Past exam of the particle physics course of the University of Oxford / 2015 / 7 / c / iii / Solution

Use a high-multiplicity hadronic mode with only one invisible neutrino, and reconstruct the total visible four-momentum $p_h$. In the tau lepton rest frame,Fit the endpoint of the hadronic invariant mass distribution, preferably together with its laboratory energy boundary at known beam energy. The two-dimensional boundary uses more information than the single largest observed mass. Detector smearing, unseen neutral products, backgrounds, beam radiation and hadronic spectral modeling must be included. Absence of a displaced endpoint generally sets an upper bound rather than a positive neutrino mass measurement. Strictly the flavour state contains several mass eigenstates; an unresolved endpoint constrains the corresponding weighted mass spectrum.