Flavor Changing Neutral Higgs Couplings and Top-Charm Production at Next Linear Collider

We explore the possibility of detecting flavor changing neutral Higgs couplings at the Next Linear Collider (NLC) through $e^+e^-\to \nu_e\bar{\nu_e} t\bar{c}$. In the framework of a general two-Higgs doublet model, we perform a complete calculation and find that $\sigma (e^+e^-\to \nu_e\nu_e t\bar{c}, \nu_e\bar{\nu_e} {\bar t}c)$ could reach $\sim 9$ fb for $\sqrt{s}=2 TeV$. This amounts to an annual production of 500 $t\bar{c}$ plus $\bar{t}c$ pairs at the NLC with an integrated luminosity of 50 fb$^{-1}$. The dependence of $tc$-production rate on the neutral scalar mixing angle is mild except when $\sin^2\alpha \to 0 or 1$. The $\nu\nu W^+W^-$ background should be manageable after $b$-tagging, while $\nu\nu t\bar t$ background should not be a problem when the signal event rate is still interesting. The process, together with $e^+e^-\to \nu_e\bar{\nu_e} W^+W^-, \nu_e\bar{\nu_e} ZZ$ studies, offer the chance of measuring the $t$-$c$-Higgs coupling.