2 - Kinematic Tests for Neutrino Mass

Summary

In this Chapter we shall discuss how neutrino mass can be determined from purely kinematic considerations of weak interaction processes. For simplicity, we assume here that only one neutrino is involved in a reaction or decay, leaving the more general situation of neutrino mixing until Chapter 4. We shall explore how finite neutrino mass will affect the momenta and energies of the charged particles emitted in a weak decay, as well as the overall decay rate. A complete review of all aspects of lepton spectroscopy can be found in Bullock & Devenish (83) and in the review article by Robertson & Knapp (88).

In treating the kinematics of weak decays, we shall first focus our attention on nuclear beta decay. We shall show that beta decay is a very sensitive tool for studying the electron antineutrino mass. Near the endpoint of the beta spectrum, a massive neutrino has so little kinetic energy that it becomes nonrelativistic, with the result that the decay probability depends linearly on mass. Of particular interest here is the low energy beta decay of tritium which, as we shall see, has the potential of determining neutrino mass down to a few eV. (It is customary to give the mass in units eV as well as eV/c².) As this is by far the most sensitive kinematic test for neutrino mass, we present in Section 2.1 a comprehensive discussion of several tritium experiments. We then turn to the muon neutrino and discuss the two-body decays of the pion into charged particles and neutrinos (Section 2.2), followed by the brief Section 2.3 on the tau neutrino mass.