We present a study of the $b-\tau$ Yukawa unified supersymmetric $SU(4{)}_c\times SU(2{)}_L\times SU(2{)}_R$ model (with $\mu >0$), which predicts the existence of gluino—neutralino and stop—neutralino coannihilation scenarios compatible with the desired relic lightest supersymmetric particle neutralino dark matter abundance and other collider constraints. The next to lightest supersymmetric particle (NLSP) gluino or NLSP stop masses vary between 400 GeV and $\sim 1\mathrm{TeV}$. The NLSP gluinos will be accessible at the 14 TeV LHC, while we hope that the NSLP stop solutions will be probed in future LHC searches. We also identify regions of the parameter space in which the gluino and the lighter stop are closely degenerate in mass, interchangeably playing the role of NLSP and next to next to lightest supersymmetric particle (NNLSP). We also update a previous study of $t-b-\tau$ Yukawa unification and show that NLSP gluino of mass $\sim 1\mathrm{TeV}$, with a mass difference between the gluino and neutralino of less than 80 GeV, can be realized, consistent with the current collider and astrophysical constraints. We present benchmark points for $b-\tau$ and $t-b-\tau$ Yukawa unification that can be accessible at the LHC.

• Received 2 January 2015

DOI:https://doi.org/10.1103/PhysRevD.92.055010