Beta-decay of the free neutron and a (near) degenerate neutrino mass

Abstract

We discuss the β-decay of the free neutron w.r.t. a nonvanishing neutrino mass around 1 eV. If the neutrino mass spectrum is not hierarchical but (almost) degenerate such direct mass determinations are unavoidable. We point out that the Dalitz plot area in the vicinity of the kinematical point where the massive neutrino is exactly at rest is substantially larger for n→ pe − ν ̄ e than the corresponding area for triton decay. Present direct neutrino mass determinations from any β-decay ( n→ pe − ν ̄ e , 3 H→ 3 He + e − ν ̄ e ; etc.) are hampered by the experimental uncertainty (37 eV) of the unified atomic mass unit u. We have calculated for the reaction n→ pe − ν ̄ e that the dynamical neutrino mass effects are either O( m ν 2) or suppressed by tiny factors proportional to deviations from the weak leptonic V– A form. The remaining neutrino mass effects are purely kinematical and linear in m ν . Partially integrated decay rates (i.e., only electrons above a certain energy are detected) are particularly sensitive to the neutrino mass.