On Some Recent Ideas on the Proton Radius Puzzle and Lepton Anomalous   Magnetic Moments
  We discuss recent suggestions on the resolution of the proton radius puzzle put forward in [1,2] and discovery of a nonperturbative quantum-electrodynamic contribution of order $(\alpha/\pi)^5$ to lepton anomalous magnetic moments announced in [3,4]. We demonstrate that the ideas of [1, 2] do not resolve the proton radius puzzle. We explain why the nonperturbative correction calculated in [3,4] does not exist. 
Michael I. Eides
hep-ph physics.atom-ph