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In the littlest Higgs model with T-parity (LHT), the mirror quarks haveflavor structures and will contribute to the top quark flavor changing neutralcurrent. In this work, we perform an extensive investigation of the top quarkrare three-body decays $t\to cVV (V=\gamma,Z,g)$ and $t\to cf\bar{f}(f=b,\tau,\mu,e)$ at one-loop level. Our results show that the branching ratiosof $t\to cgg$ and $t\to cb\bar{b}$ could reach $\mathcal {O}(10^{-3})$ in thefavorite parameter space of the littlest Higgs model with T-parity, whichimplies that these decays may be detectable at the LHC or ILC, while for theother decays, their rates are too small to be observable at the present orfuture colliders.

Top quark rare three-body decays in the littlest Higgs model with T-parity