Majorana Physics Through the Cabibbo Haze

Understand

We present a model in which the Supersymmetric Standard Model is augmented by the family symmetry $\bs{\m Z_7 \rtimes \m Z_3}$.

• Motivated by $SO(10)$, where the charge two-thirds and neutral Dirac Yukawa matrices are related, we propose, using family symmetry, a special form for the seesaw Majorana matrix; it contains a squared correlated hierarchy, allowing it to mitigate the severe hierarchy of the quark sector.
• It is reproduced naturally by the invariant operators of $\bs{\m Z_7 \rtimes \m Z_3}$, with the hierarchy carried by familon fields.
• In addition to relating the hierarchy of the $\Delta I_{\rm w}=1/2$ to the $\Delta I_{\rm w}=0$ sector, it contains a Gatto-Sartori-Tonin like relation, predicts a normal hierarchy for Tri-bimaximal and Golden Ratio mixings, and gives specific values for the light neutrino masses.