Neutrino Mass Spectrum and Future Beta Decay Experiments

We study the discovery potential of future beta decay experiments on searches for the neutrino mass in the sub-eV range, and, in particular, KATRIN experiment with sensitivity $m > 0.3$ eV. Effects of neutrino mass and mixing on the beta decay spectrum in the neutrino schemes which explain the solar and atmospheric neutrino data are discussed. The schemes which lead to observable effects contain one or two sets of quasi-degenerate states. Future beta decay measurements will allow to check the three neutrino scheme with mass degeneracy, moreover, the possibility appears to measure the CP-violating Majorana phase. Effects in the four neutrino schemes which can also explain the LSND data are strongly restricted by the results of Bugey and CHOOZ oscillation experiments: Apart from bending of the spectrum and the shift of the end point one expects appearance of small kink of ($ < 2% $) size or suppressed tail after bending of the spectrum with rate below 2 % of the expected rate for zero neutrino mass. We consider possible implications of future beta decay experiments for the neutrino mass spectrum, the determination of the absolute scale of neutrino mass and for establishing the nature of neutrinos. We show that beta decay measurements in combination with data from the oscillation and double beta decay experiments will allow to establish the structure of the scheme (hierarchical or non-hierarchical), the type of the hierarchy or ordering of states (normal or inverted) and to measure the relative CP-violating phase in the solar pair of states.
48 pages, LaTeX, 8 figures, typos removed, references and discussion of the supernova neutrino bounds added