Top Quark FCNC Decay to 125GeV Higgs boson in the Littlest Higgs Model with T-parity

Motivated by the current observation of a 125 GeV Higgs boson, we calculate $t\rightarrow cH$ and $t\rightarrow cg(\gamma)H$ in the unitary gauge in the littlest Higgs model with T-parity(LHT). Due to the large contribution from the new mirror fermions, we find that the branching ratios of $t\rightarrow cH$ and $t\rightarrow cgH$ can be greatly enhanced in the LHT model and maximally reach $\mathcal O(10^{-5})$ in the allowed parameter space. When the mirror fermion mass $M_3 > 2(1.5)$ TeV and the cut-off scale $f=500$ GeV, the process of $pp \to t\bar{t} \to 3b +c +\ell+ \slashed E_{T}^{miss}$ can reach $3\sigma$($5\sigma$) sensitivity at 8(14) TeV LHC with luminosity $\cal{L}$ $=20(300) fb^{-1}$.