Top Yukawa coupling measurement at the muon collider

We have presented a detailed study about the prospects for the measurement of the top Yukawa coupling in the vector boson fusion production of a top quark pair at high energy muon colliders. By employing the effective $W$ approximation and the high energy limit for the helicity amplitudes of the subprocess $W^{+}{W}^{-}\to t\overline{t}$, we have derived the energy scaling of the statistical signal significance in the presence of the anomalous couplings by focusing on the interference term only. The sensitivity on the top Yukawa coupling decreases as the bin energy increases. For the anomalous triple gauge boson couplings and the gauge-boson-fermion couplings with $E^2$ energy growing behavior, the signal significance has mild increase at the beginning and starts to decrease for ${\widehat{s}}_{t\overline{t}}\sim 0.2s_{{\mu }^{+}{\mu }^{-}}$. The 95% CL on the anomalous top Yukawa coupling is projected to be 5.6% (1.7%) at a 10 (30) TeV muon collider, which is comparable to the sensitivity of 2% at the 100 TeV collider.

Figure 1

Tree-level diagrams for $W^{+}{W}^{-}\to t\overline{t}$. The gauge boson propagator in the last diagrams can be either $Z$ or $\gamma$.

Figure 2

Illustration of the EWA approximation at the muon collider.

Figure 3

Cross section of SM ${\mu }^{+}{\mu }^{-}\to t\overline{t}$, ${\mu }^{+}{\mu }^{-}\to t\overline{t}h$, and ${\mu }^{+}{\mu }^{-}\to t\overline{t}\nu \overline{\nu }$ with the on shell Z contribution removed.

Figure 4

Standard Model distribution of $\theta$ and $p_T$ of the top quark at 3, 10, and 30 TeV muon colliders after the cut on the recoil mass in Eq. (34). (a) Standard Model ${\theta }_t$. (b) Standard Model ${\cancel{E}}_T$ of the top.

Figure 5

The distributions of ${\theta }^{*}$ for the SM (a) and ${\delta }_{tth}=10\%$ (b) after the all the preliminary cuts in Eqs. (34)–(36) and (38). Note that ${\theta }^{*}$ is the angle between the top and the $W^{+}$ in the $W^{+}{W}^{-}$ center-of-mass frame.

Figure 6

$\mathrm{\Delta }{\chi }^2$ plot as a function of anomalous top Yukawa coupling ${\delta }_{tth}$ for processes ${\mu }^{+}{\mu }^{-}\to t\overline{t}\nu \overline{\nu }$ and ${\mu }^{+}{\mu }^{-}\to t\overline{t}\nu \overline{\nu }h$ at 10 TeV (a) and 30 TeV (b) muon collider. Here $R_1(R_2)$ denotes the interference term and the squared term respectively. (a) ${\mu }^{+}{\mu }^{-}\to t\overline{t}\nu \overline{\nu }$ with $\sqrt{s}=10\mathrm{TeV}$ and $L=10{\mathrm{ab}}^{-1}$. (b) ${\mu }^{+}{\mu }^{-}\to t\overline{t}\nu \overline{\nu }$ with $\sqrt{s}=\text{\hspace{0.17em}30\hspace{0.17em}}\mathrm{TeV}$ and $L=\text{\hspace{0.17em}90\hspace{0.17em}}{\mathrm{ab}}^{-1}$.