  Currently, both the g factor measurement of the muon as well as the Lamb
shift 2S-2P measurement in muonic hydrogen are in disagreement with theory.
Here, we investigate possible theoretical explanations, including proton
structure effects and small modifications of the vacuum polarization potential.
In particular, we investigate a conceivable small modification of the spectral
function of vacuum polarization in between the electron and muon energy scales
due to a virtual millicharged particle and due to an unstable vector boson
originating from a hidden sector of an extended standard model. We find that a
virtual millicharged particle which could explain the muonic Lamb shift
discrepancy alters theoretical predictions for the muon anomalous magnetic
moment by many standard deviations and therefore is in conflict with
experiment. Also, we find no parameterizations of an unstable virtual vector
boson which could simultaneously explain both "muonic" discrepancies without
significantly altering theoretical predictions for electronic hydrogen, where
theory and experiment currently are in excellent agreement. A process-dependent
correction involving electron screening is evaluated to have the right sign and
order-of-magnitude to explain the observed effect in muonic hydrogen.
Additional experimental evidence from light muonic atoms and ions is needed in
order to reach further clarification.
