Neutral hadrons disappearing into the darkness

We study the invisible decay of neutral hadrons in a representative model of the dark sector. The most interesting cases are the mesons $K_L$ and $B^0$ and the neutron. The two mesons 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 model 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.