Polarizability relations across real and virtual Compton scattering processes

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.

4 pages, 1 figure; new relation is derived, figure remade and extended, major rewrite, reference added

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Cited by in corpus (10)

• The Spin Structure of the Nucleon
• The proton structure in and out of muonic hydrogen
• Two-photon exchange correction to the hyperfine splitting in muonic hydrogen
• Dispersion Theory in Electromagnetic Interactions
• Forward two-photon exchange in elastic lepton-proton scattering and hyperfine-splitting correction
• Generalized polarizabilities of the nucleon in baryon chiral perturbation theory
• Sum rules across the unpolarized Compton processes involving generalized polarizabilities and moments of nucleon structure functions
• Spin-dependent sum rules connecting real and virtual Compton scattering verified
• Virtual Compton scattering at low energies with a positron beam
• The Proton Electromagnetic Generalized Polarizabilities