Stops and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>E</mml:mi><mml:mi>T</mml:mi></mml:msub></mml:math>: The shape of things to come

LHC experiments have placed strong bounds on the production of supersymmetric colored particles (squarks and gluinos), under the assumption that all flavors of squarks are nearly degenerate. However, the current experimental constraints on stop squarks are much weaker, due to the smaller production cross section and difficult backgrounds. While light stops are motivated by naturalness arguments, it has been suggested that such particles become nearly impossible to detect near the limit where their mass is degenerate with the sum of the masses of their decay products. We show that this is not the case, and that searches based on missing transverse energy (${\mathrm{E\ensuremath{\llap{\not\;}}}}_{T}$) have significant reach for stop masses above 175 GeV, even in the degenerate limit. We consider direct pair production of stops, decaying to invisible lightest supersymmetric particles (LSPs) and tops with either hadronic or semileptonic final states. Modest intrinsic differences in ${\mathrm{E\ensuremath{\llap{\not\;}}}}_{T}$ are magnified by boosted kinematics and by shape analyses of ${\mathrm{E\ensuremath{\llap{\not\;}}}}_{T}$ or suitably chosen observables related to ${\mathrm{E\ensuremath{\llap{\not\;}}}}_{T}$. For these observables we show that the distributions of the relevant backgrounds and signals are well described by simple analytic functions, in the kinematic regime where signal is enhanced. Shape analyses of ${\mathrm{E\ensuremath{\llap{\not\;}}}}_{T}$-related distributions will allow the LHC experiments to place significantly improved bounds on stop squarks, even in scenarios where the stop-LSP mass difference is degenerate with the top mass. Assuming $20\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ of luminosity at $\sqrt{s}=8\text{ }\text{ }\mathrm{TeV}$, we conservatively estimate that experiments can exclude or discover degenerate stops with masses as large as $\ensuremath{\sim}360\text{ }\text{ }\mathrm{GeV}$, and 560 GeV for massless LSPs.