Three Generations in Minimally Extended Standard Models

TL;DR

This paper introduces a class of minimally extended Standard Models with gauge group SU(3)_C x SU(N)_L x U(1)_X, requiring three generations for anomaly cancellation, and explores the specific 3-5-1 model with N=5.

Contribution

The paper proposes a new class of models extending the Standard Model gauge symmetry, demonstrating anomaly cancellation for all N ≥ 3, and details the specific 3-5-1 model with unique charge assignments.

Findings

Anomaly cancellation requires three generations for all N ≥ 3.

At low energies, models recover the Standard Model.

Higher energy regimes predict new particles with shifted electric charges.

Abstract

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.