Neutrino masses from three-body decays

Abstract

Recent neutrino oscillation experiments have presented evidence for very small Δm 2 (eV 2)⪡1 which, if confirmed by independent experiments, can be interpreted in two different ways, namely in terms of a hierarchical neutrino mass scale but also in terms of a (near) neutrino mass degeneracy m ν τ ≈ m ν μ ≈ m ν e ≡ m ν . In the latter case direct neutrino mass determinations are called for to determine the value of m ν . Very recent data from the Sudbury Neutrino Observatory limit neutrino masses to 0.05 eV<∑ m ν i <8.4 eV which still allows m ν -values in the eV-range. We therefore take a fresh look at the principle sensitivity of weak three-body decays w.r.t. a nonvanishing neutrino mass of that order. The position of the point on the upper Dalitz plot boundary for which the final state (massive) neutrino is at rest is shown to be linearly sensitive to m ν . We present and discuss various analytical results for tritium decay, free neutron decay, pion radiative decay and tauon semi-leptonic decay.