Longitudinally polarized $ZZ$ scattering at a muon collider

Measuring longitudinally polarized vector boson scattering in, e.g., the $ZZ$ channel is a promising way to investigate the unitarization scheme from the Higgs and possible new physics beyond the Standard Model. However, at the LHC, it demands the end of the high-luminosity-LHC lifetime luminosity, $3000{\mathrm{fb}}^{-1}$, and advanced data analysis technique to reach the discovery threshold due to its small production rates. Instead, there could be great potential at future colliders. In this paper, we perform a Monte Carlo study and examine the projected sensitivity of longitudinally polarized $ZZ$ scattering at a TeV scale muon collider. We conduct studies at 14 and 6 TeV muon colliders respectively and find that a 5 standard deviation discovery can be achieved at a 14 TeV muon collider, with $3000{\mathrm{fb}}^{-1}$ of data collected. While a 6 TeV muon collider can already surpass high-luminosity LHC, reaching 2 standard deviations with around $4{\mathrm{ab}}^{-1}$ of data. The effect from lepton isolation and detector granularity is also discussed, which may be more obvious at higher energy muon colliders, as the leptons from longitudinally polarized $Z$ decays tend to be closer.

Figure 1

Example diagram of VBS processes at a muon collider.

Figure 2

Cross section dependence on the center of mass energy of a muon collider, for the LL and other components of VBS $ZZ$ through $W^{+}{W}^{-}$ fusion.

Figure 3

The invariant mass distributions of $Z_1$ (left) and $Z_2$ (right) for VBS $ZZ$ through WW fusion and its various polarization fractions, compared with all the backgrounds, corresponding to a 14 TeV muon collider with $20{\mathrm{ab}}^{-1}$ of data collected. The upper panel compares the VBS $ZZ$ signal with four background components. The lower panel compares the kinematics for different polarization fractions of the VBS $ZZ$ process.

Figure 4

BDT training results for the LL VBS $ZZ$ analysis at a 14 TeV muon collider. The left panel (a) shows the importance ranking for the top 10 features; the right panel (b) shows the Kolmogorov-Smirnov test results and score distributions for signal and background in the training and test sets, respectively.

Figure 5

ROC curve and significance dependence on the BDT cut, corresponding to a 14 TeV muon collider with $20{\mathrm{ab}}^{-1}$ of data collected.

Figure 6

Training results with the use of 150 different random seeds. The left plot shows the significance dependence on the BDT cut for all 150 scenarios. It should be noted that we pause the scanning when the backgrounds yield zero, which results in the straight horizontal line near the end of scanning. The right plot shows the lower envelope of the significance shape.

Figure 7

Distributions of $\mathrm{\Delta }{R}_{Z_2,pm}$ (a),(b), defined as the $\mathrm{\Delta }R$ between the two leptons forming $Z_2$, and $p_{\mathrm{T},4\ell }$ (c),(d) from the VBS $ZZ$ process simulated at a 14 TeV (a),(c) and a 6 TeV (b),(d) muon collider.