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I'm struggling with the most basic (in science popularization) ideas from QFTs like spontaneuous symetry breaking, Higgs mechanism etc. However I was exposed to the formal side of simplest of QFT ideas. It's just that I have a hard time connecting the two worlds: trying to understand what the Standard Model tells us about the elementary particles through analogies present in Wikipedia (as well as any textbook, YT video etc.), while relating this to what I know from QM.

Of course knowing how limited analogies are, if the answer requires a more formal language in order to pinpoint the source of my confusion, please feel free to use it.

That all being said, If I understand SSB correctly, in higher energies certain particles (e.g. photons and weak interaction bosons) regain their symmetry present in the general model (the gauge symmetries?). It's just that the particular low energy realization of this model produces different masses (the general symmetry is hidden). That's why in high energies (early Universe and specific experiments) we reach states of matter that respect the symmetry.

If all this as true (similarly to a ball on top of a mexican hat, which after losing energy and going into a lower energy state) does this mean that the differences in mass (and other properties?) between elementary particles are just a particular low energy state for the universe? Does it mean that if we experienced a second Big Bang, after the cooling the Universe could have a different set of elementary particles?

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  • $\begingroup$ I don't think spontaneous symmetry breaking and the Higgs mechanism are basic ideas at all! $\endgroup$ – Arturo don Juan Nov 22 '16 at 22:12
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All the possible Higgs vacua on the lowest point of the Mexican hat have the same absolute value, they're just different in a "phase" related to the $\mathrm{SU}(2)$-theory being broken. With the current standard model, the only "vacuum" that gives different masses is the unstable vacuum at the top, where everything is massless. If you get a different low-energy universe, you started with a different theory, not the Standard Model.

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  • $\begingroup$ But what about if the vacuum is metastable? We could end up in the true not false vacua if the BB were repeated. $\endgroup$ – innisfree Nov 22 '16 at 21:40
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    $\begingroup$ It's not so metaphysical. There have been calculations with the Fokker-Planck equation etc. Search e.g. Higgstory and see the paper by Giudice et al. $\endgroup$ – innisfree Nov 23 '16 at 1:37
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    $\begingroup$ Oh and the SM is metastable... $\endgroup$ – innisfree Nov 23 '16 at 12:41
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    $\begingroup$ Take ordinary Higgs potential, add loop corrections ie effective potential. There's a deeper minima at 1E10 GeV or so, precise value depends on mtop and alphaS etc $\endgroup$ – innisfree Nov 24 '16 at 4:41
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    $\begingroup$ @innisfree Do you have a reference? All I can find is calculations like the one referenced here where it's within $2\sigma$ that the Higgs is stable with quantum corrections. $\endgroup$ – ACuriousMind Nov 24 '16 at 14:44

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