The upper bounds on supersymmetry breaking scales in split supersymmetry from the Higgs mass and electroweak vacuum stability

The null results of the LHC searches have put strong bounds on new physics scenarios such as supersymmetry (SUSY). With the latest values for the top quark mass and strong coupling, we study the upper bounds on the sfermion masses in split SUSY from the observed Higgs boson mass and electroweak (EW) vacuum stability. To be consistent with the observed Higgs mass, we find that the largest values of supersymmetry breaking scales $M_{S}$ for $\tan\beta=2$, $\tan\beta=4$, and $\tan\beta=50$ are $10^{6.2}$, $10^{4.5}$, and $10^{4.3}\, {\rm GeV}$, respectively. In particular, split SUSY with $\tan\beta \gtrsim 4$ can be probed in future 100 TeV proton–proton colliders such as FCC-hh and SppC. In addition, the Higgs quartic coupling becomes negative at about $10^{8.2}$, $10^{8.7}$, and $10^{9.6}\, {\rm GeV}$ respectively for $m_h =$ 123, 125, and 127 GeV from EW vacuum stability. These bounds are about one order smaller than the Standard Model due to the extra Higgs–Higgsino–gaugino couplings. We briefly comment on the lifetime of gluinos in our study and compare it with the current LHC observations. Additionally, we comment on the prospects of the discovery of prompt gluinos at the FCC-hh and SppC.