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To my understanding fundamental particles gain mass due to interactions with the Higg’s field.

Yet you the majority of the mass associated with particles like Hadrons comes from the energy of them being in a bound state due to $E=mc^2 $.

Is this the same mass? Would the energy-equivalent mass exist were it not for the Higg’s field? How do both of those "masses", which to me really seem to be 2 separate concepts appear as the same thing to us?

Furthermore, particles that have the Higg’s-mass along with the energy-mass travel below $c$, yet light, which has only the energy-mass always travels at $c$, how is that?

In essense, how do these, to me seemingly completely different concepts of "mass" relate?

Qmechanic
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skytak picus
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2 Answers2

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In field theory, a scalar field $\phi $ is said to have mass if its Lagrangian possesses a non zero term $$\mathscr{L}_m=-\frac{1}{2}\mu^2 \phi^2$$ and $\mu$ is called its mass. As expounded by this answer, this number is readily identified with a mass by passing to Fourier space, wherein one obtains the Einstein momentum-mass dispersion relation. Expanding on my2cts answer, this means in a rest frame (the zero momentum mode of the field), its energy will come solely from its mass, as per $E=\mu c^2$.

So really under the definition of mass as energy in the rest frame, field theoretic and "relativistic kinematic" mass are the same concept. In a bound state between elementary massive particles that have been given mass by the Higgs mechanism, these non-zero $\mu$'s will all contribute and mix with the binding energy to result in a given energy at rest, and as such in a collective rest mass $m$. But the nature of this collective mass is the same as elementary mass; energy while at rest. A possible difference that may be argued are the mechanisms that give them energy at rest. Elementary particles have energy at rest because they are coupled to a Higgs field whose configuration has broken the full symmetry group of the Standard Model's Lagrangian; bound states have energy at rest because their constituents are coupled to the Higgs field in the way described above and also because they are interacting and as such possess binding energies.

Lourenco Entrudo
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Only the mass of truly elementary particles is theorised to be generated by coupling to the vacuum Higgs field (contradiction unintended). These contain no binding energy by definition. There is no interference with the expression E=mc$^2$.

Note that according to present insights only 0.9% of hadron mass comes from the Higgs field. See https://physics.stackexchange.com/a/673629/186017.

I define mass as the energy in the rest frame, or rather the frame in which the total momentum vanishes, divided by c$^2$.

my2cts
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