The LFV decays of Z boson in Minimal R-symmetric Supersymmetric Standard Model

A future $Z$-factory will offer the possibility to study rare $Z$ decays $Z\rightarrow l_1l_2$, as those leading to Lepton Flavor Violation final states. In this work, by taking account of the constraints from radiative two body decays $l_2\rightarrow l_1\gamma$, we investigate the Lepton Flavor Violation decays $Z\rightarrow l_1l_2$ in the framework of Minimal R-symmetric Supersymmetric Standard Model with two benchmark points from already existing literatures. The flavor violating off-diagonal entries $\delta^{12}$, $\delta^{13}$ and $\delta^{23}$ are constrained by the current experimental bounds of $l_2\rightarrow l_1\gamma$. Considering recent experimental constraints, we also investigate Br($Z\rightarrow l_1l_2$) as a function of $M_D^W$. The numerical results show that the theoretical prediction of Br($Z\rightarrow l_1l_2$) in MRSSM are several orders of magnitude below the current experimental bounds. The Lepton Flavor Violation decays $Z\rightarrow e\tau$ and $Z\rightarrow \mu\tau$ may be promising to be observed in future experiment.