# Higgs, Fermi-Dirac distribution, and Pauli exclusion principle

## Main Question or Discussion Point

hi,

I am studying the Higgs Mechanism these days. And I get two questions. I hope some ones could help me.

1>We know that due to the non-zero VEV, SSB takes place and higgs condensates give masses to bosons and fermions. I wonder that after the SSB and before the universe became as cool as today, what are different points? All the masses should be smaller, and what about renormalization?

2>When the universe was hot enough that all partiles are massless, what Fermi-Dirac distribution and Pauli exclusion principle would be ?

Thanks.

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1. The masses scale with the VEV of the Higgs. Using a Ginzburg-Landau model, the VEV grows continuously from zero, but with a divergent rate at the point of transition. However, that's assuming that the temperature corresponds to the quadratic term in the GL model. Furthermore, fluctuations (both thermal and quantum) will be important. Near the transition point fluctuations will dominate, and the quadratic treatment will be insufficient; diagrams containing the the three and four Higgs vertices will become increasing important.

2. Nothing changes.

Thank you.

In the picture, the Fig. 1 is used by many people to explain Higgs mechanism. When t<t1, SSB does not happen, and when t>t3, we have W/Z. Since I am not sure the exact meaning of "the VEV grows continuously from zero", I want to know when t1<t<t3, which one is correct, Fig.2, Fig.3 or neither?

And I cannot figure out why triple and quartic Higgs vertices are important in this case. Could you explain me more about this?

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I don't see what t1 and t3 are.

I don't see what t1 and t3 are.
t1 is the time that before t1, SSB does not take place. And t3>t1, after t3 the maxima VEV appears.