A light sneutrino rescues the light stop

Stop searches in supersymmetric frameworks with $R$-parity conservation usually assume the lightest neutralino to be the lightest supersymmetric particle. In this paper we consider an alternative scenario in which the left-handed tau sneutrino is lighter than neutralinos and stable at collider scales, but possibly unstable at cosmological scales. Moreover the (mostly right-handed) stop $\widetilde t$ is lighter than all electroweakinos, and heavier than the scalars of the third generation doublet, whose charged component, $\widetilde\tau$, is heavier than the neutral one, $\widetilde\nu$. The remaining supersymmetric particles are decoupled from the stop phenomenology. In most of the parameter space, the relevant stop decays are only into $t \widetilde\tau \tau$, $t\widetilde\nu\nu$ and $b \widetilde\nu \tau$ via off-shell electroweakinos. We constrain the branching ratios of these decays by recasting the most sensitive stop searches. Due to the "double invisible" kinematics of the $\widetilde t\to t\widetilde\nu\nu$ process, and the low efficiency in tagging the $t\widetilde\tau\tau$ decay products, light stops are generically allowed. In the minimal supersymmetric standard model with $\sim$ 100 GeV sneutrinos, stops with masses as small as $\sim$ 350 GeV turn out to be allowed at 95% CL.