How Does the Mexican Hat Potential Relate to Higgs Symmetry Breaking?

[naima]

Hi Pf

I wonder what the standard model says about "history" of masses.
Let us take Higgs symmetry breaking. Is it something that happened everywhere
after the big bang at a given temperature? And how was the hat before?
Could you give me links about that, with time differential equations.

thanks

 

[Eonic]

There are two versions of the Standard Model:
When the energy density is high enough, the electoweak symmetry is not broken and all particles are massless and the weak force is long range, because the W and Z are massless.

When the universe expanded and cooled, the Higgs mechanism applied and we ended up with the current version of the Standard Model. This happened around 10^-12 seconds after the big bang.

The Mexican hat potential does not chance in this process, that is why it is called spontaneous symmetry breaking. Look at it as a ball rolling in the potential: When the energy content in the Higgs field is high enough, the ball rolls between the high outer sides that extend up to infinity, and it does not feel the small bump in the middle. The ball oscilates around the middle. When the energy of the ball reduces, at a cetrain time it gets trapped in the lower edge of the mexican hat potential and it oscilates around the minimum of the potential. The symmetry is now broken, because the Higgs field has chosen a preferred spot and is no longer symmetric around the middle. The solution has no longer the symmetry of the potential.