Do Maxicharged particles exist?

The critical charge $Z_c$ is estimated for elementary particles using a Newton-Wigner position operator inspired model. Particles with $Z \sim Z_c$ (maxicharged particles), if they exist at all, can have unusual properties which turn them into elusive objects not easy to detect. Dirac's magnetic poles have a (magnetic) charge $g\gg Z_c$. This gives one more argument that it is unexpected that pointlike monopoles to be found in our world, where $\alpha^{-1}\simeq 137$.