Three Generations in Minimally Extended Standard Models

We present a class of minimally extended standard models with the gauge group $SU(3)_C \times SU(N)_L \times U(1)_X$ where for all $N \geq 3$, anomaly cancelation requires three generations. At low energy, we recover the Standard Model (SM), while at higher energies, there must exist quarks, leptons and gauge bosons with electric charges shifted from their SM values by integer multiples of the electron charge up to $\pm [N/2] e$. Since the value N=5 is the highest $N$ consistent with QCD asymptotic freedom, we elaborate on the 3-5-1 model.

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