Top Yukawa coupling measurement with indefinite $CP$ Higgs in $e^{+}{e}^{-}\to t\overline{t}\mathrm{\Phi }$

We consider the issue of the top quark Yukawa coupling measurement in a model-independent and general case with the inclusion of $CP$ violation in the coupling. Arguably the best process to study this coupling is the associated production of the Higgs boson along with a $t\overline{t}$ pair in a machine like the International Linear Collider (ILC). While detailed analyses of the sensitivity of the measurement—assuming a Standard Model (SM)-like coupling is available in the context of the ILC—conclude that the coupling could be pinned down to about a 10% level with modest luminosity, our investigations show that the scenario could be different in the case of a more general coupling. The modified Lorentz structure resulting in a changed functional dependence of the cross section on the coupling, along with the difference in the cross section itself leads to considerable deviation in the sensitivity. Our studies of the ILC with center-of-mass energies of 500 GeV, 800 GeV, and 1000 GeV show that moderate $CP$ mixing in the Higgs sector could change the sensitivity to about 20%, while it could be worsened to 75% in cases which could accommodate more dramatic changes in the coupling. Detailed considerations of the decay distributions point to a need for a relook at the analysis strategy followed for the case of the SM, such as for a model-independent analysis of the top quark Yukawa coupling measurement. This study strongly suggests that a joint analysis of the $CP$ properties and the Yukawa coupling measurement would be the way forward at the ILC and that caution must be exercised in the measurement of the Yukawa couplings and the conclusions drawn from it.

Figure 1

Feynman diagrams contributing to the process $e^{-}{e}^{+}\to t\overline{t}\mathrm{\Phi }$ in the Standard Model.

Figure 2

${\sigma }_{t\overline{t}\mathrm{\Phi }}$ vs $\sqrt{s}$ for different parameter values in model I (left panel) and model II (right panel).

Figure 3

$\sqrt{s}=800\mathrm{GeV}$: ${\sigma }_{t\overline{t}\mathrm{\Phi }}$ vs Yukawa multiplier for different parameter values in model I (left pane) and model II (right panel).

Figure 4

Model I: Normalized distributions for the top quark: energy ($E_t$), $\cos {\theta }_t$, the invariant mass of $t\overline{t}$ ($M_{t\overline{t}}$), the transverse momentum of $t$ [$(p_T{)}_t$], and the cosine of the angle between $b$ and $\overline{b}$ in $e^{+}{e}^{-}\to t\overline{t}\mathrm{\Phi }\to b\overline{b}t\overline{t}$. For the Higgs boson: energy ($E_{\mathrm{\Phi }}$), transverse momentum [$(p_T{)}_{\Phi }$], and $\cos {\theta }_{\Phi }$. For the $W$ boson: energy ($E_{\mathrm{\Phi }}$), transverse momentum [$(p_T{)}_W$], $\cos {\theta }_W$, and the invariant mass of $WW$ ($M_{WW}$) in $e^{+}{e}^{-}\to t\overline{t}\mathrm{\Phi }\to b\overline{b}{W}^{+}{W}^{-}\mathrm{\Phi }$. The center-of-mass energy considered is $\sqrt{s}=800\mathrm{GeV}$, and an integrated luminosity of $1000{\mathrm{fb}}^{-1}$ is used.

Figure 5

Model II: Normalized distributions for the top quark: energy ($E_t$), $\cos {\theta }_t$, the invariant mass of $t\overline{t}$ ($M_{t\overline{t}}$), the transverse momentum of $t$ [$(p_T{)}_t$], and the cosine of the angle between $b$ and $\overline{b}$ in $e^{+}{e}^{-}\to t\overline{t}\mathrm{\Phi }\to b\overline{b}t\overline{t}$. For the Higgs boson: energy ($E_{\mathrm{\Phi }}$), transverse momentum [$(p_T{)}_{\Phi }$], and $\cos {\theta }_{\Phi }$. For the $W$ boson: energy ($E_{\mathrm{\Phi }}$), transverse momentum [$(p_T{)}_W$], $\cos {\theta }_W$, and the invariant mass of $WW$ ($M_{WW}$) in $e^{+}{e}^{-}\to t\overline{t}\mathrm{\Phi }\to b\overline{b}{W}^{+}{W}^{-}\mathrm{\Phi }$. The center-of-mass energy considered is $\sqrt{s}=800\mathrm{GeV}$, and an integrated luminosity of $1000{\mathrm{fb}}^{-1}$ is used.

Figure 6

$\sqrt{s}=500\mathrm{GeV}$: ${\sigma }_{t\overline{t}\mathrm{\Phi }}$ vs Yukawa multiplier for different parameter values in model I (left panel) and model II (Right panel).

Figure 7

$\sqrt{s}=1000\mathrm{GeV}$: ${\sigma }_{t\overline{t}\mathrm{\Phi }}$ vs Yukawa multiplier for different parameter values in model I (left panel) and model II (right panel).