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

TL;DR

This study evaluates the potential of future muon colliders to precisely measure the top Yukawa coupling via vector boson scattering processes, employing helicity selection and background suppression techniques.

Contribution

It introduces a detailed analysis of $2 ightarrow 3$ VBS processes at muon colliders, highlighting sensitivity enhancements through helicity selection and providing projected limits on top Yukawa deviations.

Findings

Limits on $\delta y_t$ are around 1 ext{--}2 ext{ extperthousand} at 30 TeV.

Helicity selection significantly improves measurement sensitivity.

Semi-leptonic channels yield the best constraints.

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 $\nu\nu tth/z$. First, analyzing the partonic amplitudes of $W_LW_L\rightarrow t\bar t h/Z_L$ and simulating the full processes of $\nu\nu tth/z$ without decaying, we find they are highly sensitive to the anomalous top Yukawa $\delta y_t$. 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 $\delta y_t$ with this setting, giving $[-1.0\%, 1.1\%]$ for $\nu\nu tth$ only and $[-0.36\%, 0.92\%]$ for $\nu\nu tth$ and $\nu\nu ttz$ combined at $30$ TeV and $1\sigma$. Second, we proceed to analyze the processes after decaying and with background processes. To enhance the sensitivity to $\delta y_t$, 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 $\delta y_t$ for those channels at $10/30$ TeV and $1\sigma/2 \sigma$. The best limit is from the semi-lepton channel of $\nu\nu tth$. With spin tagging efficiency at $\epsilon_s=0.9$, it gives $[-1.6\% , 1.8\%]$ at $1\sigma$ and $ [-2.4\%, 2.7\% ]$ at $2\sigma$ at $30$ TeV; $[-7.0\%, 6.7\%]$ at $1\sigma$ and $[-9.8\%, 9.8\%]$ at $2\sigma$ at $10$ TeV.