A note on Electron self-energy in logarithmic electrodynamics by P. Gaete and J. Helayel-Neto

We propose an identification of the free parameter in the model of nonlinear electrodynamics proposed in Gaete and Helayel-Neto (Eur Phys J C 74:2816, 2014) by equating the second term in the power expansion of its Lagrangian with that in the expansion of the Heiseberg-Euler Lagrangian. The resulting value of the field-energy of a point-like charge makes 0.988 of the electron mass, if the charge is that of the electron. Recently Gaete and Helayel-Neto [1] proposed a nonlinear Lagrangian for what they called the logarithmic electrodynamics, which, in the special case of presence, in a certain Lorentz frame, of only electric field E, has the form