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In the simplest little Higgs model the new flavor-changing interactionsbetween heavy neutrinos and the Standard Model leptons can generatecontributions to some lepton flavor violating decays of $Z$-boson at one-looplevel, such as $Z \to \tau^{\pm}\mu^{\mp}$, $Z\to \tau^{\pm}e^{\mp}$, and $Z\to \mu^{\pm}e^{\mp}$. We examine the decay modes, and find that the branchingratios can reach $10^{-7}$ for the three decays, which should be accessible atthe Giga$Z$ option of the ILC.

The lepton flavor violating decays $Z\to l_i l_j$ in the simplest little Higgs model