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 $$ \left(t\overline{t}h\right) $$ and reported the signal strengths of μ ATLAS = 1.81 ± 0.80 and μ CMS = 2.75 ± 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 $$ t\overline{t}h $$ production in the presence of anomalous top-Yukawa coupling. As well known, $$ t\overline{t}h $$ 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 $$ t\overline{t}h $$ 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 $$ t\overline{t}h $$ 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, $$ b\overline{b} $$ and γγ putting a particular emphasis on the same sign dilepton events. We also discuss the prospects for the LHC Run-2 on how to disentangle thX production from $$ t\overline{t}h $$ one and how to probe the anomalous top-Yukawa coupling.