  We show that the electroweak monopole can be regularized with a non-vacuum
electromagnetic permittivity. This allows us to set a new BPS bound for the
monopole mass, which implies that the mass may not be smaller than 2.98 TeV,
more probably 3.75 TeV. We demonstrate that the same method can also regularize
the Dirac monopole, which enhances the possibility to construct the Dirac
monopole of mass of a few hundred meV in condensed matters. We discuss the
physical implications of our result.
