A Minimal Supersymmetric SU(5) Missing-Partner Model

TL;DR

This paper investigates a minimal supersymmetric SU(5) GUT model with specific Higgs representations, identifying parameter regions consistent with dark matter, Higgs mass, and proton decay constraints, and discusses implications for future experiments.

Contribution

It introduces a missing-partner SU(5) model within a super-GUT CMSSM framework, analyzing parameter space consistent with multiple experimental constraints and predicting proton decay rates.

Findings

Parameter space with stop coannihilation compatible with dark matter and Higgs mass.

Predicted proton decay lifetime within reach of upcoming experiments.

Heavy gaugino and squark masses consistent with current bounds.

Abstract

We explore a missing-partner model based on the minimal SU(5) gauge group with $\bf{75}$, $\bf{50}$ and $\bf{\overline{50}}$ Higgs representations, assuming a super-GUT CMSSM scenario in which soft supersymmetry-breaking parameters are universal at some high scale $M_{\rm in}$ above the GUT scale $M_{\rm GUT}$. 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 $M_{\rm in}$ and $M_{\rm GUT}$ to $m_{\rm LSP}, m_{\tilde t_1} \sim 2.5 - 5$~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.