# Why is the proton so heavy?

## Main Question or Discussion Point

The quarks that make the proton are up, up and down with masses of around 2, 2 and 4 MeV/c^2 respectively. So, how come when added them together we arrive at a particle with the huge mass of about 931 MeV/c^2.

The only reason I can think of to explain this mass difference is the mass equivalence of the binding energy of the 3 quarks, however, I'm a little hesitant of this explanation because the mass difference is so large.

I've looked around on the internet and in a couple of particle physics books but I can't find any information.

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In a sense, you are right, but you'll need to learn about quantum chromodynamic binding energy to get a clearer picture.

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Thanks.

I found http://nohiggs.wordpress.com/2010/06/30/simple-mass-calculation/

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.
So acording to this, we have:

mass of a hadron is equal to the sum of its quark masses minus a mass equivalent to the binding energy between them

but then also

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

I don't get it. Minus or on top of it (which would be plus!)???

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

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.

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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.
But again, what makes people say that 98 percent of the mass of a proton comes from binding energy??!

tom.stoer
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.

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.
But what we also can say and must say is that the binding energy reduces the proton mass!

Here http://echochamber.me/viewtopic.php?f=18&t=14551" where that is confused. I think the last poster got it right. (At least it sounds right to me!)

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.)

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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!

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!
Yeah, you right, I just noticed that he talks nonsense, too!

Ok, here should be then the true story of http://www.frankwilczek.com/Wilczek_Easy_Pieces/342_Origin_of_Mass.pdf" [Broken]. (Or, more precise most of mass!)

He explains how you get mass, even if you assume that the quarks are massless. You can have a theory with massless particles as building blocks for a massive particle. Why? Because of m=E/c^2 and asymptotic freedom!

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Has anything to do the dimension oh radius of compaund via Coulomb and Newton laws about the energy that binding the components, and conseguently via m=E/C^2 ,in the mass??

tom.stoer