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Are there any theoretical restrictions within the framework of QFT that fix the relative sign between charged leptons and up-type quarks?

We know that in our universe, they have opposite signs -- but would a Standard Model in which they have the same sign run into any problems?

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Yes, a Standard Model where you inverted some of the charges and not others would be inconsistent. The hypercharge assignments in the Standard Model are fixed by anomaly cancellation. See this paper, for example.

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They are not completely fixed, as you can always add new particles with charges to fix up the anomaly. The real thing that fixes the charges is only SU(5) GUT. –  Ron Maimon Jul 24 '12 at 15:37
    
Sure. But you could take it as a hint of a desert, if you want. Ultimately it's an empirical question.... –  Matt Reece Jul 24 '12 at 20:07
    
@Ron Add new particles? Aren't there constraints on the number of particle generations too? –  dbrane Jul 24 '12 at 21:44
    
@dbrane: Not in families--- just add new charged particles to absorb anomalies. I didn't mean this is a serious theory, it is just a counterexample to the overly strong suggestion that the U(1) charges are determined uniquely by anomaly cancellation. This is almost true (there is still another solution) if you include only SM matter, but isn't true if you add extra stuff by hand, so it is not possible to say that the anomalies fix the charges. You can't predict the charges from algebraic constraints on the sum alone. –  Ron Maimon Jul 24 '12 at 22:04
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Nope, there aren't any theoretical reasons that relate the charge of the two in the SM, as far as I know. It's one of those mysteries that could be explained by grand unification theories. An example would be that the gauge structure of the Standard model actually comes from an SU(5) group. In this model, it arises naturally that the charges of quarks and leptons are related.

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