A Minimal Supersymmetric SU(5) Missing-Partner Model

We explore a missing-partner model based on the minimal SU(5) gauge group with $\mathbf{75} $, $\mathbf{50} $ and $\overline{\mathbf{50 }}$ Higgs representations, assuming a super-GUT CMSSM scenario in which soft supersymmetry-breaking parameters are universal at some high scale $M_{\mathrm{in}}$ above the GUT scale $M_{\mathrm{GUT}}$. We identify regions of parameter space that are consistent with the cosmological dark matter density, the measured Higgs mass and the experimental lower limit on $\tau (p \rightarrow K^+ \nu )$. These constraints can be satisfied simultaneously along stop coannihilation strips in the super-GUT CMSSM with $\tan \beta \sim $3.5–5 where the input gaugino mass $m_{1/2} \sim $15–25 TeV, corresponding after strong renormalization by the large GUT Higgs representations between $M_{\mathrm{in}}$ and $M_{\mathrm{GUT}}$ to $m_{\mathrm{LSP}}, m_{{\tilde{t}}_1} \sim $ 2.5–5 TeV and $m_{{\tilde{g}}} \sim $ 13–20 TeV, with the light-flavor squarks significantly heavier. We find that $\tau (p \rightarrow K^+ \nu ) \lesssim 3 \times 10^{34}$ years throughout the allowed range of parameter space, within the range of the next generation of searches with the JUNO, DUNE and Hyper-Kamiokande experiments.