We investigate methods to explore the $CP$ nature of the $t\overline{t}h$ coupling at the LHC, focusing on associated production of the Higgs boson with a $t\overline{t}$ pair. We first discuss the constraints implied by low-energy observables and by the Higgs-rate information from available LHC data, emphasizing that they cannot provide conclusive evidence on the nature of this coupling. We then investigate kinematic observables that could probe the $t\overline{t}h$ coupling directly, in particular, quantities that can be constructed out of just laboratory-frame kinematics. We define one such observable by exploiting the fact that $t\overline{t}$ spin correlations do also carry information about the $CP$ nature of the $t\overline{t}h$ coupling. Finally, we introduce a $CP$-odd quantity and a related asymmetry, able to probe $CP$ violation in the $t\overline{t}h$ coupling and likewise, constructed out of laboratory-frame momenta only.

• Received 13 May 2015

DOI:https://doi.org/10.1103/PhysRevD.92.015019