A minimal supersymmetric SU(5) missing-partner model

We explore a missing-partner model based on the minimal SU(5) gauge group with $$\mathbf{75} $$ 75 , $$\mathbf{50} $$ 50 and $$\overline{\mathbf{50 }}$$ 50 ¯ Higgs representations, assuming a super-GUT CMSSM scenario in which soft supersymmetry-breaking parameters are universal at some high scale $$M_{\mathrm{in}}$$ M in above the GUT scale $$M_{\mathrm{GUT}}$$ M 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 $$\tau (p \rightarrow K^+ \nu )$$ τ ( p → K + ν ) . These constraints can be satisfied simultaneously along stop coannihilation strips in the super-GUT CMSSM with $$\tan \beta \sim $$ tan β ∼ 3.5–5 where the input gaugino mass $$m_{1/2} \sim $$ m 1 / 2 ∼ 15–25 TeV, corresponding after strong renormalization by the large GUT Higgs representations between $$M_{\mathrm{in}}$$ M in and $$M_{\mathrm{GUT}}$$ M GUT to $$m_{\mathrm{LSP}}, m_{{\tilde{t}}_1} \sim $$ m LSP , m t ~ 1 ∼ 2.5–5 TeV and $$m_{{\tilde{g}}} \sim $$ m g ~ ∼ 13–20 TeV, with the light-flavor squarks significantly heavier. We find that $$\tau (p \rightarrow K^+ \nu ) \lesssim 3 \times 10^{34}$$ τ ( p → K + ν ) ≲ 3 × 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.