Stashing the stops in multijet events at the LHC

54 pages, 5 tables, 6 figuresWhile the presence of a light stop is increasingly disfavored by the experimental limits set on R-parity conserving scenarios, the naturalness of supersymmetry could still be safely concealed in the more challenging final states predicted by the existence of non-null R-parity violating couplings. Although R-parity violating signatures are extensively looked for at the Large Hadron Collider, these searches always assume 100\% branching ratios for the direct decays of supersymmetric particles into Standard Model ones. In this paper we scrutinize the implications of relaxing this assumption by focusing on one motivated scenario where the lightest stop is heavier than a chargino and a neutralino. Considering a class of R-parity baryon number violating couplings, we show on general grounds that while the direct decay of the stop into Standard Model particles is dominant for large values of these couplings, smaller values give rise, instead, to the dominance of a plethora of longer decay chains and richer final states that have not yet been analyzed at the LHC, thus weakening the impact of the present experimental stop mass limits. We characterize the case for R-parity baryon number violating couplings in the $10^{-7} - 10^{-1}$ range, in two different benchmark points scenarios within the model-independent setting of the low-energy phenomenological Minimal Supersymmetric Standard Model. We identify the different relevant experimental signatures, estimate the corresponding proton--proton cross sections at $\sqrt{s}=14$~\TeV\ and discuss signal versus background issues