Analytic solutions for neutrino momenta in decay of top quarks

We employ a geometric approach to analytically solve equations of constraint on the decay of top quarks involving leptons. The neutrino momentum is found as a function of the 4-vectors of the associated bottom quark and charged lepton, the masses of the top quark and W boson, and a single parameter, which constrains it to an ellipse. We show how the measured imbalance of momenta in the event reduces the solutions for neutrino momenta to a discrete set, in the cases of one or two top quarks decaying to leptons. The algorithms can be implemented concisely with common linear algebra routines. -- Highlights: • Neutrino momentum from top quark decay is constrained to an ellipse. • We find analytically the best neutrino momenta given the momentum imbalance. • A reference implementation of the algorithms is included