What\'s the deepest reason why QCD bound states have integer electric charge, i.

Question

What's the deepest reason why QCD bound states have integer electric charge, i.e. equal to an integer times the electron charge?

Given that the quarks have the fractional electric charges they do, this is a consequence of color confinement. The charges of the quarks are constrained in the context of the standard model by anomaly cancellation, and can be explained by grand unification. The GUT explanation for the charges doesn't care about the bound state spectrum of the QCD sector, so it just seems to be a coincidence that hadrons (which are composite) have integer charge, and that leptons (which are elementary) also have integer charge.

Now maybe there's some anthropic argument for why such a coincidence is useful (in the case of proton and electron, it gives us atoms as we know them). Or maybe you can argue that GUTs naturally produce fractionally charged particles and strongly coupled sectors, and it's just not much of a coincidence.

But I remain curious as to whether Seiberg duality, anyons, some UV/IR relationship... could really produce something like the lepton-hadron charge coincidence, for deeper reasons. I suppose one is looking for a theory in which properties of bound states in one sector have a direct and nontrivial relationship to properties of elementary states in another sector. Is there anything like this out there?

(This question was prompted by muster-mark's many recent questions about fractional charge, and by a remark of Ron Maimon's that the hadron-lepton charge coincidence is a "semi-coincidence", which assured me that I wasn't overlooking some obvious explanation.)

Explanation / Answer

An experimentalist's view:

I do not see the need to search further for why the three quarks add up to the electron charge than that given by the group structure of the Standard Model. The SM is very successful in organizing into beautiful symmetries the particle and resonances data gathered the last sixty years or so. There is no experimental reason to assume further layers of compositness defining a "deeper" group structure from which the "measured" SU(3)xSU(2)xU(1) should emerge. It will just introduce a lower level of unnecessary complexity.

If what intrigues you is the unit one, after all we can always say the down quark has charge -1, the up quark 2 and the electron -3. The group symmetries are the same and we will have a generic unit 1 .

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