Probing Anomalous FCNC Top-Higgs Yukawa Couplings at the Large Hadron Electron Collider

In this paper, we study the anomalous flavor changing neutral current Yukawa interactions between the top quark, the Higgs boson, and either an up or charm quark ($\mathrm{t}\mathrm{q}\mathrm{H},\mathrm{q}=\mathrm{u},\mathrm{c}$). We probe these couplings in $\rm e^- p\rightarrow \nu_e \bar{t} \rightarrow \nu_e H \bar{q}$andthechannel$\rm e^- p \rightarrow \nu_e H b$. Both channels are induced by charged current interactions through ${\mathrm{e}}^{-}\mathrm{p}$ collision at the Large Hadron Electron Collider(LHeC). We study the signatures with the Higgs decay modes $\rm H\rightarrow \gamma\gamma, b\bar{b}$and$\tau^+\tau^-$. Our results show that the flavor changing couplings ${\kappa }_{\mathrm{t}\mathrm{q}\mathrm{H}}$ can be probed down to a value of 0.0162 in ${\mathrm{e}}^{-}\mathrm{p}\to {\nu }_{\mathrm{e}}\bar{\mathrm{t}}\to {\nu }_{\mathrm{e}}\mathrm{H}\bar{\mathrm{q}}$ with $\mathrm{H}\to \mathrm{b}\bar{\mathrm{b}}$ at a 14 TeV LHeC with a 150 GeV electron beam and 200 $\mathrm{f}{\mathrm{b}}^{-1}$ luminosity. This value of the coupling corresponds to the branching ratio $\mathrm{B}\mathrm{r}(\mathrm{t}\to \mathrm{q}\mathrm{H})=1.34\times 0^{-4}$.