Search Capability for $\eta \to \nu_{e,{\tau}}\bar\nu_{e,{\tau}}$ Decays in Cubic Kilometer Neutrino Detectors

We investigate the discovery potential of cubic kilometer neutrino observatories such as IceCube to set stringent limits on the forbidden decays $\eta \to \nu_e\bar\nu_e$ and $\eta \to \nu_{\tau}\bar\nu_{\tau}$. The signatures for these decays are cascade events resulting from the charged-current reactions of $\nu_e, \nu_{\tau}$, $\bar\nu_e$ and $\bar\nu_{\tau}$ on nuclei in such detectors. Background cascade events are mainly due to $\nu_e$'s from atmospheric $\mu$, $K^+$, and $K^{0}_S$ decays and to a lesser extent from atmospheric $\nu_{\mu}$ neutral current interactions with nuclei. A direct upper limit for the branching ratio $\eta \to \nu_{e,\tau} \bar\nu_{e,\tau}$ of $5.0 \times10^{-4}$ at 90\% CL can be achieved.