Signal events where multiple missing neutral particles are present in
a final state represent challenging topologies to search for new
physics at the LHC. The key to any search is the ability to separate
background-like events from signal-like events. Identifying such
signal-like events, and extracting their properties, is exacerbated by
a lack of knowledge of the particle masses and some missing kinematic
handles. In this talk we will briefly summarise the state-of-the-art
of searches for third generation Supersymmetry with the ATLAS
experiment. Then, we present a new method to search for open final
states where the decays of the two parent particles may proceed via
the same, or different, channels. For final states with weakly
interacting particles, a new basis of variables can be derived using
the “Recursive Jigsaw” technique. We discuss the application of this
procedure by considering final states containing 2 b-jets, 2 charged
leptons and missing transverse momentum. We apply the “Recursive
Jigsaw” reconstruction to extract quantities sensitive to scales and
angles on an event-by-event basis. The utility of this variable basis
is demonstrated by studying dileptonic ttbar decays in comparison to
various parameter choices for direct third generation scalar top quark
(stop) production, where each stop decays to bottom chargino, which
subsequently decay to a neutralino LSP via either on- or off-shell W
decay. The applicability of the variable basis is further demonstrated
using resonant ttbar production through a heavy graviton.