New Search for Mirror Neutron Regeneration

A sensitivity study of neutron–mirror neutron oscillation searches at GP-SANS has been performed previously Broussard:2017yev . This simulation study included total backgrounds in the region of interest of 0.3 cps, development of a 3D magnetic field control system composed of solenoidal and cosine theta coils with 2 mG uniformity, and scan of magnetic fields simultaneously in both of the separated regions of up to 125 mG in steps of 5 mG, in four directions (forming a tetrahedron) to optimize sensitivity. The results of this study indicates that a search for regeneration of neutrons would exclude $\tau<15$ s over $-125$ mG $<B^{\prime}<$ 125 mG (90% C.L.) in a one week experiment (excluding possible systematic studies). GP-SANS may also be used as a powerful cross-check in the event that an anomalous signal is discovered in current ultracold neutron searches, including outside this magnetic field range. An example of the sensitivity of a one week experiment to a search at a single magnetic field magnitude of 0.3 G is shown in Fig. 2, where an oscillation time of up to $\tau<40$ s could be probed. This measurement requires large area beam guides instead of collimation in the primary vacuum vessel, and a detailed magnetic field mapping campaign of the detector tank. We note the ultimate sensitivity is expected to be lower than current ultracold neutron efforts Prajwal .

Recently, a new idea has surfaced which attempts to explain the neutron lifetime discrepancy using mirror neutron oscillations Berezhiani:2018eds . This model suggests that the cold neutron beam lifetime experiment at NIST Yue:2013qrc is sensitive to a very high probability of oscillations at much larger magnetic field strengths, of up to 4.6 T, to compensate a small mass splitting of order 100 neV between the neutron and mirror neutron. As neutrons enter the magnet and first cross the compensating field, up to 1% are found in the mirror state, in which the decay to a mirror proton, which is not trapped by the laboratory magnetic field, is missed. The mirror neutrons which don’t decay still have a high probability of being found in the pure neutron state after exiting the magnet, resulting in a too-long measured lifetime.

A simple experiment can be performed to test the hypothesis of neutron oscillation at large (order T) magnetic fields, using a similar disappearance-regeneration style approach (Fig. 3). A neutron beamstop can be located at the high field region, so that only the neutrons which are found in the mirror state can pass through, and then transform back to the ordinary neutron state after crossing the compensating field, and be detected.

The sensitivity of this type of search at GP-SANS can be estimated using formula 20 of Berezhiani:2018eds . A monochromatic beam of 4.75Å (velocity $v=$833 m/s) with $\Delta\lambda/\lambda\sim 13\%$ is available with estimated intensity of 10⁷ n/s, and a 5 T superconducting magnet can be installed in the sample region of the instrument. For a non-adiabatic crossing of the compensating field (at position $z_{c}$), the probability for a neutron to be found in the mirror neutron state at the beamstop $P_{nn^{\prime}}\approx\frac{\pi}{4}\xi$ depends on an adiabaticity parameter $\xi$,

For example, using $\theta_{0}\sim 10^{-3}$ as in Berezhiani:2018eds , and supposing the compensating field to be $B=$2 T ($\Delta m=120$ neV), and with $\frac{d\ln B}{dz}\bigr{\rvert}_{z_{c}}=0.2$ from the calculated field map of the superconducting magnet, we find $\xi\sim 0.04$ and $P_{nn^{\prime}}\sim$3%. Therefore if mirror neutrons are the source of the lifetime discrepancy as suggested in Berezhiani:2018eds , a dramatic effect would be observed, with $10^{7}\cdot(0.03)^{2}\sim 10^{4}$ regenerated neutrons per second.

