule from the Jülich-Bonn approach