electromagnetism - Mass of the electron

In the classical limit, three quarters of the mass-energy of the electron come from the energy of the electromagnetic field of its charge (see Electromagnetic Mass). Intuitively one would expect that the exact formula in the quantum limit may be different, but the general concept would remain, meaning that at least some mass of the electron may be due to its charge.

On the other hand, the main differences between the electron and neutrino are the mass and charge. All other quantum numbers are the same. This fact as well points to an intuitive conclusion that the mass of the electron in part may be due to its charge.

However, from the Standard Model, we learn that the mass of the electron is due to its coupling to the Higgs field. What is the proper way to resolve this apparent contradiction? Does the full mass of the electron come from its interaction with the Higgs field? And if so, what is the connection (intuitive or mathematical) between the classical limit involving the energy of the electromagnetic field and the quantum limit involving the interaction with the Higgs field?

The Wiki link above states:

As to the cause of mass of elementary particles, the Higgs mechanism in the framework of the relativistic Standard Model is currently used. In addition, some problems concerning the electromagnetic mass and self-energy of charged particles are still studied.

Is there any progress or insight into these studies?

A related, but different question: Is the Higgs field needed to explain the mass of the electron?

Answer

The renormalization group running of the mass in quantum field theory, is the quantum version of the classical self-energy contribution. According to Polchinski's String Theory, section 16.2, "the self-energy... is roughly 20% of the mass of the electron". So even in the standard model, the yukawa coupling to the Higgs field is the dominant contribution to the electron mass, but it isn't everything.

This also suggests that if the mechanism of neutrino mass were exactly the same as this, but with no contribution from electromagnetic self-energy, it would still be of the same order of magnitude as the electron mass. And indeed, the typical beyond-standard-model theory explains the tiny neutrino mass quite differently, as due to a "seesaw mechanism" in which a superheavy Majorana mass and an electroweak-scale Dirac mass combine to produce a superlight observed mass.

Theories which would explain the neutrino mass without the seesaw, like the "neutrino minimal standard model", have to suppose a neutrino yukawa coupling that just happens to be many orders of magnitude smaller than any other yukawa couplings. I am not aware of any model in which the difference in masses can be attributed to the difference in charge and corresponding difference in self-energy.