  We consider SUSY-like events with two decay chains, each terminating in an
invisible particle, whose true energy and momentum are not measured in the
detector. Nevertheless, a useful educated guess about the invisible momenta can
still be obtained by optimizing a suitable invariant mass function. We review
and contrast several proposals in the literature for such ansatze: four
versions of the M_T2-assisted on-shell reconstruction (MAOS), as well as
several variants of the on-shell constrained M_2 variables. We compare the
performance of these methods with regards to the mass determination of a new
particle resonance along the decay chain from the peak of the reconstructed
invariant mass distribution. For concreteness, we consider the event topology
of dilepton ttbar events and study each of the three possible subsystems, in
both a ttbar and a SUSY example. We find that the M_2 variables generally
provide sharper peaks and therefore better ansatze for the invisible momenta.
We show that the performance can be further improved by preselecting events
near the kinematic endpoint of the corresponding variable from which the
momentum ansatz originates.
