Fine structure of beta decay end point spectrum

We note that the fine structure at the end point region of the beta decay spectrum is now essentially known using neutrino oscillation data, if the mass of one neutrino is specified. This may help to identify the effects of nonzero neutrino masses in future experiments. We also give a compact description of the entire range of allowed neutrino masses as a function of the third neutrino mass, m₃. A three neutrino assumption is being made. An exact treatment of phase space kinematics is used, in contrast to the conventional approximate formula. This work is independent of theoretical models; however, additional restrictions due to the assumption of a "complementary ansatz" for the neutrino mass matrix are also discussed. The ansatz implies that the values of the three neutrino masses should approximately be able to form a triangle. It is noted that most of the presently allowed neutrino mass sets have this triangular property.