Neutrino masses, the $\mu$-term and $\mathcal{ PSL}_2(7)$

Understand

Using an $SO(10)$-inspired form for the Dirac neutrino mass, we map the neutrino data to right-handed neutrino Majorana mass-matrix, $\mathcal M$, and investigate a special form with \emph{seesaw} tribimaximal mixing; it predicts a normal hierarchy, and the values of the light neutrino masses.

• It may be generated by mapping the top quark hierarchy onto the vacuum values of familon fields transforming under the family group $\mathcal{ PSL}_2(7)$.
• We next investigate the hypothesis that these familons play a dual role, generating a hierarchy in the supersymmetric $\mathbf \mu$-mass matrix of Higgses carrying family quantum numbers.
• A special $\mathcal{ PSL}_2(7)$ invariant coupling produces a $\mu$-matrix with a hierarchy of thirteen orders of magnitude.