Neutral hadrons disappearing into the darkness

We study the invisible decay of neutral hadrons in a representative model of the dark sector. The mesons KL 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(inv)(N) greater than or similar to 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.