Bound states in QCD: Why only bound states of 2 or 3 quarks and not more?

Why when people/textbooks talk about strong interaction, they talk only about bound states of 2 or 3 quarks to form baryons and mesons?

Does the strong interaction allow bound states of more than 3 quarks?

If so, how is the stability of a bound state of more than 3 quarks studied?

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There is no known reason that you can't have bound states like $qq\bar{q}\bar{q}$ or $qqqq\bar{q}$ or higher number excitations, but none have been observed to date.

You do have to make a color-neutral state, of course.

In the mid-2000 some folks thought that they had of pentaquark states (that the $qqqq\bar{q}$) for a while, but it was eventually concluded that they were wrong.

Added June 2013: Looks like we may have good evidence of four-quark bound states, though the detailed structure is not yet understood, and in the comments Peter Kravchuk points out that pentaquarks have come back while I wasn't paying attention (and the same state, too). Seem some egg may have moved from face to face.

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How the stability of such bound states is studied theoretically then? –  Revo Aug 6 '12 at 19:14
QCD is hard. Last time I heard, you could find theorists claiming either condition. –  dmckee Aug 6 '12 at 19:16
That is weird. Don't string theorists work with nonabelian gauge theories all the time. Since QCD is just another nonabelian gauge theory, I thought the answer to such question must have been known for sometime now. –  Revo Aug 6 '12 at 19:19
Being able to write down the theory and catalog it's properties is very different from being able to compute accurate solution to complicated problems. Full computations are very hard, which is why there is so much interest in solutions on the lattice. –  dmckee Aug 6 '12 at 19:28

In a sense every nucleus is a bound state of 3N quarks. After all, the nuclear force between nucleons (protons and neutrons) is a result of the leakage of the strong color force outside the "boundary" of the nucleon. So there are undoubtedly gluons and even quark exchanges between the nucleons of a nucleus.

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