Probing the supersymmetric grand unified theories with gravity mediation at the future proton-proton colliders and hyper-Kamiokande experiment

With the grand desert hypothesis, we have proposed to probe the supersymmetric Grand Unified Theories (GUTs) at the future proton-proton (pp) colliders and Hyper-Kamiokande experiment previously. In this paper, we study the supersymmetric GUTs with gravity mediated supersymmetry breaking in details. First, considering the dimension-six proton decay via heavy gauge boson exchange, we point out that we can probe the supersymmetric GUTs with GUT scale M${}_{GUT}$ up to 1.778 × 10${}^{16}$ GeV at the Hyper-Kamiokande experiment. Second, for the supersymmetric GUTs with M${}_{GUT}$ ≥ 1.0 × 10${}^{16}$ GeV and M${}_{GUT}$ ≥ 1.2 × 10${}^{16}$ GeV, we show that the upper bounds on the universal gaugino mass are 7.2 TeV and 3.5 TeV, respectively, and thus the corresponding upper bounds on gluino mass are 15 TeV and 8 TeV, respectively. Also, we shall study the masses for charginos, neutralinos, squarks, sleptons, and Higgs particles in details. In particular, the supersymmetric GUTs with M${}_{GUT}$ ≤ 1.2 × 10${}^{16}$ GeV can be probed at the Hyper-Kamiokande experiment, and the supersymmetric GUTs with M${}_{GUT}$ ≥ 1.2 × 10${}^{16}$ GeV can be probed at the future 100 TeV pp collider experiments such as the FCC${}_{hh}$ and SppC via gluino searches. Thus, the supersymmetric GUTs with gravity mediation can be probed by the FCC${}_{hh}$, SppC, and Hyper-Kamiokande experiments. In our previous study, we have shown that the supersymmetric GUTs with anomaly and gauge mediated supersymmetry breakings are well within the reaches of these experiments. Therefore, our proposal provides the concrete scientific goal for the FCC${}_{hh}$, SppC, and Hyper-Kamiokande experiments: probing the supersymmetric GUTs.