Comments on proposed explanations for the muonic-atom x-ray discrepancy

Two proposed explanations for the apparent muonic-atom x-ray discrepancy are the possible existence of nonperturbative vacuum polarization modifications and the possible existence of a weakly coupled light scalar boson. We show that a nonperturbative decrease in the vacuum polarization spectral function implies a reduction in the vertex for a timelike photon to couple to an electron-positron pair. This would lower by a few percent the rate for π⁰ Dalitz decay and suggests observable effects in the colliding beam reactions e⁺e⁻→e⁻e⁺, $e^{+}{e}^{-}\to {\mu }^{\pm }{\mu }^{\mp }$. Turning to the scalar-boson hypothesis, we use neutron-electron and electron-deuteron scattering data to show that a scalar particle with mass lighter than about 0.6 MeV cannot be invoked to explain the muonic discrepancy. We conclude by discussing the useful role which isotope effects and pionic-atom experiments might play in determining the phenomenological structure of the extra potential implied by the discrepancy.