An unexplained $>4\sigma$ discrepancy persists between “beam” and “bottle” measurements of the neutron lifetime. A new model proposed that conversions of neutrons $n$ into mirror neutrons $n^{\prime }$, part of a dark mirror sector, can increase the apparent neutron lifetime by 1% via a small mass splitting $\mathrm{\Delta }m$ between $n$ and $n^{\prime }$ inside the 4.6 T magnetic field of the National Institute of Standards and Technology Beam Lifetime experiment. A search for neutron conversions in a 6.6 T magnetic field was performed at the Spallation Neutron Source which excludes this explanation for the neutron lifetime discrepancy.

The possibility that a neutron can be transformed to a hidden sector particle remains intriguingly open. Proposed theoretical models conjecture that the hidden sector can be represented by a mirror sector, and the neutron n can oscillate into its sterile mirror twin $n^{\prime }$, exactly or nearly degenerate in mass with n. Oscillations $n-n^{\prime }$ can take place in vacuum or in an environment containing regular matter and a magnetic field, in which only the neutron will be subject to interactions with the environment. We describe the propagation of the oscillating $n-n^{\prime }$ system in a cold neutron beam passing through dense absorbing materials in connection to the possible regeneration type of experiments, where the effect of $n\to n^{\prime }\to n$ transformation can be observed.