We study light neutralinos \( \left({\overset{\sim }{\chi}}_1^0\right) \) with masses ranging from 10 GeV to several hundred GeV within the framework of R-parity-violating (RPV) supersymmetry. These light neutralinos can be long-lived, decaying with a macroscopic displacement (order cm) inside the LHC main detectors. Complementing previous works on the subject, here we focus on their production through the electroweak pair production of left-chiral sleptons \( \left({\tilde{e}}_L\right) \) , with the signal process pp → \( {\tilde{e}}_L^{+}{\tilde{e}}_L^{-} \) → \( {e}^{+}{\overset{\sim }{\chi}}_1^0{e}^{-}{\overset{\sim }{\chi}}_1^0 \) . In contrast to the previous study with a singly produced slepton, where the RPV coupling \( {\lambda}_{111}^{\prime } \) induces both the production and decay of the light neutralino, in our scenario the production proceeds through Drell-Yan-like processes that are essentially independent of RPV couplings. Correspondingly, we implement a displaced-vertex search strategy for which our numerical analysis shows that the high-luminosity LHC can probe \( {\lambda}_{111}^{\prime } \) values up to three orders of magnitude smaller, and neutralino masses up to about four times larger than those accessible in the previously studied single-slepton production scenario.
