Golden point of no-scale and no-parameterF−SU(5)

Abstract

The ${\cal F}$-lipped $SU(5)\times U(1)_X$ Grand Unified Theory (GUT) supplemented by TeV-scale vector-like particles from ${\cal F}$-theory, together dubbed ${\cal F}$-SU(5), offers a natural multi-phase unification process which suggests an elegant implementation of the No-Scale Supergravity boundary conditions at the unification scale $M_{\cal F} \simeq 7 \times 10^{17}$ GeV. Enforcing the No-Scale boundary conditions, including $B_\mu(M_{\cal F})=0$ on the Higgs bilinear soft term, with the precision 7-year WMAP value on the dark matter relic density isolates a highly constrained "golden point" located near $M_{1/2} = 455$ GeV and $\tan \beta = 15$ in the $\tan\beta-M_{1/2}$ plane, which simultaneously satisfies all known experiments, and moreover corresponds to an imminently observable proton decay rate. Because the universal gaugino mass is actually determined from established low energy data via Renormalization Group Equation (RGE) running, there are no surviving arbitrary scale parameters in the present model.