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In many theoretical frameworks our visible world is a $3$-brane, embedded ina multidimensional bulk, possibly coexisting with hidden braneworlds. Someworks have also shown that matter swapping between braneworlds can occur. Herewe report the results of an experiment - at the Institut Laue-Langevin(Grenoble, France) - designed to detect thermal neutron swapping to and fromanother 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 magnitudebetter than the previous bound based on the disappearance of stored ultracoldneutrons. In the simplest braneworld scenario, for two parallel Planck-scalebranes separated by a distance $d$, we conclude that $d>87$ in Planck lengthunits.

Search for passing-through-walls neutrons constrains hidden braneworlds