Searching for the neutral triple gauge couplings in the process $μ^+μ^-\to γν\barν$ at muon colliders

We investigate the sensitivity of future high-energy muon colliders to neutral triple gauge couplings (nTGCs) through the process $μ^{+}μ^{-}\toγν\barν$ within the Standard Model Effective Field Theory (SMEFT) framework. Extending beyond previous studies, we consider a set of 14 dimension-8 operators, including both Higgs-related and pure gauge structures. By computing the cross sections and performing Monte Carlo simulations at multiple center-of-mass energies (3 - 30 TeV), we demonstrate that the annihilation process dominates over vector boson fusion (VBF) at TeV scales. We also explore the impact of beam polarization and show that the $(-+)$ polarization enhances sensitivity to several operators. After the study of the event selection strategies, we show that muon colliders can impose stronger expected constraints on nTGCs operators than current LHC bounds, with two of the pure gauge operators yielding the most stringent expected constraints.