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

Using a data sample of (1310.6 +/- 7.0) x 10(6) 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, phi) via J/psi -> V-eta decays. The decay of eta -> 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 B(omega -> invisible)/B(omega -> pi(+)pi(-)pi(0)) < 8.1 x 10(-5) and B(phi -> invisible)/B(phi -> K+K-) < 3.4 x 10(-4). By using the world average values of B(omega -> pi(+)pi(-)pi(0) and B(phi -> K+K-,) the upper limits on the decay branching fractions at the 90% confidence level are set as B(omega -> invisible) < 7.3 x 10(-5) and B(phi -> invisible) < 1.7 x 10(-4), respectively.