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.

For neutrons bound inside nuclei, baryon instability can manifest itself as a decay into undetectable particles (e.g., $\overrightarrow{n}\nu \nu \overline{\nu }),$ i.e., as a disappearance of a neutron from its nuclear state. If electric charge is conserved, a similar disappearance is impossible for a proton. The existing experimental lifetime limit for neutron disappearance is 4–7 orders of magnitude lower than the lifetime limits with detectable nucleon decay products in the final state. In this paper we calculated the spectrum of nuclear de-excitations that would result from the disappearance of a neutron or two neutrons from ${}^{12}\mathrm{C}.$ We found that some de-excitation modes have signatures that are advantageous for detection in the modern high-mass, low-background, and low-threshold underground detectors, where neutron disappearance would result in a characteristic sequence of time- and space-correlated events. Thus, in the KamLAND detector, a time-correlated triple coincidence of a prompt signal, a captured neutron, and a ${\beta }^{+}$ decay of the residual nucleus, all originating from the same point in the detector, will be a unique signal of neutron disappearance allowing searches for baryon instability with sensitivity 3–4 orders of magnitude beyond the present experimental limits.

We found that spin-one new light particle exchanges are strongly bounded by high-energy and small momentum transfer $np$ elastic scattering data; the analogous bound for a scalar particle is considerably weaker, while for a pseudoscalar particle no bounds can be set. These bounds are compared with the bounds extracted from low-energy $n\mathrm{\text{−}}\mathrm{Pb}$ scattering experiments and from the bounds of ${\pi }^0$ and $K^{+}$ meson decays.

We discuss the possibility of the transition magnetic moments (TMM) between the neutron n and its hypothetical sterile twin “mirror neutron” $n^{\prime }$ from a parallel particle “mirror” sector. The neutron can be spontaneously converted into mirror neutron via the TMM (in addition to the more conventional transformation channel due to $n-n^{\prime }$ mass mixing) interacting with the magnetic field $\mathbf{B}$ as well as with mirror magnetic field ${\mathbf{B}}^{\prime }$. We derive analytic formulae for the average probability of $n-n^{\prime }$ conversion and consider possible experimental manifestations of neutron TMM effects. In particular, we discuss the potential role of these effects in the neutron lifetime measurement experiments leading to new, testable predictions.

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.