Generally we want 511meV mass of electron to completely come from energy of its field configuration.

Cutting out radius ~1.4fm ball in the center, the remaining electric field has ~511keV energy, hence we need deformation of electric field (from of perfect point charge) in a bit larger distance.

Here is Faber's energy density per radius from: https://iopscience.iop.org/article/10.1 ... 012022/pdf for r0~2.2fm:

It drops to zero in r=0 as it contains multiplication by area of sphere.

Red is from electric field - without regularization it would go to infinity in r=0. It was prevented by activated potential - blue plot corresponding to weak/strong interactions.