  Relativistic lepton-proton bound-state eigenvalue equations for Hamiltonians
derived from quantum field theory using second-order renormalization group
procedure for effective particles, are reducible to two-body Schroedinger
eigenvalue equations with the effective Coulomb potential that exhibits a tiny
sensitivity to the characteristic momentum-scale of the bound system. The scale
dependence is shown to be relevant to the theoretical interpretation of
precisely measured lepton-proton bound-state energy levels in terms of a 4
percent difference between the proton radii in muon-proton and electron-proton
bound states.
