b - τ Yukawa unification in SUSY SU(5) with mirage mediation: LHC and dark matter implications

We consider a class of b − τ Yukawa unified Supersymmetric (SUSY) SU(5) GUTs, in which the asymptotic gaugino M1,2,3 masses are generated through the mirage mediated supersymmetry breaking, which is a combination of the gravity and anomaly mediation. Due to the contributions from the anomaly contribution, M3 is always lighter than M1 and M2, and consequently for the range of asymptotic masses considered, the gluino mass $$ {m}_{\tilde{g}} $$ at low scale is bounded from above at about 4 TeV. We realize two different regions, in one of which the MSSM μ−term is less than about 3 TeV. This region yields a stop mass up to 5 TeV, and the stop mass is nearly degenerate with the LSP neutralino for mass around 0.8 to 1.7 TeV. A stau mass can be realized up to about 5 TeV, and the stau mass is approximately degenerate with the LSP neutralino for mass around 2 to 3 TeV. In addition, an A-funnel solution with $$ {m}_A\approx 2{m}_{{\tilde{\chi}}_1^0} $$ and $$ {m}_{{\tilde{\chi}}_1^0}\sim 700-900 $$ GeV is realized. These three cases yield LSP dark matter abundance in accordance with observations. A second region, on the other hand, arises for $$ {m}_{\tilde{g}}\lesssim 1.1{m}_{{\tilde{\chi}}_1^0} $$ . The μ−term is rather large (≳20 TeV), and the LSP neutralino is a bino-wino mixture. The gluino mass (∼ 0.8−1.2 TeV) is nearly degenerate with the LSP neutralino mass and hence, the gluino-neutralino coannihilation processes play a role in reducing the relic abundance of LSP neutralino down to ranges allowed by the current WMAP measurements. The two regions above can be distinguished through the direct detection experiments. The first region with relatively low μ values yields Higgsino-like DM, whose scattering on the nucleus typically has a large cross-section. We find that such solutions are still allowed by the current results from the LUX experiment, and they will be severely tested by the LUX-Zeplin (LZ) experiment. The second region contains bino-wino DM whose scattering cross-section is relatively low. These solutions are harder to rule out in the foreseeable future.