After playing around with possible charges for new fermionic fields, I came to the conclusion that ONLY the U(1) gauge group allows different particles to have different charge. This seems to be purely due to its commutative properties and since SU(N) gauge groups are not commutative, all particles must have the same charge with respect to that gauge field. This is supported by the standard model, where all couplings to the SU(2) field are g(adsbygoogle = window.adsbygoogle || []).push({}); _{2}/2 and all couplings to the SU(3) field are g (including self-coupling terms). So in reality it seems the only free parameters for the charge of a new fermionic field are its U(1) coupling strength, and whether or not it couples to the other two fields (2 discrete possibilities per field instead of an infinite number).

Is this conclusion correct? And can anyone explain it qualitatively with some higher-level reason? I understand mathematically why its not possible (it breaks gauge symmetry), but I have no idea why this makes sense physically...

Also take a meson for example. It contains two tightly bound quarks, and can be described by an effective field theory that treats the meson as a single field. We already know the U(1) charges add, but what would be the SU(2) charge of this meson in the effective theory?? If it's not g_{2}/2 I dont see how gauge invariance can be recovered..

*edit* I just realized that the meson would necessarily have 0 SU(2) charge if the charges of the quarks just add. So lets deal with baryons instead, where you have 3 quarks (no antiquarks) with the same SU(2) charge coupling.

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# Yang Mills SU(N) charge couplings

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