Hiding missing energy in missing energy

Searches for supersymmetry (SUSY) often rely on a combination of hard physics objects (jets, leptons) along with large missing transverse energy to separate New Physics from Standard Model hard processes. We consider a class of "double-invisible" SUSY scenarios: where squarks, stops and sbottoms have a three-body decay into two (rather than one) invisible final-state particles. This occurs naturally when the LSP carries an additional conserved quantum number under which other super-partners are not charged. In these topologies, the available energy is diluted into invisible particles, reducing the observed missing energy and visible energy. This can lead to sizable changes in the sensitivity of existing searches, dramatically changing the qualitative constraints on superpartners. In particular, for m(LSP) greater than or similar to 160 GeV, we find no robust constraints from the LHC at any squark mass for any generation, while for lighter LSPs we find significant reductions in constraints. If confirmed by a full reanalysis from the collaborations, such scenarios allow for the possibility of significantly more natural SUSY models. While not realized in the MSSM, such phenomenology occurs naturally in models with mixed sneutrinos, Dirac gauginos and NMSSM-like models.