Dirac or inverse seesaw neutrino masses with B−LB−L gauge symmetry and S3S3 flavor symmetry

Many studies have been made on extensions of the standard model with B−LB−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−LB−L is accomplished by a singlet scalar field carrying two units of B−LB−L charge. This results in a very natural implementation of the Majorana seesaw mechanism for neutrinos. However, there exists in fact another simple anomaly-free solution which allows Dirac or inverse seesaw neutrino masses. We show for the first time these new possibilities and discuss an application to neutrino mixing with S3S3 flavor symmetry.