Polarizability relations across real and virtual Compton scattering processes

TL;DR

This paper derives new relations involving spin polarizabilities of protons, linking empirical data with theoretical models, and discusses their implications for understanding the low-energy spin structure of nucleons.

Contribution

It introduces two novel relations involving spin polarizabilities and explores their empirical implications for proton structure analysis.

Findings

Relations are consistent with dispersive model evaluations.

Empirical data constrains generalized polarizabilities.

Potential for experimental tests at major facilities.

Abstract

We derive two relations involving spin polarizabilities of a spin-1/2 particle and consider their empirical implications for the proton. Using the empirical values of the proton anomalous magnetic moment, electric and magnetic charge radii, moments of the spin structure functions $g_1$, $g_2$, and of two spin polarizabilities, the present relations constrain the low-momentum behavior of generalized polarizabilities appearing in virtual Compton scattering. In the case of the proton, the dispersive model evaluations of the spin and generalized polarizabilities appear to be consistent with these relations. The ongoing measurements of different electromagnetic observables at the MAMI, Jefferson Lab, and HI$\gamma$S facilities may be able to put these relations to a test, or use them to unravel the low-energy spin structure of the nucleon.