Constraints on Anomalous Quartic Gauge Couplings via $γγ$ and $Zγ$ Vector Boson Scattering at Muon Colliders

TL;DR

This work assesses the sensitivity of future high-energy muon colliders to dimension-8 anomalous quartic gauge couplings within an EFT framework, focusing on neutral VBS processes $μ^{+}μ^{-}→μ^{+}γγμ^{-}$ and $μ^{+}μ^{-}→μ^{+}Zγμ^{-}$ at $ ext{3 TeV}$ and $ ext{10 TeV}$. Using MG5_aMC@NLO, Pythia8, Delphes, and a TMVA-based Boosted Decision Tree approach, the study implements an energy-dependent unitarity clipping to keep EFT predictions within validity and builds a comprehensive multivariate analysis of kinematic and reconstructed observables. The results show EFT contributions grow as $s^{2}/mbda^{8}$, leading to substantial improvements in projected limits on the tensorial operators $f_{T,i}/mbda^{4}$, with 10 TeV achieving bounds down to the $10^{-3}$–$10^{-4}$ TeV$^{-4}$ range for many operators and typically the $μ^{+}μ^{-}→μ^{+}Zγμ^{-}$ channel delivering the strongest constraints due to missing energy from $Z o νar{ν}$. Systematics at the 10% level mildly relax these limits, but the muon collider’s sensitivity remains significantly superior to current LHC bounds, highlighting its potential for precision electroweak tests and BSM searches in the gauge sector.

Abstract

In the Standard Model, the couplings between gauge bosons are tightly constrained by the principles of gauge symmetry and renormalizability. However, the presence of anomalous couplings suggests the possibility of new physics beyond the Standard Model (BSM). In this study, we focus on the sensitivities of anomalous quartic gauge couplings (aQGCs), specially the dimension-8 operators associated with field-strength tensor structures within the effective field theory (EFT) framework, at future Muon Colliders. Our analysis targets the neutral aQGC-sensitive processes $μ^{+}μ^{-} \to μ^+ γγμ^-$ and $μ^{+} μ^{-} \to μ^+ Z γμ^-$, simulated at center-of-mass energies of 3 TeV and 10 TeV. Signal and background events are generated using {\sc MadGraph5\_aMC@NLO}, interfaced with Pythia8 for parton showering and hadronization, and Delphes for fast detector simulation. A multivariate analysis based on Boosted Decision Trees (BDTs) is employed to enhance signal-to-background discrimination, utilizing a comprehensive set of kinematic and reconstructed observables from the final-state particles. Unitarity is preserved through the application of an energy-dependent clipping procedure within the EFT validity regime. Our findings indicate that future muon colliders offer significant sensitivity improvements over current experimental constraints on aQGCs. Furthermore, a comparison with other future collider scenarios shows that the 10 TeV Muon Collider, even with a 10\% systematic uncertainty, provides substantially stronger projected limits at 95\% confidence level than those currently reported by the ATLAS collaboration at the LHC as well as projected limits by future hadron colliders. These results underscore the enhanced potential of high-energy muon collider to probe new physics in the electroweak sector through precision measurements of aQGCs.

Figures (10)

• Figure 1: Feynman diagrams illustrating the contribution of aQGC to (a)and (d) the VBS processes , (b) and (e) the non-VBS processes , and (c) and (f) SM processes in $\mu^+\gamma\gamma\mu^-$ and $\mu^+Z\gamma\mu^-$ productions at a Muon Collider.
• Figure 2: The dependence of the unitarity violation scale on the anomalous coupling strengths $f_{T,i}/\Lambda^{4}$ (i=0,..,9) , obtained using the analytical expressions given in Ref. Almeida:2020ylr.
• Figure 3: The total cross sections of the processes $\mu^{+}\mu^{-}\to\mu^+\gamma\gamma\mu^-$ and $\mu^{+}\mu^{-}\to\mu^+Z\gamma\mu^-$ as a function of center of mass energy for different anomalous coupling values.
• Figure 4: The total cross sections as a function of anomalous quartic gauge couplings $f_{T,i}/\Lambda^{4}$ (i=0,..,9) for the $\mu^{+}\mu^{-}\to\mu^+\gamma\gamma\mu^-$ and $\mu^{+}\mu^{-}\to\mu^+Z\gamma\mu^-$ processes at $\sqrt{s} =$ 3 TeV (top row) and $\sqrt{s}$ 10 TeV (bottom row) Muon Collider.
• Figure 5: T Two–dimensional distributions of the photon centrality observables ($\gamma\gamma$–cent for $\mu^{+}\mu^{-}\to\mu^+\gamma\gamma\mu^-$ and $\gamma$–cent for $\mu^{+}\mu^{-}\to\mu^+Z\gamma\mu^-$) as a function of the dilepton invariant mass $m_{\mu\mu}$ for the signal $f_{T8}/\Lambda^{4} = 0.0007$ and corresponding SM at $\sqrt{s}=10$ TeV Muon Collider.