Strictly solvable $d=4$ quantum field theory models with unitarity violation. Possible implications for baryon asymmetry of the Universe and dark matter

Abstract

In this paper we consider quantum field theory with unitarity violation. We construct several $d = 4$ strictly solvable models with unitarity violation. As a possible application of the models with unitarity violation we construct two models explaining the observed baryon asymmetry of the Universe and the dark matter existence. In considered models dark matter particles have nonzero baryon number and the total baryon number of the Universe being the sum of the baryon number of the matter and dark matter is equal to zero. Dark matter paricles have mass $\sim 6~GeV$. Proposed models predict negligible cross sections of the dark matter with nuclei and electrons. It means that underground experiments will fail to discover dark matter.