The littlest Higgs model with discrete symmetry named T-parity(LHT) is an interesting new physics model which does not suffer strong constraints from electroweak precision data. One of the important features of the LHT model is the existence of new s
ource of FC interactions between the SM fermions and the mirror fermions. These FC interactions can make significant loop-level contributions to the couplings $tcV$, and furthermore enhance the cross sections of the FC single-top quark production processes. In this paper, we study some FC single-top quark production processes, $ppto tbar{c}$ and $ppto tV$, at the LHC in the LHT model. We find that the cross sections of these processes are strongly depended on the mirror quark masses. The processes $ppto tbar{c}$ and $ppto tg$ have large cross sections with heavy mirror quarks. The observation of these FC processes at the LHC is certainly the clue of new physics, and further precise measurements of the cross scetions can provide useful information about the free parameters in the LHT model, specially about the mirror quark masses.
With high luminosity and energy at the ILC and clean SM backgrounds, the top-charm production at the ILC should have powerful potential to probe new physics. The littlest Higgs model with discrete symmetry named T-parity(LHT) is one of the most promi
sing new physics models. In this paper, we study the FC processes $e^+e^-(gammagamma)to tbar{c}$ at the ILC in the LHT model. Our study shows that the LHT model can make a significant contribution to these processes. When the masses of mirror quarks become large, these two processes are accessible at the ILC. So the top-charm production at the ILC provides a unique way to study the properties of the FC couplings in the LHT model and furthermore test the model.
