The Heavy Gluino in Natural No-Scale $\cal{F}$-$SU$(5)

In light of recent 80-137 $\rm{fb}^{-1}$ results at the LHC Run 2 establishing a lower gluino mass limit of 2.25 TeV, we revisit the supersymmetric GUT model Flipped $SU$(5) with extra vector-like particles, known as $\cal{F}$-$SU$(5), with vanishing No-Scale Supergravity boundary conditions at the string scale of about $2 \times 10^{17}$ GeV, including the supersymmetry breaking $B_{\mu}$ parameter which is strictly enforced as $B_{\mu} = 0$. Given the proportional dependence of all model scales on a single parameter $M_{1/2}$, No-Scale $\cal{F}$-$SU$(5) was shown to possess no electroweak fine-tuning and thus persists as a $natural$ one-parameter model. In this fresh analysis here, we demand consistency with the measured 125 GeV light Higgs boson mass, though we forgo an upper limit on the lightest neutralino relic density. The resulting phenomenology delivers a gluino mass of $M(\widetilde{g}) \lesssim 7.5$ TeV and a lightest supersymmetric particle (LSP) of $M(\widetilde{\chi}_1^0) \lesssim 1.6$ TeV. In order to dilute the relic density down to the WMAP and Planck measurements, we rely upon a single cosmological master coupling $\lambda_6$.