The golden strip of correlated top quark, gaugino, and vector-like mass in no-scale, no-parameter F-SU(5)

We systematically establish the hyper-surface within the tanβ, top quark mass mt, universal gaugino mass M1/2, and vector-like mass MV parameter volume which is compatible with the application of the no-scale supergravity boundary conditions, particularly the vanishing of the Higgs bilinear soft term Bμ, near to the Planck mass at the point MF of ultimate F-lipped SU(5) unification. MF is elevated from the penultimate partial unification near the traditional GUT scale at a mass M32 by the inclusion of extra F-theory derived heavy vector-like multiplets. We demonstrate that simultaneous adherence to all current experimental constraints, most importantly contributions to the muon anomalous magnetic moment (g−2)μ, the branching ratio limit on (b→sγ), and the 7-year WMAP relic density measurement, dramatically reduces the allowed solutions to a highly non-trivial “golden strip” with tanβ≃15, mt=173.0-174.4 GeV, M1/2=455-481 GeV, and MV=691-1020 GeV, effectively eliminating all extraneously tunable model parameters. We emphasize that the consonance of the theoretically viable mt range with the experimentally established value is an independently correlated “postdiction”. The predicted range of MV is testable at the Large Hadron Collider (LHC). The partial lifetime for proton decay in the leading (e|μ)+π0 channels falls around 4.6×1034 Y, testable at the future DUSEL and Hyper-Kamiokande facilities.