Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 305 / 1 / vii / Solution

In neutrino oscillation, a neutrino produced with definite flavor is a coherent superposition $|{\nu }_{\alpha }⟩={\sum }_i{U}_{\alpha i}^{\ast }|{\nu }_i⟩$ of mass eigenstates. Propagation gives the components different phases, producing a baseline- and energy-dependent probability to detect another flavor. Oscillation requires nonzero mass-squared differences and nontrivial mixing, so its observation proves that at least two neutrinos are massive and that individual flavor lepton numbers are not conserved. It measures mass differences and mixing parameters, though not the absolute neutrino-mass scale.