# Why are there 3 quarks in proton?

A few quark related questions (I don't knowmuch about them other than there are 2 flavours concerning protons and neutrons)

Why are there 3 quarks in a proton or neutron? Why not 2 or 4?

Is there an upper limit to the size of an atom, before gravity starts combining protons and neutrons?

I've heard in here that quarks don't make up all the mass of a neutron/proton, if so what does?

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I think each of these 3 could (perhaps should) be a separate question. Although you do have an answer that addresses all three, I don't know if that should justify keeping it as is... –  David Z Dec 2 '10 at 2:11

## Why three quarks?

In very simple terms bound states of quarks (hadrons) have to be color neutral so that means either color quark + anticolor antiquark (mesons) or three quarks carrying R, G and B color charge respectively (baryons). (Note: There should also exist exotic particles like tetraquarks and pentaquarks but these haven't been observed yet and there is quark-gluon plasma which was observed. But none of this exotic matter can play role of a proton)

Now, it turns out that the most stable of all those hadronic particles is proton (which happens to be baryon). Everything else decays to other particles sooner or later (usually very soon) and can't possibly make up the stable matter around us. Neutron makes an exception to this because when it is bound in nucleus it becomes stable (well, not quite, radioactive beta decay can still occur).

Also note that even if some meson particle were stable, mesons are still bosons. So they wouldn't obey Pauli's exclusion principle and it would probably be impossible to build anything like nucleus from them. One very likely needs fermions for that and that means baryons and three quarks.

## Size of an atom

This has nothing to do with gravity. Big atoms are unstable purely for nuclear reasons (i.e. their nuclei decay extremely fast via radioactivity). Gravitational considerations are only important for huge objects (typically stars and their afterlife products like white dwarfs and neutron stars).

## Mass of a proton

Since Einstein we know that $E=mc^2$, i.e. energy is mass. So anytime there is some interaction you have to account for its binding energy when computing mass of a composite object. Mass of a proton comes almost exclusively from strong interactions that bind the three quarks together.

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Concerning the mass: it is very difficult to measure the intrinsic mass of quarks because they are never found free (a fact known as "confinement"), but the up and down quarks that make up the proton are thought to be very light (less than 10 MeV) so most of the proton's mass is binding energy. –  dmckee Dec 2 '10 at 1:29
@dmckee: sure it's difficult to measure but it still has some definite value in Standard Model and so it can be extrapolated from indirect measurements. And what do you mean that up quarks are thought to be light? They are known to have mass in the range 1.7-3.3 MeV. Are you just talking about statistical significance? –  Marek Dec 2 '10 at 11:14
That was meant as a further exposition (still at a rather pop-sci level) rather than a criticism. I left my value for the light quark masses inexact because the PDF has the down at about twice the values (that you list) for the up. –  dmckee Dec 2 '10 at 18:45
@dmckee: ah, all right then. Anyway, I understand perfectly well that concept of mass is far from being trivial in QFT and moreover so for quarks. So your comment certainly has its merits. By the way, right: down quarks are more massive. I only included up quark's mass because I misread the part of your comment that said "...make up the proton..." as referring to up quark :-) –  Marek Dec 2 '10 at 19:00