Thermal Dependence of the Higgs Mechanism

[bluecap]

I'm familiar with the Higgs mechanism.. but what perplexed me so much is the temperature dependence. I know about superconductivity or magnetic-temperature analogy.. or generally I understand what's written in wiki https://en.wikipedia.org/wiki/Higgs_mechanism

"Below some extremely high temperature, the field causes spontaneous symmetry breaking during interactions. The breaking of symmetry triggers the Higgs mechanism, causing the bosons it interacts with to have mass."

But how exactly does the temperature part work? I've been googling a lot about it. What exact equation does relate temperature to the higgs field undergoing phase transition or the higgs mechanism. Is it related to the fact that the energy of the higgs boson or goldstone or others only occur when the temperature is high enough? For example temperature corresponding to 125 GeV? What is the equivalent temperature for 125 GeV? Any conversion table. Or are they unrelated?

What must you adjust in the equation (just for sake of illustration) such that the temperature can be lowered say to only 1000 Fahrenheit such that when the higgs field go above 1000 Fahrenheit.. it can produce the unbroken symmetry state and make matter become massless? Again just as illustration to understand how exactly temperature can change the higgs field.

Thank you.

 

[mfb]

The required energy is much higher, but I don't find the number now.

It is very similar to nonrelativistic quantum mechanics or even classical mechanics. If you have a double well potential (Mexican Hat potential in 1 D) and a particle with low energy, it will be in one of the small wells - the symmetry is broken. If the energy is very high, it won't be localized in either well, but move freely around in the double well - the particle distribution is symmetric.

What is the equivalent temperature for 125 GeV?

Divide by the Boltzmann constant.

 

[bluecap]

The required energy is much higher, but I don't find the number now.

It is very similar to nonrelativistic quantum mechanics or even classical mechanics. If you have a double well potential (Mexican Hat potential in 1 D) and a particle with low energy, it will be in one of the small wells - the symmetry is broken. If the energy is very high, it won't be localized in either well, but move freely around in the double well - the particle distribution is symmetric.

I know about the Mexican Hat. But what exactly is the equation or mechanism that relates temperature to the higgs initiating the higgs mechanism?

Divide by the Boltzmann constant.

 

[bluecap]

The required energy is much higher, but I don't find the number now.

It is very similar to nonrelativistic quantum mechanics or even classical mechanics. If you have a double well potential (Mexican Hat potential in 1 D) and a particle with low energy, it will be in one of the small wells - the symmetry is broken. If the energy is very high, it won't be localized in either well, but move freely around in the double well - the particle distribution is symmetric.Divide by the Boltzmann constant.

I read stuff like the following http://www.quantumdiaries.org/2011/...s-boson-part-i-electroweak-symmetry-breaking/

where the details of electroweak symmetry breaking is detailed.. but what I want to know is how exactly does temperature set off the phase transition? and at what particular temperature and why? any idea? anyone got a clue?

 

[bluecap]

Let me rephrase my question. Higgs mechanism usually uses the analogy of superconductor where when a superconductor is heated above its so-called 'critical temperature' it becomes a normal conductor... so

higgs superconducting state = our broken symmetry world where particles have masses
higgs normal conductor = above critical temperature where symmetry is restored and particles have no masses

1. In the LHC, does the particle collision heat up the Higgs field in the neighborhood of the particle until this field is no longer in a superconducting state? or does LHC simply produce collision with energy enough to create the higgs boson at energy of about 125 GeV? Does this correspond to temperature above the critical temperature?

2. Can't this be used to test quarks confinement in QCD if they really might be due to strings of flux plus a kind of condensation that forces the charges at the end of the string together? Is it not when collision heats up the quarks such that it goes above the critical temperature, the higgs superconducting state will disappear and hence become normally conducting state and would therefore destroy the string bonds between the quarks in the particle, destroying the confining property of the colour force, which would no longer become stronger, further apart they were?