Leptonic unitarity triangles and effective mass triangles of the Majorana neutrinos

Given the best-fit results of six neutrino oscillation parameters, we plot the Dirac and Majorana unitarity triangles (UTs) of the 3×33×3 lepton flavor mixing matrix to show their real shapes in the complex plane. The connections of the three Majorana UTs with neutrino–antineutrino oscillations and neutrino decays are explored, and the possibilities of right or isosceles UTs are discussed. In the neutrino mass limit of m1→0m1→0 or m3→0m3→0, which is definitely allowed by current data, we show how the six triangles formed by the effective Majorana neutrino masses 〈m〉αβ〈m〉αβ (for α,β=e,μ,τα,β=e,μ,τ) and their corresponding component vectors look like in the complex plane. The relations of such triangles to the Majorana phases and to the lepton-number-violating decays H++→α+β+H++→α+β+ in the type-II seesaw mechanism are also illustrated.