We explore how the seesaw sector in neutrino mass models may be constrained through symmetries to be completely determined in terms of low-energy mass, mixing angle and $CP$-violating phase observables. The key ingredients are intrafamily symmetries to determine the neutrino Dirac mass matrix in terms of the charged-lepton or quark mass matrices, together with interfamily or flavor symmetries to determine diagonalization matrices. Implications for leptogenesis and collider detection of heavy neutral leptons are discussed. We show that leptogenesis can succeed in small regions of parameter space for the case where the neutrino Dirac mass matrix equals the up-quark mass matrix. The model where the neutrino Dirac mass matrix equals the charged-lepton mass matrix can yield a heavy neutral lepton as light as about 1 TeV, but detecting such a particle will be difficult.

• Received 13 October 2008

DOI:https://doi.org/10.1103/PhysRevD.78.113001