The Higgs Mass and Spontaneous Symmetry Breaking in Cosmology

[kalish]

Hello, I am searching for information about the higgs mass before and after the symetry breaking. Does it depend on the temperature? I know other particles are not expected to have a mass before symetry breaking, but I suppose the higgs itself does. I don't find much informations about and I don't find the involvment in cosmology anymore.

Maybe I don't search well. Could anyone help me?

 

[Bill_K]

The Higgs potential is usually taken to be V(φ) = μ²φ² + λφ⁴ where λ > 0 and μ² < 0. If you take this to be literally true, then in the initial unbroken phase the Higgs would be tachyonic. No one knows whether the form assumed for V(φ) has any connection with reality other than the fact that there is a minimum.

 

[kalish]

Ok so there has never been an unbroken phase in the universe? for example with $\mu^2>0$

I still quote the paper of sean carroll talking about the cosmological constant:

In the Weinberg-Salam electroweak model, the phases of broken
and unbroken symmetry are distinguished by a potential energy difference of approximately
MEW ∼ 200 GeV (where 1 GeV = 1.6 × 10−3 erg); the universe is in the broken-symmetry
phase during our current low-temperature epoch, and is believed to have been in the symmetric phase at sufficiently high temperatures in the early universe.

I just want to know why do we believe this , and thus the dependence of $\mu$ on T.
I just can't find a clear paper about this.

 

[Bill_K]

μ² does not depend on T, or anything else. And as I said, μ² < 0. I said there was an initial unbroken phase. With, guess what: μ² < 0.

 

[kalish]

Hello, do you have some source about that? I am sorry but I very doubt about your claim. The unbroken symetry imply $\mu^2>0$ since the derivative shows that the zero are for $\phi = 0$ or $\phi^2 = -\frac{\mu^2}{4 \lambda}$, it follows when $\mu^2 < 0$, then $\phi_0 = \pm \sqrt{-\frac{\mu^2}{4 \lambda}}$ has real solutions they are minimum of the potential, and then it is a broken phase.

 

[Bill_K]

I'll try one more time, kalish. The Higgs potential is not supposed to change. It has a minimum at φ = √(- μ²/4λ), V(φ) = - μ²/4λ, which is about 200 GeV. This point is a stable vacuum state. Under present conditions the Higgs field sits down at the bottom of the valley and the symmetry is broken.

V(φ) also has a maximum at φ = 0, V(φ) = 0. This point is unstable, a false vacuum. For extremely high temperatures, E >> 0 and where is the Higgs field? Everywhere. It is not confined to the valley. In fact for very high temperatures it does not even notice the valley, the details of the potential no longer matter. Certainly the sign of μ² does not matter. This is why you won't find an answer to your question about the Higgs mass. Rest mass is a property of particles at rest or nearly so. In the early universe the kinetic energy greatly exceeded the current energy scale of 200 GeV, and at that high energy scale by comparison the rest mass is insignificant.

 

[kalish]

ok, thanks that's what i wanted to know, indeed at our epoch the higgs is just supposed to get it's vacuum expectation value, and an hypothetical symmetric vev when $\mu^2 > 0$ has never happend? I am sorry for the trouble, I am not a real retard, but I read everywhere the presentation talking about the two values of $\mu^2$ to present what was a spontaneous symmetry breaking, (I can quote!) so I effectively expected this to be a physical process (you know the parabol and the hat). So the point is just now it is almost at the vev, but at earlier time it was just not. It is different than the vev was different earlier.

Thanks a lot you avoid me troubles.