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We explore the implications of third family ($t-b-\tau$) quasi-Yukawaunification (QYU) for collider and dark matter (DM) searches within theframework of a supersymmetric $SU(4)_c \times SU(2)_L \times SU(2)_R$ model.The deviation from exact Yukawa unification is quantified through the relation$y_t : y_b : y_\tau = |1+C|:|1-C|:|1+3C|$, with $C$ being a real parameter($|C| \leq 0.2$). We allow for the breaking of left-right symmetry both by thesoft scalar and gaugino mass parameters and obtain a variety of viablesolutions that predict the sparticle mass spectrum including LSP DM (whosestability is guaranteed by a $Z_2$ gauge symmetry). We highlight solutions thatinclude an NLSP gluino with mass $\sim$ 1.3-2.5 TeV, which should be accessibleat LHC Run 3. There also exist NSLP stop solutions with masses heavier thanabout 1.8 TeV, which are consistent with the LSP neutralino dark matter relicdensity through stop-neutralino coannihilation. We identify A-resonancesolutions with DM mass $\sim$ 0.8 - 2 TeV, as well as bino-chargino,bino-slepton and bino-stau co-annihilation scenarios. Finally, we also identifyWino-like ($\sim99\%$) and Higgsino-like ($\sim99\%$) solutions whose massesare heavier than about 1.5 TeV and 1 TeV, respectively. These solutions arecompatible with the desired dark matter relic density and testable in ongoingand future direct detection experiments.

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