Gluino-SUGRA scenarios in light of FNAL muon g-2 anomaly

Gluino-SUGRA ($\tilde{g}$SUGRA), which is an economical extension of the predictive mSUGRA, adopts much heavier gluino mass parameter than other gauginos mass parameters and universal scalar mass parameter at the unification scale. It can elegantly reconcile the experimental results on the Higgs boson mass, the muon $g-2$, the null results in search for supersymmetry at the LHC and the results from B-physics. In this work, we propose several new ways to generate large gaugino hierarchy (i.e. $M_3\gg M_1,M_2$) for $\tilde{g}$SUGRA model building and then discuss in detail the implications of the new muon $g-2$ results with the updated LHC constraints on such $\tilde{g}$SUGRA scenarios. We obtain the following observations: (i) For the most interesting $M_1=M_2$ case at the GUT scale with a viable bino-like dark matter, the $\tilde{g}$SUGRA can explain the muon $g-2$ anomaly at $1σ$ level and be consistent with the updated LHC constraints for $6\leq M_3/M_1 \leq 9$ at the GUT scale; (ii) For $M_1:M_2=5:1$ at the GUT scale with wino-like dark matter, the $\tilde{g}$SUGRA model can explain the muon $g-2$ anomaly at $2σ$ level and be consistent with the updated LHC constraints for $3\leq M_3/M_1 \leq 3.2$ at the GUT scale; (iii) For $M_1:M_2=3:2$ at the GUT scale with mixed bino-wino dark matter, the $\tilde{g}$SUGRA model can explain the muon $g-2$ anomaly at $1σ$ level and be consistent with the updated LHC constraints for $6.9\leq M_3/M_1 \leq 7.5$ at the GUT scale. Although the choice of heavy gluino will always increase the FT involved, some of the $1σ/2σ$ survived points of $Δa_μ^{combine}$ can still allow low EWFT of order several hundreds and be fairly natural. Constraints from (dimension-five operator induced) proton decay are also discussed.