2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/203169With 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 promising new physics models. In this paper, we study the FC processes $e^+e^-(γγ)\to t\bar{c}$ 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.19 pages, 5 figuresHigh Energy Physics - Phenomenologytext