# Dynamics in Higgs mechanism

In "everyday" particle physics, we assume the $SU(2)_L \times U(1)_Y$ is spontaneously broken to $U(1)_{EM}$. But in high enough energies the symmetry is restored, otherwise as far as I understand there is no point in this mechanism and we can just impose this symmetry to begin with.

I have a few questions on this matter, and I think I don't understand this process well enough to even phrase my question in a way that makes sense, so bear with me.

Suppose we are at low energies under SSB. We do some scattering experiment, in which we choose a basis and expand around the minimum to obtain the field content we now call particles. Is the chosen vacuum constant? If I have some energy to "float" above that minimum, can the system "flow" away from that vacuum to some other vacuum in the degenerate space, such that the previous basis is no longer a good approximation to the system and we need to "recalibrate" our basis and thus redefine the field configuration that we consider as particles? If so, is there dynamics that governs this transition from one vacuum to another? It seems that there has to be, because we can increase the energy to a point the original symmetry is recovered and then lower it back to obtain a new SSB, and there shouldn't be a reason for the breaking to lead to the same vacuum.

This also points to another notion I'm not very confident in my grasping, which is what we mean when we say "we are at low/high energy". For example, in the early universe we say we had high enough energy to have the original symmetry, and at some point the energy decreased and SSB occured. What is it that defines the amount of energy that is considered when asking where we are in the Mexican hat picture?

• In the absence of the Higgs mechanism, genuine Goldstone bosons of zero momentum & energy, added to the original vacuum may shift you to an equivalent degenerate vacuum. All measurable correlation functions/amps, however, are unique, no matter which of these vacua you chose and stuck with. At "high energies" (s, t, anything) the effects of the symmetry breaking lose significance as $v^2/s$, etc, where v is the SSB scale. For the SM, multi-TeV amps are quite similar to the unbroken phase in some ways ("equivalence theorem"). – Cosmas Zachos Jul 12 '18 at 21:49
• – Cosmas Zachos Jul 13 '18 at 14:15
• Essentially related – Cosmas Zachos Jul 13 '18 at 14:21