Probing Z/W Pole Physics at High-energy Muon Colliders via Vector-boson-fusion Processes

A future $e^+e^-$ collider could run at the Z-pole to perform important electroweak (EW) precision measurements, while such a run may not be viable for a future muon collider. This however can be compensated by the measurements of other EW processes, taking advantage of the high energy and large luminosity of the muon collider. In this paper, we consider the measurements of the vector boson fusion processes of $WW/WZ/W\gamma$ to a pair of fermions (along with a $\nu_{\mu}\bar{\nu}_{\mu}$ or $\nu_{\mu}\mu^+/\bar{\nu}_{\mu}\mu^-$ pair) at a high-energy muon collider and study their potential in probing the EW observables. We consider two run scenarios for the muon collider with center-of-mass energy of 10 TeV and 30 TeV, respectively, and focus on the processes involving $f=b,c,\tau$ and the dimension-6 operators that directly modify the corresponding fermions coupling to the $Z/W$ bosons. The invariant mass distribution of the $f\bar{f}$ pair helps to separate the events from the $Z/W$ resonance and the high-energy ones, while the polar angle of the outing fermion also provides additional information. By performing a chi-squared analysis on the binned distributions and combining the information from the $WW$ and $WZ/W\gamma$ fusion processes, all relevant Wilson coefficients can be constrained simultaneously. The precision surpasses the current EW measurement constraints and is even competitive with future $e^+e^-$ colliders. Our analysis can be included in a more complete framework which is needed to fully determine the potential of muon colliders in EW precision measurements.