Exploring the Supersymmetric Grand Unified Theories with Gauge Mediation at the Future Proton-Proton Colliders and Hyper-Kamiokande Experiment

Abstract

As a continuation of our previous work, with the grand desert hypothesis, we prove that we can probe the Supersymmetric Grand Unified Theories (GUTs) with gauge meidation at the future proton-proton collider and Hyper-Kamiokande experiment. For the GUT scale $M_{\rm GUT}$ less than or equal to $0.84\times10^{16}$~GeV, the proton lifetime for dimension-six proton decay via heavy gauge boson exchange is less than or around $5\times10^{34}$ years, and thus we can probe it at the Hyper-Kamiokande experiment. For $ M_{\rm GUT} \ge 0.84 \times 10^{16}$ GeV, the lightest neutralino is the Next to the Lightest Supersymmetric Particle (NLSP), as well as the upper mass bounds on the gluino and first two generation squarks are 8.64 TeV and 11.82 TeV, respectively. Therefore, the gluino and first two generation squarks can be probed at the future 100 TeV proton-proton collider such as ${\rm FCC}_{\rm hh}$ and SppC. Moreover, we discuss the mass spectra for the colored sparticles, sleptons, pseudo-scalar Higgs and electroweakinos. If the sparticles were discovered, it might give us hint on the messenger scale, the effective supersymmetry breaking scale, and the renormalization group evolution of the supersymmetry breaking soft terms.