Entangling Higgs production associated with a single top and a top-quark pair in the presence of anomalous top-Yukawa coupling

The ATLAS and CMS collaborations observed a mild excess in the associated Higgs production with a top-quark pair ($t\bar t h$) and reported the signal strengths of $ \mu_{tth}^{\rm ATLAS}=1.81\pm 0.80$ and $\mu_{tth}^{\rm CMS}=2.75\pm 0.99 $ based on the data collected at $\sqrt{s}$= 7 and 8 TeV. Although, at the current stage, there is no obvious indication whether the excess is real or due to statistical fluctuations, here we perform a case study of this mild excess by exploiting the strong entanglement between the associated Higgs production with a single top quark ($thX$) and $t\bar t h$ production in the presence of anomalous top-Yukawa coupling. As well known, $t\bar t h$ production only depends on the absolute value of the top-Yukawa coupling. Meanwhile, in $thX$ production, this degeneracy is lifted through the strong interference between the two main contributions which are proportional to the top-Yukawa and the gauge-Higgs couplings, respectively. Especially, when the relative sign of the top-Yukawa coupling with respect to the gauge-Higgs coupling is reversed, the $thX$ cross section can be enhanced by more than one order of magnitude. We perform a detailed study of the influence of $thX$ production on $t\bar{t}h $ production in the presence of the anomalous top-Yukawa coupling and point out that it is crucial to include $thX$ production in the analysis of the $t\bar t h$ data to pin down the sign and the size of the top-Yukawa coupling in future. While assuming the Standard Model (SM) value for the gauge-Higgs coupling, we vary the top-Yukawa coupling within the range allowed by the current LHC Higgs data. We consider the Higgs decay modes into multileptons, $b\bar b$ and $\gamma\gamma$ putting a particular emphasis on the same sign dilepton events. We also discuss ...