  We study the invisible decay of neutral hadrons in a representative model of
the dark sector. The mesons $K_L$ and $B^0$ decay into the dark sector with
branching rates that can be at the current experimental limits. The neutron
decays with a rate that could either explain the neutron lifetime puzzle
(although only for an extreme choice of the parameters and a fine tuned value
of the masses) or be just above the current limit of its invisible decay
($\tau_N^{\rm inv} \ge 10^{29}$ years) if kinematically allowed. These
invisible decays of ordinary matter provide a novel and promising window into
new physics that should be vigorously pursued.
