Measuring Top Yukawa Coupling through $2\rightarrow 3$ VBS at Muon Collider

Abstract

We study the measurement of top Yukawa coupling through $2\rightarrow 3$ VBS at future muon colliders, focusing on the lepton and semi-lepton channels of $ννtth/z$. First, analyzing the partonic amplitudes of $W_LW_L\rightarrow t\bar t h/Z_L$ and simulating the full processes of $ννtth/z$ without decaying, we find they are highly sensitive to the anomalous top Yukawa $δy_t$. This sensitivity is enhanced by selecting helicities of the final $t\bar t$ and $Z$ to be $t_L\bar t_L+t_R\bar t_R$ and $Z_L$, which serves as the default and core setting of our analysis. We then obtain the limits on $δy_t$ with this setting, giving $[-1.0\%, 1.1\%]$ for $ννtth$ only and $[-0.36\%, 0.92\%]$ for $ννtth$ and $ννttz$ combined at $30$ TeV and $1σ$. Second, we proceed to analyze the processes after decaying and with background processes. To enhance the sensitivity to $δy_t$, our settings include selecting the helicities of the final particles, as well as applying suitable cuts. However, we don't do bin-by-bin analysis. We obtain the limits on $δy_t$ for those channels at $10/30$ TeV and $1σ/2 σ$. The best limit is from the semi-lepton channel of $ννtth$. With spin tagging efficiency at $ε_s=0.9$, it gives $[-1.6\% , 1.8\%]$ at $1σ$ and $ [-2.4\%, 2.7\% ]$ at $2σ$ at $30$ TeV; $[-7.0\%, 6.7\%]$ at $1σ$ and $[-9.8\%, 9.8\%]$ at $2σ$ at $10$ TeV.