Explaining a CMS $eejj$ Excess With $\mathcal{R}-$parity Violating Supersymmetry and Implications for Neutrinoless Double Beta Decay

A recent CMS search for the right handed gauge boson $W_R$ reports an interesting deviation from the Standard Model. The search has been conducted in the $eejj$ channel and has shown a 2.8$\sigma$ excess around $m_{eejj}\sim 2$ TeV. In this work, we explain the reported CMS excess with R-parity violating supersymmetry (SUSY). We consider resonant selectron and sneutrino production, followed by the three body decays of the neutralino and chargino via an $\mathcal{R}-$parity violating coupling. We fit the excess for slepton masses around 2 TeV. The scenario can further be tested in neutrinoless double beta decay ($0\nu \beta \beta$) experiments. GERDA Phase-II will probe a significant portion of the good-fit parameter space.