Sum rules across the unpolarized Compton processes involving generalized polarizabilities and moments of nucleon structure functions

Abstract

We derive two new sum rules for the unpolarized doubly virtual Compton scattering process on a nucleon, which establish novel low-$Q^2$ relations involving the nucleon's generalized polarizabilities and moments of the nucleon's unpolarized structure functions $F_1(x,Q^2)$ and $F_2(x,Q^2)$. These relations facilitate the determination of some structure constants which can only be accessed in off-forward doubly virtual Compton scattering, not experimentally accessible at present. We perform an empirical determination for the proton and compare our results with a next-to-leading-order chiral perturbation theory prediction. We also show how these relations may be useful for a model-independent determination of the low-$Q^2$ subtraction function in the Compton amplitude, which enters the two-photon-exchange contribution to the Lamb shift of (muonic) hydrogen. An explicit calculation of the $\Delta (1232)$-resonance contribution to the muonic-hydrogen $2P-2S$ Lamb shift yields $-1\pm 1$ $\mu$eV, confirming the previously conjectured smallness of this effect.

22 pages, 5 figures, minor modifications, published version

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• Gold-plated moments of nucleon structure functions in baryon chiral perturbation theory
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• Polarizability relations across real and virtual Compton scattering processes
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Cited by in corpus (17)

• The proton charge radius
• The proton structure in and out of muonic hydrogen
• Comprehensive theory of the Lamb shift in light muonic atoms
• Lattice QCD evaluation of the Compton amplitude employing the Feynman-Hellmann theorem
• Dispersion Theory in Electromagnetic Interactions
• The next generation of laser spectroscopy experiments using light muonic atoms
• Magnetic polarisability of the nucleon using a Laplacian mode projection
• Sum rule for the Compton amplitude and implications for the proton-neutron mass difference
• Forward doubly-virtual Compton scattering off the nucleon in chiral perturbation theory: the subtraction function and moments of unpolarized structure functions
• Beam-normal single-spin asymmetry in elastic scattering of electrons from a spin-0 nucleus
• Nucleon polarizabilities in covariant baryon chiral perturbation theory with explicit $\Delta$ degrees of freedom
• Electromagnetic proton-neutron mass difference
• Low energy doubly-virtual Compton scattering from di-lepton electroproduction on a nucleon
• Two-photon exchange in (muonic) deuterium at N3LO in pionless effective field theory
• Forward doubly-virtual Compton scattering off an unpolarised deuteron in pionless effective field theory
• Soft-photon radiative corrections to the $e^{-}p\to e^{-}p{l}^{-}{l}^{+}$ process
• A reassessment of nuclear effects in muonic deuterium using pionless effective field theory at N3LO