Is the list of particles complete and unique?

tom.stoer

that's right, anomaly cancellation basically fixes the relation between different charges of different fermions within one multiplet; that was one reason why everybody believed in the existence of the top quark

friend

OK, then what physical properties does the U(1)SU(2)SU(3) symmetry determine in the SM? It's not the mass, nor the charge, nor the spin, not the speed, nor the position, nor the strength of interactions. Then what?

I understand that with symmetries come conserved "charges". So I suppose that the U(1)SU(2)SU(3) symmetry specifies the existence if the electromagnetic charge and the color charge and the, what is it, the weak force charge. So it tells us what interacts with what. But am I right to say that the SM symmetry does not specify the strength of those charges?