Elementary particles and their interactions are described by the theory, known as the Standard Model. Despite the fact that it successfully describes an enormous amount of experimental data, the Standard Model cannot describe neutrino masses, baryon asymmetry and does not provide a source for the dark matter. These aspects suggest that the Standard Model should be a part of a more fundamental theory, examples of which are the Grand Unified Theories. Grand Unified Theories propose the source of the dark matter to be an invisible right-handed fermion, which can be interpreted as the right-handed neutrino, a particle not included in the Standard Model. Interactions between this dark matter candidate and quarks are induced by a colored scalar particle, called leptoquark, the couplings of which are suppressed due to its extremely high mass. This work studies hypothetical proton and neutron decays, induced by the massive colored scalars. The emphasis is on the search of such neutron decays into dark matter particle, which simultaneously prevent destabilization of the proton, and on the search of neutron decay mode, explaining the neutron lifetime anomaly. The results of this work serve as a basis for future theoretical and experimental researches of nucleon decays as well as for future searches of dark particles.
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