A possible shortcut for neutron-antineutron oscillation through mirror world

Existing bounds on the neutron-antineutron mass mixing, $\epsilon_{n\bar n} < {\rm few} \times 10^{-24}$ eV, impose a severe upper limit on $n - \bar n$ transition probability, $P_{n\bar n}(t) < (t/0.1 ~{\rm s})^2 \times 10^{-18}$ or so, where $t$ is the neutron flight time. Here we propose a new mechanism of $n- \bar n$ transition which is not induced by direct mass mixing $\epsilon_{n\bar n}$ but is mediated instead by the neutron mixings with the hypothetical states of mirror neutron $n'$ and mirror antineutron $\bar{n}'$. The latter can be as large as $\epsilon_{nn'}, \epsilon_{n\bar{n}'} \sim 10^{-15}$ eV or so, without contradicting present experimental limits and nuclear stability bounds. The probabilities of $n-n'$ and $n-\bar{n}'$ transitions, $P_{nn'}$ and $P_{n\bar{n}'}$, depend on environmental conditions in mirror sector, and they can be resonantly amplified by applying the magnetic field of the proper value. This opens up a possibility of $n-\bar n$ transition with the probability $P_{n\bar n} \simeq P_{nn'} P_{n\bar{n}'}$ which can reach the values $\sim 10^{-8}$ or even larger. For finding this effect in real experiments, the magnetic field should not be suppressed but properly varied. These mixings can be induced by new physics at the scale of few TeV which may also originate a new low scale co-baryogenesis mechanism between ordinary and mirror sectors.