I’ve been thinking about the electroweak phase transition in the early universe, and I have some questions about the form of Coulomb’s law during that epoch.
As I understand it, before the electroweak phase transition, the electromagnetic and weak forces were still united as one force. The Higgs had not yet obtained a non-zero VEV, and the three $W$ particles that correspond to the generators of $SU(2)$, and the $B$ that corresponds to the generator of $U(1)$, were still massless. Here my understanding becomes confused: is it the case that the electroweak force was mediated by all of these particles, i.e. that it was a long range force mediated by four massless gauge bosons? If so, can we derive a classical result that corresponds to something like Coulomb’s law for the electroweak interaction (for e.g. two electrons)? As a very naive guess I could imagine that it looks like Coulomb’s law, but with the electric charge replaced by some combination of the weak isospin and/or hypercharge.
So my questions are:
- Is the above picture essentially correct? I would appreciate it if anyone could correct any misconceptions I may have.
- What was/were the gauge boson(s) associated with this united electroweak force? The three massless $W’s$, and the $B$?
- Can the form of the electroweak interaction during that epoch be derived (‘Coulomb’s law’ at that time) at tree level? If not, can we make an educated guess?