Recent ideas on the calculation of lepton anomalous magnetic moments

We discuss the recent claim [G. Mishima, arXiv:1311.7109; M. Fael and M. Passera, arXiv:1402.1575 [Phys. Rev. D (to be published)]] about discovery of a nonperturbative quantum-electrodynamic contribution of order $(\alpha /\pi {)}^5$ to lepton anomalous magnetic moments. We explain why this nonperturbative correction does not exist.

Figure 1

Polarization operator contribution to AMM.

Figure 2

Singularities in the complex $k_0$ plane.