# Electroweak to Electro/Weak Bosons?

I apologise in advance, this is something I just can't seem to get my head around. So it's my understanding that before the electroweak force split, there were four bosons - $$W^1$$, $$W^2$$, $$W^3$$ and $$B$$ - and that they mix or interact to form photons $$\gamma$$, $$W^+$$/$$W^-$$ and $$Z$$ bosons. So, in our current universe with the split weak nuclear and electromagnetic forces, what happens to $$W^1$$, $$W^2$$, $$W^3$$ and $$B$$? If photons are mixes of $$W^3$$ and $$B$$, does that mean the $$W^3$$ and $$B$$ bosons are created for an instant and then mix to form a photon in the heart of a star? Or can photons be made without W3 and B?

• Related question here. Commented May 8, 2020 at 8:03

This strictly depends of the scale.

At the electroweak scale $$\Lambda_{EW}$$ symmetry breaking occurs.

At $$E>\Lambda_{EW}$$ no SSB occurs and 4 massless fields propagates:

$$W^1 ; W^2 ; W^3 ; B$$

Those 4 fields have each 2 polarizations as you should know for massless vector bosons.

Then your energy goes under such a scale, the Higgs mass, which depends on the energy of your process, triggers spontaneous symmetry breaking.

At $$E < \Lambda_{EW}$$ then you have simmetry breaking. 3 Goldstone modes are created and a new symmetry is now present. You have the same 4 fields above to propagate and the new 3 Goldstone modes to propagate.

There is a catch. Your 4 bosons can no longer propagate freely due to the new symmetry established after SSB. They are propagated only in a specific combination:

$$W^1$$ and $$W^2$$ propagate ONLY in the combinations $$W^{\pm} = W^1 \mp iW^2$$

$$W^3$$ and $$B$$ propagate only in yhe combinations $$A = cos(\theta_W)B + sin(\theta_W)W^3$$ and $$Z = -sin(\theta_W)B + cos(\theta_W)W^3$$.

Those are still massless tho. The $$W^{\pm}$$ and $$Z$$ boson gain mass because they are propagated togheter with the 3 Goldstone bosons, each of those provide the longitudinal polarization needed for a massive vector field.

So for example photons are the simultaneous propagation of $$W^3$$ and $$B$$. Inside a star you generate $$W^3$$ and $$B$$ bosons which are constrained by the new symmetry to propagate only in a way we label photons. Photons are not the real fields. The electroweak bosons are the real fields, but when a SSB occurs they are constrained to propagate togheter in such a way that we interpret as photons.

The same is valid for the 3 weak force bosons.

I had the same question about a month ago when i tried to interprete the mathematics of electroweak SSB(sponteneous symmetry breaking). I investigated the obvious resolutions: either [1]maths is givining wrong interpretations or [2]It is giving correct interpretations.

Since Standard Model of EW interaction is so profound, I assumed [2] is correct.

So, what is the interpretation then if we analyze the math?

Consider this (understand in terms of fields, which are more fundamental than particles):

[a]Before SSB, above electroweak unification energy($$E_{ew}$$), we had 4 fields.

[b]At $$E_{ew}$$, these 4 fields start interacting with each other and mix in different combinations.

[c]After SSB, we have 4 new fields.

{$$E_{ew}$$ is about 246 GeV(approximately $$10^{15}$$ K, a temperature exceeded until shortly after the Big Bang)}

i.e., the real world is energy dependent. The cases [a], [b] and [c] do not exist together. The fields in [c] are completely new and its like resultant fields of combinations. And Our current stage of the universe falls under [c], therefore only [c] fields exist.

"what happens to $$W^1$$, $$W^2$$, $$W^3$$ and $$B$$?" These fields do not exist in this stage of the universe.

"does that mean the $$W^3$$ and $$B$$ bosons are created for an instant and then mix to form a photon in the heart of a star?"

No!. Only photons are created directly. The reason is that $$W^3$$ and $$B$$ fields do not exist in this stage and therefore we can't have $$W^3$$ and $$B$$ quanta. Only $$A$$ and $$Z$$ fields exist.

• So the previous electroweak fields no longer exist, and the fields themselves mixed to result in the new fields. Just to make sure I'm understanding this correctly, so at the electroweak unification energy, the interaction of the fields split (metaphorically) the electroweak fields, and the new fields resulted from the components of the interactions? Commented Oct 12, 2018 at 6:58
• @kay L yes. Also, if we again go to this energy, the mixing decoupling occurs and we get the old fields again. Commented Oct 12, 2018 at 7:06
• This plot helps in your argument, you are really talking of the timeline of the universe, as far as we know it. hyperphysics.phy-astr.gsu.edu/hbase/Astro/timlin.html Commented Oct 12, 2018 at 7:11