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

TL;DR

This paper derives new sum rules linking nucleon structure functions and polarizabilities, enabling model-independent insights into nucleon structure and contributions to the muonic hydrogen Lamb shift.

Contribution

It introduces novel low-$Q^2$ sum rules for unpolarized doubly virtual Compton scattering, connecting measurable quantities to nucleon structure constants.

Findings

Empirical determination of proton structure constants.

Comparison with chiral perturbation theory predictions.

Calculation of the $ riangle(1232)$-resonance contribution to the Lamb shift.

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 $-1 \pm 1$ $\mathsf\mu$eV, confirming the previously conjectured smallness of this effect.