Can neutron disappearance/reappearance experiments definitively rule out the existence of hidden braneworlds endowed with a copy of the Standard Model?

Many works, aiming to explain the origin of dark matter or dark energy, consider the existence of hidden (brane)worlds parallel to our own visible world — our usual Universe — in a multidimensional bulk. Hidden braneworlds allow for hidden copies of the Standard Model. For instance, atoms hidden in a hidden brane could exist as dark matter candidates. As a way to constrain such hypotheses, the possibility for neutron–hidden neutron swapping can be tested thanks to disappearance-reappearance experiments also known as passing-through-walls neutron experiments. The neutron-hidden neutron coupling g can be constrained from those experiments. While g could be arbitrarily small, previous works involving a M ₄ × R ₁ bulk, with DGP branes, show that g then possesses a value which is reachable experimentally. It is of crucial interest to know if a reachable value for g is universal or not and to estimate its magnitude. Indeed, it would allow, in a near future, to reject definitively — or not — the existence of hidden braneworlds from experiments. In the present paper, we explore this issue by calculating g for DGP branes, for M ₄ × S ₁/Z2, M ₄ × R ₂ and M ₄ × T ² bulks. As a major result, no disappearance-reappearance experiment would definitively universally rules out the existence of hidden worlds endowed with their own copy of Standard Model particles, except for specific scenarios with conditions reachable in future experiments.