  The results of many LHC searches for supersymmetric particles are interpreted
using simplified models, in which one fixes the masses and couplings of most
sparticles then scans over a few remaining masses of interest. We present a new
technique for combining multiple simplified models (that requires no additional
simulation) thereby highlighting the utility and limitations of simplified
models in general, and demonstrating a simple way of improving LHC search
strategies. The technique is used to derive limits on the stop mass that are
model independent, modulo some reasonably generic assumptions which are
quantified precisely. We find that current ATLAS and CMS results exclude stop
masses up to 340 GeV for neutralino masses up to 120 GeV, provided that the
total branching ratio into channels other than top-neutralino and
bottom-chargino is small, and that there is no mass difference smaller than 10
GeV in the mass spectrum. In deriving these limits we place upper bounds on the
branching ratios for complete stop pair decay processes for many values of the
stop, neutralino and chargino masses. These are available with this paper.
