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Majorana ghosts: From topological superconductor to the origin of neutrino masses, three generations and their mass mixing

Recently, Majorana's spirit returns to modern condensed matter physics, in the context of Majorana zero mode in certain classes of topological superconductors. In this talk, I investigate the topological nature of a Majorana fermion by assuming that it is made up of four Majorana zero modes. First, I show that a pair of Majorana zero modes can realize a T^4 = -1 time reversal symmetry, a P^4 = -1 parity symmetry and even a nontrivial C^4= -1 charge conjugation symmetry. Next, I propose a CPT super algebra for the Majorana fermion made up of four Majorana zero modes. Furthermore, the origin of three generations of neutrinos can be naturally explained as three distinguishable ways to form a pair of (local) complex fermions out of four Majorana zero modes. Finally, I compute the mass mixing matrix and mass ratios of the three mass eigenstates from a first principle at leading order(in the absence of CP violation and charged lepton corrections). We obtain \theta_{12} = 31.7 , \theta_{ 23} = 45 , \theta_{13} = 0 and m1=m3 = m2=m3 = 3/\sqrt{5}. We also predict the effective mass in neutrinoless double beta decay to be m_{\beta\beta}= m1/\sqrt{5}.