Analytic solutions for neutrino momenta in decay of top quarks

TL;DR

This paper introduces an analytical geometric method to determine neutrino momenta in top quark decays involving leptons, simplifying the process by reducing solutions to discrete sets using measured momentum imbalances.

Contribution

It presents a novel geometric approach that analytically solves for neutrino momenta in top quark decays, incorporating event momentum imbalance constraints.

Findings

Neutrino momentum expressed as a function of known 4-vectors and masses.

Reduction of solutions to discrete sets using measured momentum imbalance.

Algorithms are concise and implementable with standard linear algebra routines.

Abstract

We employ a geometric approach to analytically solving 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.