Sensitivity of polarizations and spin correlations of $Z$ boson to anomalous neutral triple gauge couplings at lepton collider with polarized beams

We investigate the effects of anomalous neutral triple gauge couplings in $ZZ$ and $Z\gamma$ production processes, followed by the leptonic decay of the $Z$ boson, at a lepton collider with center-of-mass energy $\sqrt{s}=250\mathrm{GeV}$ and polarized beams. We use an effective Lagrangian formalism to parametrize the anomalous couplings in terms of dimension-8 operators $c_{\tilde{B}W}$, $c_{BW}$, $c_{WW}$, and $c_{BB}$, and study the sensitivity of observables such as cross section, polarization, and spin correlation as functions of these couplings. We perform a Bayesian statistical analysis using Markov Chain Monte Carlo methods to determine simultaneous limits on the anomalous couplings, taking into account various luminosities $L\in \{0.1{\mathrm{ab}}^{-1},0.3{\mathrm{ab}}^{-1},1{\mathrm{ab}}^{-1},3{\mathrm{ab}}^{-1},10{\mathrm{ab}}^{-1}\}$ and systematic uncertainties. We find that polarization and spin correlation observables significantly enhance the sensitivity to anomalous couplings, providing stringent constraints on these couplings.