Why is the proton so heavy?

By definition, the nuclear mass is equal to the sum of its constituents’ masses minus a mass equivalent to the binding energy between them. This is because it takes energy to separate 2 bound particles. The binding energy of protons and neutrons inside atomic nuclei amounts to less than 1% of their global mass, and one can therefore consider that the mass of protons and neutrons in the nucleus is very similar to that of free protons and neutrons.

The situation in hadrons is much more complex, because their binding energy is much higher, due to the Strong Interactions. Theoretically, separating the quarks from each other would require a huge amount of energy. Since energy is equivalent to mass, adding such a significant amount of energy to the system means greatly increasing the quark’s mass. Therefore, if the quark could exist outside the hadron, its mass would have been much larger. In fact, the bound quarks’ mass would have been dozens of times heavier had they not been bound. This is very different from what we know about electric forces. The binding energy of quarks inside the hadrons is a major component of the composite’s particle mass, on top of the masses of the quarks composing it.

Ok, the mass of a bound state of two particles is smaller than the mass of the two particles if they were free. It's of course because of binding energy.

Why on earth do some people then say that binding energy explains most of the mass of hadrons?

that makes no sense

Key phrase: "if they were free". But quarks are not free, and can never be*. Then you need to rethink what is meant by binding energy. In this case, you get a conflict between uncertainty principle and potential energy of the colour field, and although a compromise minimised the energy, it is still quite large.

* In the normal vacuum; if you put things into a different phase, different things come out.

Quarks and gluons inside the proton have kinetic energy which contributes to the mass as well. In a full QCD treatment it's difficult to talk about contributions like free quarks with masses, kinetic energy, potential energy / binding energy; all what one can say is that it's NOT the quark mass term which dominates the mass of the proton.

No, binding energy reduces mass, that's how protons and nuclei can be stable, because it takes energy to pull them apart, that energy becomes the mass of the constituent parts. Most of the proton's mass is in the gluons, that's the part that your magazine forgets about, but the gluons have a much much larger mass than a proton. The binding energy of the proton is so large though (because the strong force holds it together really well, hence the name Strong Force), that its mass is much lower than that of its constituent parts. This is also why the decay lifetime of the proton is/should be so cosmologically large (many order of magnitude larger than astronomically large.)

Is it do with the fact that the force holding quarks together increases as the distance between the quarks increases?


Also, the guy who you are quoting is wrong about the gluons, gluons are massless!