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$(Z\to {\tilde{\chi }}_1^0{\tilde{\chi }}_1^0)={10}^{-3}$ and $m_{{\tilde{\chi }}_1^0}\sim 40$ GeV, the model parameter $\lambda’{112} / m^2{\tilde{f}}$canbediscovereddowntoaslowas$\sim 1.5 \times 10^{-14}$($3.9 \times 10^{-14}$)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).