Quantization of electric charge from anomaly constraints and a Majorana neutrino

In gauge models of electroweak interactions where the gauge group contains an explicit U(1) factor contributing to U(1)ₑₘ, due to the arbitrariness of the U(1) quantum numbers, electric charge is not quantized. While requiring the cancellation of gauge and gravitational anomalies reduces the arbitrariness considerably, it is still not restrictive enough to fix all the quark and lepton charges. Analyzing a large class of gauge models that contain the right-handed neutrino νR, we find that the anomaly constraints, together with the requirement of nonvanishing fermion masses, lead to charge quantization only if the neutrino is a Majorana particle. The basic reason for this is the appearance of a hidden anomaly-free local U(1)_B-L symmetry in the Lagrangian, once νR is included, leading to a one-parameter family of solutions to the anomaly constraints. The Majorana mass of the neutrino breaks this hidden local symmetry. We also show that this phenomenon of charge ``dequantization'' occurs in models without νR due to the appearance of hidden anomaly-free horizontal U(1) symmetries. In these models, quantization of electric charge is restored by including Dirac mass terms that break the hidden symmetry. Our work provides a new way to understand charge quantization outside the framework of grand unified theories.