Spin-dependent sum rules connecting real and virtual Compton scattering verified

Abstract

We present a detailed derivation of the two sum rules relating the spin polarizabilities measured in real, virtual, and doubly-virtual Compton scattering. For example, the polarizability ${\delta }_{LT}$, accessed in inclusive electron scattering, is related to the spin polarizability ${\gamma }_{E1E1}$ and the slope of generalized polarizabilities $P^{(M1,M1)1}-P^{(L1,L1)1}$, measured in, respectively, the real and the virtual Compton scattering. We verify these sum rules in different variants of chiral perturbation theory, discuss their empirical verification for the proton, and prospect their use in studies of the nucleon spin structure.

21 pages, 4 figures, RevTeX 4, typos corrected, matches published version

References in corpus (9)

• Unitary Isobar Model - MAID2007
• Electromagnetic excitation of the Delta(1232)-resonance
• Spin Structure of the Nucleon - Status and Recent Results
• Using effective field theory to analyse low-energy Compton scattering data from protons and light nuclei
• Gold-plated moments of nucleon structure functions in baryon chiral perturbation theory
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• Generalized polarizabilities of the nucleon in baryon chiral perturbation theory
• Polarizability relations across real and virtual Compton scattering processes

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
• Forward doubly-virtual Compton scattering off the nucleon in chiral perturbation theory: II. Spin polarizabilities and moments of polarized structure functions
• Effective theory tower for $\mu \to e$ conversion
• Sum rules across the unpolarized Compton processes involving generalized polarizabilities and moments of nucleon structure functions
• Virtual Compton scattering at low energies with a positron beam
• The Proton Electromagnetic Generalized Polarizabilities