Dirac or Inverse Seesaw Neutrino Masses with $B-L$ Gauge Symmetry and $S_3$ Flavour Symmetry

Understand

Many studies have been made on extensions of the standard model with $B-L$ gauge symmetry.

• The addition of three singlet (right-handed) neutrinos renders it anomaly-free.
• It has always been assumed that the spontaneous breaking of $B-L$ is accomplished by a singlet scalar field carrying two units of $B-L$ charge.
• This results in a very natural implementation of the Majorana seesaw mechanism for neutrinos.