  Full event reconstruction is known to be challenging in cases with more than
one undetected final-state particle, such as pair production of two states each
decaying semi-invisibly. On the other hand, full event reconstruction would
allow to access angular distributions sensitive to the spin fractions of the
decaying particles, thereby dissecting their production mechanism. We explore
this possibility in the case of Standard-Model t-tbar production followed by a
leptonic decay of both W bosons, implying two undetected final-state neutrinos.
We estimate the t and tbar momentum vectors event by event using information
extracted from the kinematic variable MT2. The faithfulness of the estimated
momenta to the true momenta is then tested in observables sensitive to top
polarization and t-tbar spin correlations. Our method thereby provides a novel
approach towards the evaluation of these observables, and towards testing
t-tbar production beyond the level of the total cross section. While our
discussion is confined to t-tbar production as a benchmark, the method is
applicable to any process whose decay topology allows to construct MT2.
