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

In the littlest Higgs model with T-parity (LHT), the mirror quarks have flavor structures and will contribute to the top quark flavor changing neutral current. In this work, we perform an extensive investigation of the top quark rare 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 ratios of $t\to cgg$ and $t\to cb\bar{b}$ could reach $\mathcal {O}(10^{-3})$ in the favorite parameter space of the littlest Higgs model with T-parity, which implies that these decays may be detectable at the LHC or ILC, while for the other decays, their rates are too small to be observable at the present or future colliders.