Phenomenological Study of Lepton Flavor Violation in Z Boson Decays with Constrained MSSM Extended by Type-II Seesaw Model

In this work, we study the lepton flavor violation (LFV) of Z boson decays in the framework of the constrained minimal supersymmetric standard model (CMSSM) extended by the type-II seesaw model. The branching ratios of $Z⟶l_i{l}_j$ decays are calculated in this model. Here, $l_i$ and $l_j$ are different flavor charged leptons. After fitting to the experimental mass limits of the neutrino and supersymmetric particles, we have found that the branching ratios for LFV decays of Z boson are in the order of $6\times {10}^{-10}$ for $e\mu$ channel and of $1\times {10}^{-9}$ for both $\tau \mu$ and $\tau e$ decay channels. Considering recent experimental constraints on $l_i\to l_j\gamma$ decays, the branching ratios for LFV decays of Z boson get an additional suppression of ${10}^{-8}$ for $e\mu$ channel and of ${10}^{-3}$ for both $\tau \mu$ and $\tau e$ decay channels. The branching ratios theoretical predictions are several orders below the recent experimental limits for both scenarios, which give a very low probability to observe the LFV decays of Z boson in the future experiments.