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

Lensky, Vadim; Hagelstein, Franziska Elfriede; Pascalutsa, Vladimir; Vanderhaeghen, Marc (2018). Sum rules across the unpolarized Compton processes involving generalized polarizabilities and moments of nucleon structure functions. Physical review. D - particles, fields, gravitation, and cosmology, 97(7) American Physical Society 10.1103/PhysRevD.97.074012

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We derive two new sum rules for the unpolarized doubly virtual Compton scattering process on a nucleon, which establish novel low-Q² relations involving the nucleon’s generalized polarizabilities and moments of the nucleon’s unpolarized structure functions F₁(x;Q²) and F₂(x;Q²). 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-Q² 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 Δ(1232)-resonance contribution to the muonic-hydrogen 2P − 2S Lamb shift yields −1 ± 1 μeV, confirming the previously conjectured smallness of this effect.

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