Search for invisible decays of $\omega $ and $\varphi $ with $J/\psi $ data at BESIII

Using a data sample of $\left(1310.6±7.0\right)×{10}^{6}\text{}\text{}J/\psi $ events collected with the BESIII detector operating at the BEPCII collider, we perform the first experimental search for invisible decays of a light vector meson ($V=\omega $, $\varphi $) via $J/\psi \to V\eta $ decays. The decay of $\eta \to {\pi }^{+}{\pi }^{-}{\pi }^{0}$ is utilized to tag the $V$ meson decaying into the invisible final state. No evidence for a significant invisible signal is observed, and the upper limits on the ratio of branching fractions at the 90% confidence level are determined to be $\frac{B\left(\omega \to \text{invisible}\right)}{B\left(\omega \to {\pi }^{+}{\pi }^{-}{\pi }^{0}\right)}<8.1×{10}^{-5}$ and $\frac{B\left(\varphi \to \text{invisible}\right)}{B\left(\varphi \to {K}^{+}{K}^{-}\right)}<3.4×{10}^{-4}$. By using the world average values of $B\left(\omega \to {\pi }^{+}{\pi }^{-}{\pi }^{0}\right)$ and $B\left(\varphi \to {K}^{+}{K}^{-}\right)$, the upper limits on the decay branching fractions at the 90% confidence level are set as $B\left(\omega \to \text{invisible}\right)<7.3×{10}^{-5}$ and $B\left(\varphi \to \text{invisible}\right)<1.7×{10}^{-4}$, respectively.