A Minimal Supersymmetric SU(5) Missing-Partner Model

Abstract

We explore a missing-partner model based on the minimal SU(5) gauge group with $75$, $50$ and $\overline{50}$ 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 $\tau (p\to K^{+}\nu )$. 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 $\tau (p\to K^{+}\nu )\lesssim 3\times 10^{34}$~yrs throughout the allowed range of parameter space, within the range of the next generation of searches with the JUNO, DUNE and Hyper-Kamiokande experiments.

30 pages, 13 figures