Naughty Neutrons

Those who are paying attention will recall Graham Dungworth's thread on mirror matter at Galaxy Zoo. They may also recall that antineutrons are reported to have a mass distinct from neutrons, just as in the neutrino sector. In a lovely (albeit somewhat theoretically misguided) paper on mirror neutrons, Zurab Berezhiani demonstrates that neutron mirror neutron oscillations are not ruled out by experiment. On page $1$ it is said:

... the $n \rightarrow n'$ transition can only manifest as anomalous disappearance of the neutrons, in addition to the decay, absorption and other regular channels of their losses.

Using reported data, and with an analysis based on an hypothesised mirror magnetic field for the Earth, Berezhiani notes an anomalous delta of $- 3.5 \pm 2.5 \times 10^8$ in recorded event counts. Hmm. I wonder what effect a neutron disappearance might have on estimated cross sections for a reactor antineutrino anomaly?