The CP nature of the Higgs coupling to top quarks is addressed in this paper, in single charged lepton final states of $tbar{t}h$ events produced in proton-proton collisions at the LHC. Pure scalar ($h=H$) and pseudo-scalar ($h=A$) Higgs boson signal events, generated with MadGraph5_aMC@NLO, are fully reconstructed using a kinematic fit. Angular distributions of the decay products, as well as CP-sensitive asymmetries, are exploited to separate and gain sensitivity to possible pseudo-scalar components of the Higgs boson and reduce the contribution from the dominant irreducible background $tbar{t}bbar{b}$. Significant differences are found between the pure CP-even and -odd signal hypotheses as well as with respect to the Standard Model background, in particular the $tbar{t} bbar{b}$ contribution. Such differences survive the event reconstruction, allowing to define optimal observables to extract the Higgs couplings parameters from a global fit. A dedicated analysis is applied to efficiently identify signal events and reject as much as possible the expected Standard Model background. The results obtained are compared with a similar analysis in the dilepton channel. We show that the single lepton channel is more promising overall and can be used in combination to study the CP nature of the Higgs coupling to top quarks.
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