Probing the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>C</mml:mi><mml:mi>P</mml:mi></mml:math> nature of the Higgs coupling in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>t</mml:mi><mml:mover accent="true"><mml:mi>t</mml:mi><mml:mo stretchy="false">¯</mml:mo></mml:mover><mml:mi>h</mml:mi></mml:math> events at the LHC

The determination of the $CP$ nature of the Higgs coupling to top quarks is addressed in this paper, using $t\overline{t}h$ events produced in $\sqrt{s}=13\text{ }\text{ }\mathrm{TeV}$ proton-proton collisions at the LHC. Dileptonic final states are employed, with two oppositely charged leptons and four jets, corresponding to the decays $t\ensuremath{\rightarrow}b{W}^{+}\ensuremath{\rightarrow}b{\ensuremath{\ell}}^{+}{\ensuremath{\nu}}_{\ensuremath{\ell}}$, $\overline{t}\ensuremath{\rightarrow}\overline{b}{W}^{\ensuremath{-}}\ensuremath{\rightarrow}\overline{b}{\ensuremath{\ell}}^{\ensuremath{-}}{\overline{\ensuremath{\nu}}}_{\ensuremath{\ell}}$, and $h\ensuremath{\rightarrow}b\overline{b}$. Pure scalar ($h=H$), pure pseudoscalar ($h=A$), and $CP$-violating Higgs boson signal events, generated with MadGraph5_aMC@NLO, are fully reconstructed through a kinematic fit. We furthermore generate samples that have both a $CP$-even and a $CP$-odd component in the $t\overline{t}h$ coupling in order to probe the ratio of the two components. New angular distributions of the decay products, as well as $CP$ angular asymmetries, are explored in order to separate the scalar from the pseudoscalar components of the Higgs boson and reduce the contribution from the dominant irreducible background, $t\overline{t}b\overline{b}$. Significant differences between the angular distributions and asymmetries are observed, even after the full kinematic fit reconstruction of the events, allowing to define the best observables for a global fit of the Higgs couplings parameters.