Third family quasi-Yukawa unification: Higgsino dark matter, NLSP gluino, and all that

We explore the implications of third family (t - b - z) quasi-Yukawa unification (QYU) for collider and dark matter (DM) searches within the framework of a supersymmetric SU(4)c x SU(2)L x SU(2)R model. The deviation from exact Yukawa unification is quantified through the relation yt:yb:yz = (1 + C):(1 - C):(1 + 3C), with C being a real parameter (ICI & LE; 0.2). We allow for the breaking of left-right symmetry both by the soft scalar and gaugino mass parameters and obtain a variety of viable solutions that predict the sparticle mass spectrum including the lightest supersymmetric particle (LSP) DM (whose stability is guaranteed by a Z2 gauge symmetry). We highlight solutions that include a next to LSP (NLSP) gluino with mass & SIM;1.3-2.5 TeV, which should be accessible at LHC Run 3. There also exist NSLP stop solutions with masses heavier than about 1.8 TeV, which are consistent with the LSP neutralino dark matter relic density through stop-neutralino coannihilation. We identify A-resonance solutions, which arise when the CP-odd Higgs boson is in resonance with a pair of LSP neutralinos (mA = 2m & chi;& SIM;01) with DM mass & SIM;0.8-2 TeV, as well as bino-chargino, bino-slepton and bino-stau coannihilation scenarios. Finally, we also identify Wino-like (& SIM;99%) and Higgsino-like (& SIM;99%) solutions whose masses are heavier than about 1.5 and 1 TeV, respectively. These solutions are compatible with the desired dark matter relic density and testable in ongoing and future direct detection experiments.