Higgs boson form factor effects in $t\overline{t}$ production by $W^{-}{W}^{+}$ and $ZZ$ fusion

We study the fusion processes $W^{-}{W}^{+}\to t\overline{t}$ and $ZZ\to t\overline{t}$ observable at a future $e^{-}{e}^{+}$ collider and we discuss their sensitivity to an $Htt$ form factor which may be due to compositeness, in particular when the $H$ and the top quark have common constituents. We make an amplitude analysis and illustrate which helicity amplitudes and cross sections for specific final $t\overline{t}$ polarizations are especially sensitive to this form factor.

Figure 1

The shapes of the real parts (left panel) and imaginary parts (right panel) of the $Ht\overline{t}$ form factors; the crude lines are based on (16) and (17), the effective lines on (19) and (17) and the resonance lines are based on (20).

Figure 2

Energy dependence of the H-insensitive tree-level SM amplitudes for $W_{\lambda }^{-}{W}_{{\lambda }^{\prime }}^{+}\to t_{\tau }{\overline{t}}_{{\tau }^{\prime }}$. Upper panels are for the HC amplitudes of (23), and lower panels are for the HV ones of (24) at $\theta =60°$. Left panels present TT amplitudes, while right panels involve amplitudes containing at least one longitudinal $W$.

Figure 3

The SM results and the effects of the anomalous $Htt$ form factor on the form factor sensitive amplitudes $W_{\lambda }^{-}{W}_{{\lambda }^{\prime }}^{+}\to t_{\tau }{\overline{t}}_{{\tau }^{\prime }}$ listed in (25). Real (imaginary) parts are shown in the left (right) panels respectively. The definition of crude STS, effective and resonance form factor models, as in Fig. 1.

Figure 4

$d\sigma (e^{-}{e}^{+}\to \nu {\nu }^{\prime }{t}_{\tau }{\overline{t}}_{{\tau }^{\prime }})/d\cos \theta$ cross sections. The upper panel gives energy dependencies for (left-right) and (right-left) $t\overline{t}$ helicities, while the middle panels for (left-left) and (right-right) $t\overline{t}$ helicities, always at $\theta =60°$. The lower panels give energy (at $\theta =60°$) and angular (at $\sqrt{s}=1\mathrm{TeV}$) dependencies when $t\overline{t}$-helicities are not observed. The contribution from the $H$ form factors of the three cases of Fig. 1 exist only for the $t\overline{t}$ polarizations contributing to the middle and lower panels.

Figure 5

Energy dependence of the H-insensitive tree-level SM amplitudes for $Z_{\lambda }{Z}_{{\lambda }^{\prime }}\to t_{\tau }{\overline{t}}_{{\tau }^{\prime }}$ at $\theta =60°$. Upper panels are for the HC amplitudes in (26) and lower panels are for the HV ones in (27).

Figure 6

The SM results and the effects of the anomalous $Htt$ form factor on the sensitive to it amplitudes $Z_{\lambda }{Z}_{{\lambda }^{\prime }}\to t_{\tau }{\overline{t}}_{{\tau }^{\prime }}$ listed in (28). Real (imaginary) parts are shown in the left (right) panels respectively. The definition of crude STS, effective and resonance form factor models, as in Fig. 1.

Figure 7

Energy dependencies of the differential cross sections for $d\sigma (e^{-}{e}^{+}\to e^{-}{e}^{+}{t}_{\tau }{\overline{t}}_{{\tau }^{\prime }})/d\cos \theta$ at $\theta =60°$. The $ZZ$ intermediate state, the background induced by anything non-$ZZ$, and the complete result denoted as “total” are separately given. The left (right) panel corresponds to $\tau =-{\tau }^{\prime }=-1/2(\tau =-{\tau }^{\prime }=+1/2)$ and they both contain no $H$ contribution.

Figure 8

Differential cross sections as in Fig. 7, with upper and lower panels respectively corresponding to $\tau ={\tau }^{\prime }=\pm 1/2$ and both receiving $H$ form factor contributions (see Fig. 1) modifying the $ZZ$ (left) and the total (right) panel results.

Figure 9

Energy dependencies at $\theta =60°$ (upper panels) and angular dependencies at $\sqrt{s}=1\mathrm{TeV}$ (lower panels) of the unpolarized differential cross sections for $\sum _{\tau {\tau }^{\prime }}d\sigma (e^{-}{e}^{+}\to e^{-}{e}^{+}{t}_{\tau }{\overline{t}}_{{\tau }^{\prime }})/d\cos \theta$. The $ZZ$ intermediate state, the background induced by anything non-$ZZ$, and the complete result indicated as total are separately given in SM and after including the $H$ form factor (see Fig. 1) contribution.