Constraining $t\to u$ flavor changing neutral Higgs coupling at the LHC

We study the constraints on $t\to u$ flavor changing neutral Higgs (FCNH) coupling, and how it may be explored further at the Large Hadron Collider (LHC). In the general two Higgs doublet model, such transitions can be induced by a nonzero ${\rho }_{tu}$ Yukawa coupling. We show that such couplings can be constrained by existing searches at the LHC for $m_H$, $m_A$ and, $m_{H^{+}}$ in the sub-TeV range, where $H$, $A$ and $H^{+}$ are the exotic $CP$-even, $CP$-odd and charged scalars. We find that a dedicated $ug\to tH\mathrm{/}tA\to tt\bar{u}$ search can probe the available parameter space of ${\rho }_{tu}$ down to a few percent level for $200GeV\lesssim m_H,m_A\lesssim 600$ GeV, with discovery possible at high luminosity. Effects of how other extra top Yukawa couplings, such as ${\rho }_{tc}$ and ${\rho }_{tt}$, dilute the sensitivity of the ${\rho }_{tu}$ probe are discussed.