Search for new physics effects in νbar{ν}γ production at a Tera-Z factory

Rare decays of the Z boson provide a sensitive probe for physics beyond the Standard Model (SM). This study investigates the $e^{+}e^{-} \to Z \to \nu\bar{\nu}\gamma$ process within the context of the Tera-Z programmes at future colliders such as the FCC-ee and CEPC. The SM predicts a one-loop branching ratio of $7.16 \times 10^{-10}$ for $Z \to \nu\bar{\nu}\gamma$, a value four times smaller than the current experimental limit from the LEP. To explore this window for new physics, we parameterize anomalous $Z\nu\bar{\nu}\gamma$ interactions using an Effective Field Theory framework, considering both dimension-6 and dimension-8 operators. A detailed simulation is performed by generating signal and background events with MadGraph, modeling particle showers with Pythia, and simulating detector effects with Delphes. The analysis employs key kinematic variables-including the photon energy ($E_\gamma$), missing transverse energy ($\not{E}_T$), and the missing transverse energy significance ($S_{\not{E}_T}$) to isolate the signal. The results yield upper limits on the anomalous couplings, from which we infer branching ratios for $Z \to \nu\bar{\nu}\gamma$ on the order of $10^{-9}$. This represents a significant improvement of several orders of magnitude over the LEP sensitivity. Consequently, this study demonstrates the unique potential of the Tera-Z runs not only to test the SM loop-level predictions with unprecedented precision but also to tightly constrain or reveal new anomalous interactions.