Long-lived light neutralinos at future $Z-$factories

Future lepton colliders such as the CEPC and FCC-ee would run as high-luminosity $Z-$boson factories, which offer a unique opportunity to study long-lived particles which couple to Z-bosons. In order to exemplify this particular advantage, in this work we consider one benchmark physics scenario where the long-lived lightest neutralinos pair $(\tilde{\chi}_1^0\tilde{\chi}_1^0)$ is produced from $Z-$decays in the context of the R-parity violating supersymmetry. Our analysis indicates that when assuming BR$(Z\rightarrow \tilde{\chi}_1^0\tilde{\chi}_1^0) = 10^{-3}$ and $m_{\tilde{\chi}_1^0} \sim 40$ GeV, the model parameter $\lambda'_{112} / m^2_{\tilde{f}}$ can be discovered down to as low as $\sim 1.5 \times 10^{-14}$ ($3.9 \times 10^{-14}$) GeV$^{-2}$ at the FCC-ee (CEPC) with center-of-mass energy $\sqrt{s} = 91.2$ GeV and 150 (16) ab$^{-1}$ integrated luminosity. These limits exceed the projected sensitivity reaches of the ATLAS experiment at the HL-LHC and the proposed LHC experiments with far detectors (AL3X, CODEX-b, FASER, and MATHUSLA).