We revisit proton decay via the color-triplet Higgs multiplets in the minimal supersymmetric grand unified model with heavy sfermions. Although the model has been believed to be excluded due to the too short lifetime of proton, we have found that it is possible to evade the experimental constraints on the proton decay rate if the supersymmetric particles have masses much heavier than the electroweak scale. With such heavy sfermions, the 126 GeV Higgs boson is naturally explained, while they do not spoil the gauge coupling unification and the existence of dark matter candidates. Since the resultant proton lifetime lies in the regions which may be reached in the future experiments, proton decay searches may give us a chance to verify the scenario as well as the supersymmetric grand unified models.

A constraint on masses of superheavy gauge and Higgs multiplets at the grand unification (GUT) scale is obtained from the gauge coupling unification in the case of high-scale supersymmetry. We found that all of the particles may lie around a scale of 10 16 GeV so that the threshold corrections to the gauge coupling constants at the GUT scale are smaller than those in the case of the low-energy supersymmetry. In addition, the GUT scale tends to be slightly lower when the gauginos are heavier and, thus, the proton decay rate via the X-boson exchange process is expected to be enhanced.

Composite asymmetric dark matter scenarios naturally explain why the dark matter mass density is comparable with the visible matter mass density. Such scenarios generically require some entropy transfer mechanism below the composite scale; otherwise, their late-time cosmology is incompatible with observations. A tiny kinetic mixing between a dark photon and the visible photon is a promising example of the low-energy portal. In this paper, we demonstrate that grand unifications in the dark and the visible sectors explain the origin of the tiny kinetic mixing. We particularly consider an ultraviolet completion of a simple composite asymmetric dark matter model, where asymmetric dark matter carries a B − L charge. In this setup, the longevity of asymmetric dark matter is explained by the B −L symmetry, while the dark matter asymmetry originates from the B − L asymmetry generated by thermal leptogenesis. In our minimal setup, the Standard Model sector and the dark sector are unified into SU (5) GUT × SU (4) DGUT gauge theories, respectively. This model generates required B − L portal operators while suppressing unwanted higher-dimensional operators that could wash out the generated B − L asymmetry.

We calculate the high and low scale threshold corrections to the D = 6 proton decay mode in supersymmetric SU (5) grand unified theories with higher-dimensional representation Higgs multiplets. In particular, we focus on a missing-partner model in which the grand unified group is spontaneously broken by the 75-dimensional Higgs multiplet and the doublet-triplet splitting problem is solved. We find that in the missing-partner model the D = 6 proton decay rate gets suppressed by about 60%, mainly due to the threshold effect at the GUT scale, while the SUSY-scale threshold corrections are found to be less prominent when sfermions are heavy.

About 80% of the mass of the present Universe is made up of the unknown (dark matter), while the rest is made up of ordinary matter. It is a very intriguing question why the mass densities of dark matter and ordinary matter (mainly baryons) are close to each other. It may be hinting the identity of dark matter and furthermore structure of a dark sector. A mirrored world provides a natural explanation to this puzzle. On the other hand, if mirror-symmetry breaking scale is low, it tends to cause cosmological problems. In this letter, we propose a mirrored unification framework, which breaks mirror-symmetry at the grand unified scale, but still addresses the puzzle. The dark matter mass is strongly related with the dynamical scale of QCD, which explains the closeness of the dark matter and baryon masses. Intermediate-energy portal interactions share the generated asymmetry between the visible and dark sectors. Furthermore, our framework is safe from cosmological issues by providing low-energy portal interactions to release the superfluous entropy of the dark sector into the visible sector.