Lab-frame observables for probing the top-Higgs interaction

We investigate methods to explore the CP nature of the $ t\bar{t}h $ coupling at the LHC, focusing on associated production of the Higgs with a $t \bar{t}$ 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\bar{t}h $ coupling directly, in particular quantities that can be constructed out of just lab-frame kinematics. We define one such observable by exploiting the fact that $t \bar{t}$ spin correlations do also carry information about the CP-nature of the $ t\bar{t}h $ coupling. Finally, we introduce a CP-odd quantity and a related asymmetry, able to probe CP violation in the $ t\bar{t}h $ coupling and likewise constructed out of lab-frame momenta only.
Comment: 32 pages, updated with latest data from ATLAS and references added