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Write every fermion as a left-handed Weyl field. One Standard Model generation then haswith an optional neutral ${\nu }_R^c:(1,1{)}_0$. The purely colored anomaly vanishes becauseThe mixed non-Abelian-hypercharge coefficients areThe cubic hypercharge anomaly also cancels:as does the mixed gauge-gravitational anomaly,There is no perturbative cubic $SU(2)$ anomaly because its representations are pseudoreal. There are four left-handed weak doublets after counting the three colors of $Q_L$, so the global Witten SU(2) anomaly also vanishes. This proves Standard Model anomaly cancellation generation by generation.

The equality of proton and positron charges follows from the same constraints. Let the Higgs hypercharge be $Y_H=1/2$. Gauge-invariant Yukawa interactions implywhile cancellation of $[SU(2{)}_L{]}^{2}U(1{)}_Y$ gives $3Y_Q+Y_L=0$. Since electric charge is $Q=T^3+Y$,Thereforeshowing how anomaly cancellation, together with Yukawa gauge invariance and the normalization fixed by the neutral Higgs vacuum, enforces this instance of charge quantization.