Using a data sample of 58 \times 10 ^ { 6 } J / \psi decays collected with the BES II detector at the BEPC , searches for invisible decays of \eta and \eta ^ { \prime } in J / \psi to \phi \eta and \phi \eta ^ { \prime } are performed .
The \phi signals , which are reconstructed in K ^ { + } K ^ { - } final states , are used to tag the \eta and \eta ^ { \prime } decays .
No signals are found for the invisible decays of either \eta or \eta ^ { \prime } , and upper limits at the 90 % confidence level are determined to be 1.65 \times 10 ^ { -3 } for the ratio \frac { B ( \eta \to \text { invisible } ) } { B ( \eta \to \gamma \gamma ) } and 6.69 \times 10 ^ { -2 } for \frac { B ( \eta ^ { \prime } \to \text { invisible } ) } { B ( \eta ^ { \prime } \to \gamma \gamma ) } .
These are the first searches for \eta and \eta ^ { \prime } decays into invisible final states .