Leptonic $Z$ decays in the littlest $Higgs$ model with T-parity

The littlest $Higgs$ model with T-parity (called the $LHT$ model) predicts the existence of the T-odd leptons, which can generate contributions to some leptonic processes at the one-loop level. We calculate their contributions to the leptonic $Z$ decay processes $Z\to l\bar{l'}$, $Z\to l\bar{l}$, and $Z\rightarro \nu\bar{\nu}$. We find that the T-odd leptons can give significant contributions to the branching ratios of these decay processes in most of the parameter space. The experimental measurement values might generate constraints on the free parameters of the $LHT$ model.