The ABC of RPV: Classification of R-Parity Violating Signatures at the LHC for Small Couplings

We perform a classification of all potential supersymmetric $R$-parity violating signatures at the LHC to address the question: are existing bounds on supersymmetric models robust, or are there still signatures not covered by existing searches, allowing LHC-scale supersymmetry to be hiding? We analyze all possible scenarios with one dominant RPV trilinear coupling at a time, allowing for arbitrary LSPs and mass spectra. We consider direct production of the LSP, as well as production via gauge-cascades, and find 6 different experimental signatures for the $LL\bar{E}$-case, 6 for the $LQ\bar{D}$-case, and 5 for the $\bar{U}\bar{D}\bar{D}$-case; together these provide complete coverage of the RPV-MSSM landscape. This set of signatures is confronted with the existing searches by $\mathtt{\text{ATLAS}}$ and $\mathtt{\text{CMS}}$. We find all signatures have been covered at the LHC, although not at the sensitivity level needed to probe the direct production of all LSP types. For the case of a dominant $LL\bar{E}$-operator, we use $\mathtt{\text{CheckMATE}}$ to quantify the current lower bounds on the supersymmetric masses and find the limits to be comparable to or better than the $R$-parity conserving case. Our treatment can be easily extended to scenarios with more than one non-zero RPV coupling.