Speaker
Michael Perez
(University of Flordia)
Description
We present a model with the family group $\mathcal{PSL}_2(7)$ wherein the top quark hierarchy, through $SO(10)$ and the Seesaw mechanism, is mapped onto the vacuum values of familon fields and transferred to the $\Delta I_{\rm w}=0$ parameters of the $\nu$MSSM: the right-handed neutrino Majorana mass $\mathcal{M}$ and the mu term. It predicts tribimaximal mixing, and a normal hierarchy for the light neutrinos. The familon vacuum is used to derive the supersymmetric $\mu$-masses of Higgs fields with family quantum numbers, as well as the Yukawa matrices of the quarks and leptons. We find, through the magic of $\mathcal{PSL}_2(7)$ invariants, a $\mu$-matrix with a hierarchy of thirteen orders of magnitude. Only one Higgs field (per hypercharge sector) is light enough (with a $\mu$-mass ~ 10-100 GeV) to be destabilized by SUSY soft breaking at the TeV scale. Remarkably, their vacuum values generate unsupressed masses only for $t$, $b$, and $\tau$.
Primary author
Michael Perez
(University of Flordia)
