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

TL;DR

This paper investigates electroweak precision measurements at a future high-energy muon collider via vector-boson-fusion to 2f final states, focusing on dimension-6 SMEFT operators that modify fermion couplings to W and Z bosons. By exploiting differential information from the invariant-mass of the fermion pair and angular observables, and by combining WW and WZ/Wγ fusion channels across 10 TeV and 30 TeV run scenarios, the authors perform a chi-squared global fit to constrain flavor-specific Wilson coefficients. They demonstrate that differential binning and channel combination yield bounds reaching the 10^-2 to a few x10^-3 level, with 30 TeV results competitive with projected e+e- Z-pole programs like CEPC. The study highlights the potential of a muon collider to perform competitive electroweak precision tests and outlines future directions for more complete SMEFT analyses including detector realism and systematic uncertainties.

Abstract

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 $WW/WZ/Wγ$ to a pair of fermions (along with a $ν_μ\barν_μ$ or $ν_μμ^+/\barν_μμ^-$ 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 $f=b,c,τ$ 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 $WZ/Wγ$ 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.

Figures (15)

• Figure 1: Typical Feynman diagrams for the process $\mu^{-}\mu^{+}\rightarrow b\bar{b}\nu_{\mu}\bar{\nu}_{\mu}$. Diagram (a) to (c) are examples of $2f\to 2f$ processes with an additional initial or final state $Z/\gamma$. Other diagrams of the same type are not explicitly shown. Diagram (d) is neutral diboson production, while (e) and (f) is VBF. BSM vertexes are indicated by black dots.
• Figure 2: The missing transverse momentum ($\slashed{p}_T$) distribution for $b\bar{b}\nu_\mu\bar{\nu}_\mu$ (red) and $b\bar{b}\mu^-\mu^+$ (green) at $\sqrt{s}=10\,$TeV. For $b\bar{b}\mu^-\mu^+$, a cut on the muon rapidity of $|\eta_\mu|>6$ is imposed, corresponding to both muons being untagged.
• Figure 3: The differential Cross Section distribution on the invariant mass of $b\bar{b}$ pair ($M_{b\bar{b}}$) for the $\mu^-\mu^+ \rightarrow b\bar{b}\nu_{\mu}\bar{\nu}_{\mu}$ process with $\sqrt{s}=10\,\text{ TeV}$. A bin width of 20 GeV is chosen. The red curve corresponds to the SM value while the other three curves each corresponds to one of the three Wilson coefficients $c_{H q}^{(1)} ,\, c_{H q}^{(3)} ,\, c_{H d}$ setting to a reference value of 1 (with $\Lambda=1\,\text{ TeV}$) while the other two are set to zero. Note that the low energy bins (with $M_{b\bar{b}}\ll m_Z$) are subject to large statistical uncertainties in our simulation.
• Figure 4: Differential cross section of the $|\cos{\bar{\theta}}|$ variable, defined as $|\cos{\bar{\theta}}|\equiv \frac{1}{2}\left(\left|\cos\theta_{\mu^{-}b}\right|+\left|\cos\theta_{\mu^{+}b}\right|\right)$, where $\theta_{\mu^-b}$ ($\theta_{\mu^+b}$) is the angle between $\mu^-$ ($\mu^+$) and $b$ in the c.o.m. frame of the $b\bar{b}$ system. A reference value of 10 is chosen here for each Wilson coefficient (assuming $\Lambda=1\,$TeV, and setting the other two to zero), with only linear contribution considered. The bin width is chosen to be 0.05. A (different) invariant mass selection is applied for each of the 9 plots, which corresponds to the 9 bins listed in \ref{['tab:invbin']}.
• Figure 5: Typical Feynman diagram for the process $\mu^{-}\mu^{+} \rightarrow \tau^+ \nu_\tau \bar{\nu}_{\mu} \mu^-$. Diagram (a) to (c) are examples of $2f\to 2f$ processes with additional $W$ in the initial or final state, diagram (d) and (e) are diboson production, while (f) and (g) is VBF. BSM vertexes are indicated by black dots.