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High precision spectroscopy can provide a sensitive tool to test Coulomb'slaw on atomic length scales. This can then be used to constrain particles suchas extra "hidden" photons or minicharged particles that are predicted in manyextensions of the standard model, and which cause small deviations fromCoulomb's law. In this paper we use a variety of transitions in atomichydrogen, hydrogenic ions, and exotic atoms to probe Coulomb's law. Thisextends the region of pure Coulomb's law tests to larger masses. For hiddenphotons and minicharged particles this region is already tested by otherastrophysical and laboratory probes. However, future tests of true muonium andmuonic atoms are likely to probe new parameter space and therefore have gooddiscovery potential for new physics. Finally, we investigate whether thediscrepancy between the theoretical calculation of the 2s_{1/2}^{F=1} -2p_{3/2}^{F=2} transition in muonic hydrogen and its recent experimentalmeasurement at PSI can be explained by the existence of a hidden photon. Thisexplanation is ruled out by measurements of the Lamb shift in ordinaryhydrogen.

Spectroscopy as a test of Coulomb's law - A probe of the hidden sector