The Role of the $t{\bar t}h$ Rest Frame in Direct Top-Quark Yukawa Coupling Measurements

Abstract

This paper studies new possibilities to directly measure a hypothetical $CP$-odd (pseudoscalar) component in the top-quark Yukawa coupling. In particular, the role of the $t{\bar t} h$ center-of-mass rest frame in the associated production of a top pair and a $h$ boson at the LHC is explored. The $h$ boson is assumed to have both a $CP$-even (scalar) and a $CP$-odd coupling to the top quark. The relative strength of the scalar and pseudoscalar components is regulated by an angle $\alpha$. Observables sensitive to the nature of the top-quark Yukawa coupling are proposed. These observables are defined in terms of the transverse and longitudinal projections of $t$, $\bar{t}$ and $h$ momenta with respect to the beam axis in the $t{\bar t} h$ rest frame. Distributions differential with respect to those observables are evaluated up to NLO in QCD. These distributions are found to be sensitive to the $CP$ nature of the coupling. Dileptonic final states of the $t{\bar t} h$ system (with $h\rightarrow b\bar b$) are used, after fast DELPHES detector simulation and full event reconstruction through a kinematic fit, as a case study to test the observables' sensitivity to the $CP$ nature of the coupling. Confidence levels are presented as a function of the total integrated LHC luminosity for the case of exclusion of a pure $CP$-odd coupling against the Standard Model $CP$-even hypothesis. By using observables evaluated in the $t{\bar t} h$ system, the luminosity needed to directly probe the $CP$ properties of the top-quark Yukawa coupling at the High-Luminosity run of the LHC can be decreased by a few hundred inverse femtobarns, when compared to analyses that use observables in the laboratory rest frame. In addition, transverse momentum distributions of the $h$ boson and top quarks are found to provide no more discriminant power than a counting experiment.