Search for passing-through-walls neutrons constrains hidden braneworlds

In many theoretical frameworks our visible world is a $3$-brane, embedded in a multidimensional bulk, possibly coexisting with hidden braneworlds. Some works have also shown that matter swapping between braneworlds can occur. Here we report the results of an experiment - at the Institut Laue-Langevin (Grenoble, France) - designed to detect thermal neutron swapping to and from another braneworld, thus constraining the probability $p^2$ of such an event. The limit, $p<4.6\times 10^{-10}$ at $95 \%$ C.L., is $4$ orders of magnitude better than the previous bound based on the disappearance of stored ultracold neutrons. In the simplest braneworld scenario, for two parallel Planck-scale branes separated by a distance $d$, we conclude that $d>87$ in Planck length units.