Nonperturbative lepton-sea fermions in the nucleon and the proton radius puzzle

A potential explanation [U. D. Jentschura, Phys. Rev. A 88, 062514 (2013)] of the proton radius puzzle originating from the nonperturbative lepton-pair content of the proton is studied. Well-defined quantities that depend on this lepton-pair content are evaluated. Each is found to be of the order of 10(alpha/pi)(2), so that such a lepton-pair content does exist in the proton. However, I argue that this relatively large result and general features of loop diagrams rule out the possibility of lepton-pair content as an explanation of the proton radius puzzle. The contributions of a class of potential explanations of the proton radius puzzle (for which the dependence on the mu p relative distance is as contact interaction) are shown to be increase very rapidly with atomic number.