I know the electromagnetic force is mediated by a photon and the weak nuclear force is mediated by two massive bosons. Are there any other insights into why the masses are so different?
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The details of this is a somewhat convoluted set of ideas that would be a whole chapter of a quantum field theory textbook when done correctly. What I offer below is a brief, popular-level overview. I gloss over several details, and yadda yadda through many things. I tried to be as accurate as possible, but given the brevity of the discussion, I'm sure that some of the things I say below are wrong under certain circumstances.
That said, let's go.
The core idea here is that the fundamental equation governing the electroweak force is a theory coupling three SU(2) bosons with matter. This equation is invariant under an arbitrary rotation of the SU(2) bosons into each other-- you could replace $A_{1}$ and $A_{2}$ with $A_{a} = n A_{1} + m A_{2}$ and $A_{b} = kA_{1} + \ell A_{2}$, and the fundamental equation would be the same, so long as $n^{2} + m^{2} = k^{2} + \ell^{2} =1$ and $nk + m\ell = 0$ Similarly, thanks to the SU(2) symmetry, the interacting matter particles can be arbitrarily replaced with each other, and the theory doesn't know the difference--the "left-handed" component of the neutrino can be replaced with the "left handed" component of the electron, and the SU(2) interaction would be none the wiser.
The electroweak interaction also includes a U(1) interaction that behaves like ordinary electrodynamics. If there is no Higgs particle, the whole thing behaves like this, and none of the bosons has mass.
Then, the higgs comes into the picture. It turns out that the Higgs boson has a potential energy function such that its potential energy function is higher when it is absent than when it is present. Since the Higgs field interacts with the SU(2) field and the U(1) field, it takes values in these spaces, and therefore, the nonzero way that its potential energy is minimized means that if a Higgs particle is present and near this minimum value, real-world physics does NOT respect the rotations talked about above. This lack of respect for rotations picks out very special physical values of the rotation coeficcients that respect the value taken by the Higgs. When all of this is said and done, the four vector bosons (three SU(2) ones and the one U(1) one) have combined in a very particular way to form three three weakly interacting bosons, which acquire a mass as a result of the symmetry breaking, and the beginning symmetry group of rotations gets to maintain one single U(1) symmetry, which produces a photon, which, since it is still related to a symmetry, gets to retain its masslessness.
Zo the Relativist
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The Higgs field separates Electromagnetism and Weak force. This primarily due to the fact that the Higgs boson gave the W and Z bosons mass. Also at the time the bosons were B, and the three W bosons. Then the B interacted with the third W creating the photon and Z boson. The Higgs interacted here giving the Z boson 90 times the mass of a proton. Whereas the photon has no mass and moves at the speed of light. The two W bosons got charge and mass from the Higgs field. This separated Electromagnetism and the Weak nuclear force.
Roghan Arun
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