Search for dark matter decay of the free neutron from the UCNA experiment: n $\rightarrow \chi + e^+e^-$

It has been proposed recently that a previously unobserved neutron decay branch to a dark matter particle ($\chi$) could account for the discrepancy in the neutron lifetime observed in experiments that use two different measurement techniques. One of the possible final states discussed includes a single $\chi$ along with an $e^{+}e^{-}$ pair. We use data from the UCNA (Ultracold Neutron Asymmetry) experiment to set limits on this decay channel. Coincident electron-like events are detected with $\sim 4\pi$ acceptance using a pair of detectors that observe a volume of stored Ultracold Neutrons (UCNs). The summed kinetic energy ($E_{e^{+}e^{-}}$) from such events is used to set limits, as a function of the $\chi$ mass, on the branching fraction for this decay channel. For $\chi$ masses consistent with resolving the neutron lifetime discrepancy, we exclude this as the dominant dark matter decay channel at $\gg~5\sigma$ level for $100~\text{keV} < E_{e^{+}e^{-}} < 644~\text{keV}$. If the $\chi+e^{+}e^{-}$ final state is not the only one, we set limits on its branching fraction of $< 10^{-4}$ for the above $E_{e^{+}e^{-}}$ range at $> 90\%$ confidence level.