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I read a pop sci book on the Higgs which said that particles get their mass due to interacting with the Higgs field. If that is true, could we use first principles to derive the mass of, say, an electron? After all, QED is built on the interactions of particles and fields, right?

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    $\begingroup$ Not using the Standard Model: the Yukawa couplings are free parameters. $\endgroup$ – dukwon May 12 '17 at 20:50
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    $\begingroup$ @dukwon It's true that the in the standard model the yukawa's are free parameters. But some of them have been now measured explerimentally at the LHC, e.g. the one for the top and bottom quarks. Hence from the measurement of these trilinear couplings one can calculate the mass of the fermion, in great agreement with the independent measuremets of its mass. This is in fact a great success of the Standard Model. $\endgroup$ – TwoBs May 12 '17 at 21:09
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    $\begingroup$ Hadron masses are due to QCD effects which can be computed quite accurately, see e.g. here. $\endgroup$ – Count Iblis May 13 '17 at 1:12
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We could if we'd know the coupling between the Higgs field and other particles. Instead, we use the measured mass of particles to get the value of this coupling.

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  • $\begingroup$ Some couplings, e.g. the top and bottom Yukawa's are indeed measured at the LHC, independently from the bottom and top quark masses, from the rate of the higgs production and decay. This means, that using these couplings as an input one could extract the masses using the SM prediction $m_f=y_f v/\sqrt{2}$, which happens to be experimentally verified, hence confirming once more the success of the Standard Model. $\endgroup$ – TwoBs May 13 '17 at 22:23
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This is the table of the elementary particles of the standard model, SM.

elempart

The masses have been measured experimentally and the whole table is part of the postulates/axioms of the standard model. These masses within the SM are generated by the Higgs mechanism. The SM up to now is very successful in describing and predicting data. No theory has come up with a prediction of these postulated masses , while embedding the successes of the SM, so the answer is no for the elementary particles.

All other masses are composites of these elementary particles. For the mass of the hadrons the internal dynamics of QCD have to be used, and there has been a laborious lattice calculation that does give the hadron masses.

In the work presented here, a full calculation of the light hadron spectrum in QCD, only three input parameters are required: the light and strange quark masses and the coupling g .

qcdmass

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At the moment there is no experimentally proven theory which could predict the masses of the elementary particles (for composed particles predictions can be made using mainly SM and to less extent the masses of the elementary particles) of the standard model(SM). The standard model does not make any prediction on the masses of its "members". That's one of the reasons why the physicists consider the standard model as not complete. One SM-extension (among a couple of other theories) is supersymmetry of which some of its variants together with the Grand Unified Theories (GUT) predict to some extent masses for the standard model particles (it's still not fully worked out), but actually there is no experimental evidence of supersymmetry (neither of GUT) at the moment. The particle masses still remain a mystery, in particular its bandwidth from neutrino masses of a few eV up to the top-quark mass of ~172GeV. The Higgs, so to say, only makes particles massive, but does not give us a clue about their values.

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