Abstract
A consistent renormalization of a quantum theory of axion-electrodynamics requires terms beyond the minimal coupling of two photons to a neutral pseudoscalar field. This procedure is used to determine the self-energy operators of the electromagnetic and the axion fields with an accuracy of second-order in the axion-diphoton coupling. The resulting polarization tensor is utilized for establishing the axion-modified Coulomb potential of a static pointlike charge. In connection, the plausible distortion of the Lamb-shift in hydrogenlike atoms is established and the scopes for searching axionlike particles in high-precision atomic spectroscopy and in experiments of Cavendish-type are investigated. Particularly, we show that these hypothetical degrees of freedom are ruled out as plausible candidates for explaining the proton radius anomaly in muonic hydrogen. A certain loophole remains, though, which is linked to the nonrenormalizable nature of axion-electrodynamics.
Highlights
That the path integral measure in quantum chromodynamics (QCD) is not invariant under an axial chiral Uð1ÞA-transformation provides a clear evidence that this classical symmetry does not survive the quantization procedure
As a consequence of the mentioned feature, high-precision spectroscopy lacks of sufficient sensitivities as to improve the existing laboratory constraints on the parameter space of axionlike particles (ALPs)
Combining the described method with a dimensional analysis, we find that the renormalization of the self-energy operators in quantum electrodynamics (QEDA) should be handled by two local operators of dimension 6: Z Sg2 1⁄4
Summary
That the path integral measure in quantum chromodynamics (QCD) is not invariant under an axial chiral Uð1ÞA-transformation provides a clear evidence that this classical symmetry does not survive the quantization procedure. Precision tests of the Coulomb’s law via atomic spectroscopy and experiments of Cavendishtype have not been used so far in the search for ALPs, they are known to constitute powerful probes for other well-motivated particle candidates [34,35,36,37]. Against the background of these circumstances, it is relevant to derive modifications of the Coulomb potential due to quantum vacuum fluctuations of axionlike fields and to study their potential consequences The former are encompassed in the corresponding vacuum polarization tensor whose calculation, is not a straightforward task as far as axion quantum electrodynamics (QEDA) is concerned. II A and II B, techniques known from effective field theories are exploited for establishing the vacuum polarization tensor within an accuracy of the second order in the axion-diphoton coupling. In Appendix B the sensitivity levels associated with precision tests of the axion-modified Coulomb law via experiments of Cavendish-type are presented
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