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

摘要

We derive two new sum rules for the unpolarized doubly-virtual Comptonscattering (VVCS) process on a nucleon, which establish novel low-$Q^2$relations involving the so-called generalized polarizabilities (GPs) andmoments of the nucleon's unpolarized structure functions $F_1$ and$F_2(x,Q^2)$. These relations facilitate the determination of some structureconstants which can only be accessed in off-forward VVCS, not experimentallyaccessible at present. We perform an empirical determination for the proton andcompare our results with a next-to-leading order chiral perturbation theoryprediction. We also show how these relations may be useful for amodel-independent determination of the low $Q^2$ subtraction function in theCompton amplitude, which enters the two-photon-exchange contribution to theLamb shift of (muonic) hydrogen. An explicit calculation of the$\Delta(1232)$-resonance contribution to the muonic-hydrogen $2P-2S$ Lamb shiftyields: $-1 \pm 1$ $\mathsf\mu$eV, confirming the previously-conjecturedsmallness of this effect.