A Realistic Intersecting D6-Brane Model after the First LHC Run

With the Higgs boson mass around 125 GeV and the LHC supersymmetry search constraints, we revisit a three-family Pati-Salam model from intersecting D6-branes in Type IIA string theory on the $\mathbf{T^6/(\Z_2 \times \Z_2)}$ orientifold which has a realistic phenomenology. We systematically scan the parameter space for $\mu<0$ and $\mu>0$, and find that the gravitino mass is generically heavier than about 2 TeV for both cases due to the Higgs mass low bound 123 GeV. In particular, we identify a region of parameter space with the electroweak fine-tuning as small as $\Delta_{EW} \sim$ 24-32 (3-4$\%$). In the viable parameter space which is consistent with all the current constraints, the mass ranges for gluino, the first two-generation squarks and sleptons are respectively $[3, ~18]$ TeV, $[3, ~16]$ TeV, and $[2, ~7]$ TeV. For the third-generation sfermions, the light stop satisfying $5\sigma$ WMAP bounds via neutralino-stop coannihilation has mass from 0.5 to 1.2 TeV, and the light stau can be as light as 800 GeV. We also show various coannihilation and resonance scenarios through which the observed dark matter relic density is achieved. Interestingly, the certain portions of parameter space has excellent $t$-$b$-$\tau$ and $b$-$\tau$ Yukawa coupling unification. Three regions of parameter space are highlighted as well where the dominant component of the lightest neutralino is a bino, wino or higgsino. We discuss various scenarios in which such solutions may avoid recent astrophysical bounds in case if they satisfy or above observed relic density bounds. Prospects of finding higgsino-like neutralino in direct and indirect searches are also studied. And we display six tables of benchmark points depicting various interesting features of our model.