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I have read these questions:

How does the Higgs mechanism work?

How does the Higgs boson give mass to other elementary particles like electrons?

What is the difference between the Higgs Boson particle and an electron moving through the Higgs field?

Now my question is NOT about HOW they acquire mass. I understand SSB, and the Higgs mechanism, and Yukagawa coupling.

What these questions do not talk about though is, WHEN the W, Z, and the fermions gain their masses.

This question:

How does the Higgs boson give mass to other elementary particles like electrons?

And Prahar's answer says:

Thus, we find that if the Higgs field has a base value h, then the Higgs boson (described by f) has mass mHiggs=3λh2−m2−−−−−−−−−√ and the electron (described by ψ) has mass mel=gh. This process is the Higgs mechanism. If h=0, the electron is massless and this was the case a long time ago. At some point, the Higgs field attained a vev (base value) and h became nonzero and the electron was now massive!

This means that the W, Z bozons, and the fermions gain their masses at the SSB, when the Higgs field attained its nonzero VEV, so the W, Z bozons, and the fermions gained their masses at that point, and have mass since then.

This question:

What is the difference between the Higgs Boson particle and an electron moving through the Higgs field?

And Alfred Centauri's answer says:

In summary, The electroweak bosons become massive in the electroweak-charged Higgs condensate in a way analogous to the photon becoming massive in a superconductor. The matter particles, fermions, become massive in the condensate due to a Yukawa interaction. The Higgs boson would be massive regardless.

So this answer handles the Higgs field as a superconductor, and the W, Z bozons and fermions in it interact with the condensate, and gain their masses by interacting with the field. This means, that the W, Z bozons and fermions need to constantly interact with the Higgs field to gain their masses.

Now the two answers are contradictory. It cannot happen at the same time, that the W, Z bozons and the fermions gained their masses when the Higgs field gained its nonzero VEV at the SSB, and have their masses ever since, and at the same time, the W, Z bozons, and the fermions need to interact with the Higgs fiels constantly, and this constant interaction with the condensate gives them their masses.

Question:

  1. Which theory is right, when do the W, Z bozons, and the fermions gain their masses:

    a) they gain their masses at the SSB when the Higgs field gained its nonzero VEV

    b) they gain their masses whenever they interact with the Higgs field's condensate, that acts like a superconductor

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    $\begingroup$ They didn't gain mass to keep. They are gaining it every moment in the interactions since SSB. Both answers state the same. $\endgroup$
    – safesphere
    Commented Feb 20, 2019 at 5:01
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    $\begingroup$ The two answers are the same because the "Higgs condensate" (nonzero vev) came into being after SSB. $\endgroup$
    – Mitchell Porter
    Commented Feb 20, 2019 at 5:22
  • $\begingroup$ Perhaps you might have a skewed notion of incessant virtual interactions in QFT and what SSB consists of? $\endgroup$
    – Cosmas Zachos
    Commented Feb 20, 2019 at 16:10
  • $\begingroup$ When the universe was very young and hot, a long time ago, before SSB ... $\endgroup$
    – Bert Barrois
    Commented Feb 21, 2019 at 13:06
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    $\begingroup$ General comment, but a huge huge amount of your questions would be answered by just picking up a standard QFT textbook and reading it. You certainly have the time, drive, and mathematical background to do it; why not? $\endgroup$
    – knzhou
    Commented Feb 21, 2019 at 16:17

1 Answer 1

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Lets put it this way:

We have a mathematical theory/model that fits all the observed symmetries measured in elementary particle interactions called the standard model. This theory, to fit measurements and predict new ones with accuracy, includes the Higgs mechanism.

Without the Higgs mechanism everything would be massless, but then the model would not fit the real world data where few particles are massless. With the Higgs mechanism there is a satisfactory fit.

What is the Higgs mechanism? That all elementary particle fields entering the standard model field theory have zero vacuum expectation value, VEV, except the Higgs field which with a value of 246 GeV fits the data. So in our present world this is the status.

The particles do not interact with the Higgs field in the usual way of particle interactions, i.e. exchanging energy and momentum. Their mass is the effect that as they interact between themselves with the usual feynman diagrams they have a mass whose origin is the existence of the non zero expectation value of the Higgs field. It is all in the , complicated, mathematics.

This is the validated model. Since we have the mathematics, we can try and see when at cosmological times the Higgs field's VEV had zero value, and we find it is zero before electroweak symmetry breaking time, where at the break the nonzero VEV of the Higgs field of 246 GeV manifests.

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