Lepton Flavor Violation of Z Gauge Boson Decays in Supersymmetric Type-III Seesaw Model

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 τ μ, Z τ e and Z μ 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 τ μ and τ e decay channels and 6.40 × 10⁻¹⁰ for the μ e channel. After applying the constraints from the experimental bounds on the radiative two body decays lᵢ→ lⱼ γ, the branching ratios of the LFV of Z boson decays get an additional suppression of 10⁻³ for the τ μ and τ e decay channels and 10⁻⁸ for the μ 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.