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A future lepton collider, such as the proposed CLIC or ILC, would allow tostudy top quark properties with unprecedented precision. In this paper, wepresent a method to reconstruct the $t \bar{t}$ decay in the dilepton channelat future $e^+e^-$ colliders. We derive a simple, closed analytical expressionfor the neutrino four-momenta as a function of the $W$ boson mass and develop amaximization procedure to find the optimal solution for the reconstruction ofthe full $t \bar{t}$ event. We show that our method is able to reconstructneutrino four-momenta with an error of less than $2 \, \%$ in $60 \, \%$ of thetimes. Finally, we test the performance of this reconstruction method in thecalculation of the helicity fractions of the $W$ boson. A precise measurementof these observables could be used to probe new physics effects in the $Wtb$vertex. We find that, from a large $t \bar{t}$ sample, our reconstructionmethod allows to calculate these observables with an accuracy better than $1 \,\%$.

Improving $t \bar{t}$ reconstruction in the dilepton channel at future lepton colliders