Electric charge quantization from gauge invariance of a Lagrangian: A catalogue of baryon-number-violating scalar interactions

In gauge theories such as the standard model, the electric charges of the fermions can be heavily constrained from the classical structure of the theory and from the cancellation of anomalies. There is, however, mounting evidence suggesting that these anomaly constraints are not as well motivated as the classical constraints. In light of this we discuss possible modifications of the minimal standard model that will give us complete electric charge quantization from classical constraints alone. Because these modifications to the standard model involve the consideration of baryon-number-violating scalar interactions, we present a complete catalogue of the simplest ways to modify the standard model so as to introduce explicit baryon number violation. This has implications for proton decay searches and baryogenesis.