Much more sensitive limits than needed to explain the lifetime discrepancy can be placed with a reasonably high suppression beamstop. The background from transmission through the beamstop could be subtracted by comparing the observed rate with and without the presence of a large magnetic field. Large changes in neutron backgrounds from scattering from other instruments in the facility can be monitored using detectors outside the beamline, and sensitivity to background can be reduced by positioning the GP-SANS detector further back in the shielded detector tank. Because the oscillation probability depends strongly on the neutron velocity, a useful cross-check of any unexplained magnetic field-dependent effect can quickly be obtained by selecting different neutron wavelengths using the GP-SANS velocity selector. This kind of experiment can be performed quickly, involving only the development of a beamstop with $<$10^-6 transmission, required for all future stages of oscillation searches.

An alternative model for mirror neutron oscillations has recently been suggested where the neutron and mirror neutron have an additional magnetic moment, a Transition Magnetic Moment (TMM) $\eta$ of common magnitude, which enters in the non-diagonal part of the Hamiltonian operator that couples the neutron and mirror neutron correspondingly with the ordinary and mirror electromagnetic fields ntrans . In this model, if both $B$ and $B^{\prime}$ are above a few mG, the n$\rightarrow$n’ transition probability is constant and doesn’t depend on the magnitude of the magnetic field, but only on the magnitude of $\eta$. This model can shed light on the neutron lifetime anomaly, in which the ultracold neutron bottle lifetime experiments are susceptible to an unaccounted loss due to oscillations into mirror neutrons in the volume. In a material or magnetic bottle, the neutron has a chance to collapse into the mirror neutron state (and be lost) at each bounce from the material walls or when accelerated by magnetic gradients. A n$\rightarrow$n’ transition probability of 10^-7–10^-9 due to the TMM of order $\eta/\mu\sim$10^-4–10^-5 could explain the lifetime discrepancy.

A sensitive search for a TMM can be performed by using an applied magnetic field gradient to more rapidly force a decoherence of the entangled ordinary and mirror neutron states. The length scale of the decoherence $\Delta x$ for neutrons passing through a magnetic field gradient can be estimated using the relation (adapted from formula 17 of ntrans )

By maximizing the gradient, the number of decoherence lengths $\Delta x$ that the neutron passes through is maximized. Each $\Delta x$ represents an opportunity for a n$\rightarrow$n’ transition.

A preliminary search for a neutron TMM can be performed in a simple regeneration experiment using a beamstop inside the superconducting magnet at GP-SANS. The calculated magnetic field gradient and corresponding decoherence length along the neutron beam axis inside the magnet is plotted in Figure 4. The unusual magnetic profile is due to the split coil which accommodates a perpendicular bore to allow insertion of samples in the magnet center. The 4.75 Å neutron beam will pass through roughly 450 decoherence lengths on each side of a beamstop centered in the magnet, enabling a sensitivity of up to $\eta/\mu<2\times 10^{-4}$ to be probed with a beamtime allocation of $\sim 1$ day. With the velocity selector removed and operating in white beam mode, this limit can be improved to $\eta/\mu<8\times 10^{-5}$.

Large gradients over longer flight paths could also be implemented using a series of coils with alternating currents as suggested in ntrans or with a cylindrical Halbach array composed of permanent magnets to create strong longitudinal or radial gradients. Gradients of about 2 kG/m could be constructed in this way, enabling a sensitivity to a n$\rightarrow$n’ transition probability approaching 10^-9 or a TMM of $\eta/\mu\sim 10^{-5}$. An alternate scheme that balances the magnetic potential and Fermi potential of a gas has also been described which enable even higher sensitivity ntrans .

To achieve the sensitivity required for a TMM search, a cold neutron beamstop with a transmission rate of less than 1 in 10¹² is required. Using the PHITS phits transport code, we estimate that 1 cm of boron carbide B₄C (about 20$\%$ natural abundance of ¹⁰B) is sufficient for the neutron spectrum available at GP-SANS. The beamstop will be implemented using a re-entrant design to limit backscattering. To characterize fluctuating neutron backgrounds in the facility, due to changing conditions of instruments on other beamlines, a secondary detector of 8 cylindrical ³He gas chambers with similar geometry to the GP-SANS primary detector has been installed outside the detector tank.