Questions on electroweak symmetry breaking

[karlzr]

I have some questions or thoughts about EW symmetry breaking.

(1) Higgs mechanism gives mass to SM particles after the background higgs field rolls from $h=0$ to $h=v$ and symmetry is broken. We are talking about pole mass, aren't we? So pole mass changes continuously from $0$ to $m$ for those massive particles in SM.

(2) What does the Higgs potential energy look like at high energy scales? Does the shape change? More specifically, does the nonzero vacuum still exist. If true, the physical higgs field can always be defined as excitation around this global vacuum for equilibrium state at $T=0 K$. In other words, symmetry will not be restored simply by going to high energy scales if we stick to zero temperature. Actually in my impression we can set $V'(h=v)=0$ as the renormailization condition when regularizing the quantum corrected potential. I don't understand why it is a valid condition, because I think the vacuum will run at different energy scales.

(3) It is totally arbitrary to set the potential energy of the vacuum in particle physics and usually people choose zero. But this arbitrariness might play an important role in cosmology, so how do we deal with this problem in that situation?

 

[ChrisVer]

That the potential gets its minimum to zero... (or effectively at zero)

 

[TEFLing]

I think there is something about mass and spin...

Massless photons can only spin forwards or backwards... Only have 2 DoF...

Massive particles have 3 DoF, they can spin orthogonal to their direction of motion... Or equally in all 3 xyz in rest frame

At high energy = short distance scales
Weak bosons act Massless, only showing 2DoF for spin, not 3... They lose the m=0 orthogonal spin projection mode at the super-high energies of the Weak / Higgs bosons

Is this crudely correct?

 

[karlzr]

That the potential gets its minimum to zero... (or effectively at zero)

Why does the minimum go to zero at high energy scale? since the minimum of potential energy is always at $\sqrt{\mu^2/\lambda}$, even though its value is different from electroweak scale.

 

[karlzr]

I think there is something about mass and spin...

Massless photons can only spin forwards or backwards... Only have 2 DoF...

Massive particles have 3 DoF, they can spin orthogonal to their direction of motion... Or equally in all 3 xyz in rest frame

At high energy = short distance scales
Weak bosons act Massless, only showing 2DoF for spin, not 3... They lose the m=0 orthogonal spin projection mode at the super-high energies of the Weak / Higgs bosons

Is this crudely correct?

It's true that EW gauge bosons have only two dofs because they don't eat goldstone boson until symmetry breaking ( when $H \neq 0$ ) when there begins to be interaction between them.

 

[ChrisVer]

The minimum of the potential you are referring to, is the one you get after the EW SSB... sufficiently above the EW SSB scale, the potential has a parabolic shape with the minimum at zero, and EW symmetry is restored.
There is some phase transition going on inbetween, but I haven't studied what goes on during that time.

 

[karlzr]

Phase transition occurs due to temperature correction to the potential energy when the temperature of the universe cools down. I don't think there is phase transition at zero temperature even if we go to very high energy scale and thus I don't see why symmetry is restored by increasing energy. This is why I am confused when people make this kind of statement.

 

[ChrisVer]

Phase transition occurs due to temperature correction to the potential energy when the temperature of the universe cools down. I don't think there is phase transition at zero temperature even if we go to very high energy scale and thus I don't see why symmetry is restored by increasing energy. This is why I am confused when people make this kind of statement.

The phase transition occurs because you go from a vacuum expectation value A to a vacuum expectation value B. In the case of the EWSB this is a transition from a vacuum at zero, to a vacuum at v you gave.

In the Universe evolution, there is no T=0. The temperature/energies started from some high value, and started evolving (dropping) with the scale of the Universe. At some point, you get condensates that break your EW symmetry.
Raising the energies is like raising temperatures. Reaching at some energy enough above the transition's energy (critical energy/temperature) , you can restore your symmetry.

 

[karlzr]

……
Raising the energies is like raising temperatures. Reaching at some energy enough above the transition's energy (critical energy/temperature) , you can restore your symmetry.

I don't understand why raising the energy is the same as raising temperature. As I understand it, temperature comes into play by changing the occupation number. But raising the energy is possible even for a single scattering process without any statistical distribution of the particles.