In this study, we investigate the lepton flavor violation (LFV) of Z gauge boson decaying into two different flavor charged leptons Z lᵢ lⱼ (Z, Z e and Z e). This work is performed in the framework of the constrained minimal supersymmetric standard model (CMSSM) which is extended by the type-III seesaw mechanism. By considering constraints from the current experimental bounds on neutrino and supersymmetric particle masses, we calculate the branching ratios of the LFV of Z boson decays. The numerical results are found to be 1. 30 10^-9 for both the and e decay channels and 6. 40 10^-10 for the e channel. After applying the constraints from the experimental bounds on the radiative two body decays l₈ l₉, the branching ratios of the LFV of Z boson decays get an additional suppression of 10^-3 for the and e decay channels and 10^-8 for the e channel. The prediction of the branching ratios is found to be several orders of magnitude below the current experimental bounds for both scenarios. Thus the LFV of Z boson decays could be observed with low likelihood in the future collider experiments.
Hajahmad et al. (2025) studied this question.