Search for the Invisible Decay of Neutrons with KamLAND

The Kamioka Liquid scintillator Anti-Neutrino Detector (KamLAND) is used in a search for single neutron or two neutron intra-nuclear disappearance that would produce holes in the $\it{s}$-shell energy level of $^{12}$C nuclei. Such holes could be created as a result of nucleon decay into invisible modes ($inv$), e.g. $n \to 3\nu$ or $nn \to 2\nu$. The de-excitation of the corresponding daughter nucleus results in a sequence of space and time correlated events observable in the liquid scintillator detector. We report on new limits for one- and two-neutron disappearance: $\tau(n\to inv)> 5.8\times 10^{29}$ years and $\tau (nn \to inv)> 1.4 \times 10^{30}$ years at 90% CL. These results represent an improvement of factors of $\sim$3 and $>10^4$ over previous experiments.Comment: 5 pages, 3 figure