What makes a quark different from an electron in the "eyes" of the Higgs Field? Does it have to do with the specific values of hypercharge and isospin associated with these particles? What is the "source" of the specific mass values that arise for these particles?
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asked Aug 22, 2022 at 17:46
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1$\begingroup$ Each elementary species that owes its mass to the Higgs boson has a "charge" (for which I don't recall any technical term) to which that mass is proportional, but it's not any of the quantum numbers you suggest. Theory can't currently predict values for these, although it has something to say about $M_W/M_Z$. $\endgroup$– J.G.Commented Aug 22, 2022 at 17:59
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$\begingroup$ @J.G. Somehow the Higgs scalar and W-Z vectors seem related. Can't we say the Higgs is the scalar version of the W- and Z-vectors? $\endgroup$– GeraldCommented Aug 22, 2022 at 18:23
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1$\begingroup$ There's no such thing as a "scalar version" of them. Higgs & W/Z solve completely different theoretical problems. $\endgroup$– J.G.Commented Aug 22, 2022 at 18:53
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1 Answer
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The yukawa couplings $g$ of the individual particles to the higgs field are independent parameters of the model, and the coupling terms all look like $g\,\phi {\bar \psi}\psi$, which, in the low-energy approximation that the Higgs field is simply a constant at its minimum $\langle \phi\rangle $, comes out to $g\langle \phi\rangle {\bar \psi}{\psi}$, and, then, we merely label $g\langle \phi\rangle $ as $m$, and this term behaves like a mass term at low energies when compared to the weak scale.
Coming up with a reason why the yukawa couplings take the values they do is an open problem whose solution would probably mean a nobel prize to the person who does it.
answered Aug 22, 2022 at 18:00
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$\begingroup$ Oh so the values for the masses of the quarks and electrons aren't theoretical observations, then? We only can say for sure from the theory that they get "a" mass value? $\endgroup$ Commented Aug 22, 2022 at 18:54
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3$\begingroup$ @HritikNarayan: correct. We know all of the yukawa couplings because we've measured them in particle accelerators. There is no known a priori reason why they are what they are. $\endgroup$ Commented Aug 22, 2022 at 19:21