Exploring the anomalous Higgs-top couplings

The top quark with its large Yukawa coupling is crucially important to explore TeV scale physics. Therefore, the study of the Higgs-top sector is highly motivated to look for any deviations from the standard model predictions. The most general lowest-order Lagrangian for the Higgs-top Yukawa coupling has scalar ($\ensuremath{\kappa}$) and pseudoscalar ($\stackrel{\texttildelow{}}{\ensuremath{\kappa}}$) components. Currently, these couplings are constrained indirectly using the present experimental limits on the Higgs-$\ensuremath{\gamma}$-$\ensuremath{\gamma}$ and Higgs-gluon-gluon couplings. Furthermore, stronger bounds on $\ensuremath{\kappa}$ and $\stackrel{\texttildelow{}}{\ensuremath{\kappa}}$ are obtained using the limits on the electric dipole moments (EDM). In this paper, we propose an asymmetrylike observable ${O}_{\ensuremath{\phi}}$ in $t\overline{t}H$ production at the LHC to probe the Higgs-top coupling and to distinguish between the scalar and pseudoscalar components. We also show that the presence of the pseudoscalar component in the Higgs-top Yukawa coupling leads to a sizeable value for the top quark EDM. It is shown that a limit of $1{0}^{\ensuremath{-}19}\text{ }\text{ }e.\mathrm{cm}$, which is achievable by the future ${e}^{\ensuremath{-}}{e}^{+}$ collider, allows us to exclude a significant region in the $(\ensuremath{\kappa},\stackrel{\texttildelow{}}{\ensuremath{\kappa}})$ plane.