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A consistent renormalization of a quantum theory of axion-electrodynamicsrequires terms beyond the minimal coupling of two photons to a neutralpseudoscalar field. This procedure is used to determine the self-energyoperators of the electromagnetic and the axion fields with an accuracy ofsecond-order in the axion-diphoton coupling. The resulting polarization tensoris utilized for establishing the axion-modified Coulomb potential of a staticpointlike charge. In connection, the plausible distortion of the Lamb-shift inhydrogenlike atoms is established and the scopes for searching axionlikeparticles in high-precision atomic spectroscopy and in experiments ofCavendish-type are investigated. Particularly, we show that these hypotheticaldegrees of freedom are ruled out as plausible candidates for explaining theproton radius anomaly in muonic hydrogen. A certain loophole remains, though,which is linked to the nonrenormalizable nature of axion-electrodynamics.

Axion-modified photon propagator, Coulomb potential and Lamb-shift