Measuring CP nature of top-Higgs couplings at the future Large Hadron electron Collider

We investigate the sensitivity of top-Higgs coupling by considering the associated vertex as CP phase (ζ<inf>t</inf>) dependent through the process pe⁻→t¯hν<inf>e</inf> in the future Large Hadron electron Collider. In particular the decay modes are taken to be h→bb¯ and t¯ → leptonic mode. Several distinct ζ<inf>t</inf> dependent features are demonstrated by considering observables like cross sections, top-quark polarisation, rapidity difference between h and t¯ and different angular asymmetries. Luminosity (L) dependent exclusion limits are obtained for ζ<inf>t</inf> by considering significance based on fiducial cross sections at different σ-levels. For electron and proton beam-energies of 60 GeV and 7 TeV respectively, at L=100 fb⁻¹, the regions above π/5<ζ<inf>t</inf>≤π are excluded at 2σ confidence level, which reflects better sensitivity expected at the Large Hadron Collider. With appropriate error fitting methodology we find that the accuracy of SM top-Higgs coupling could be measured to be κ=1.00±0.17(0.08) at s=1.3(1.8) TeV for an ultimate L=1ab⁻¹.