Further search for magnetic-field-induced neutron disappearance in an ultracold neutron beam

This paper reports the results of a second iteration of an experiment at the ILL PF2 facility searching for neutron-hidden-neutron oscillations via magnetic-field-induced neutron disappearance, finding no evidence for such oscillations and establishing new 95% confidence level lower limits on the oscillation period ($\tau_{nn'}$) of over 200 ms and 100 ms for mass splittings in the ranges of 60–400 peV and 400–1550 peV, respectively.

The Gist

The Great Neutron Disappearance Hunt: A Story of Invisible Twins

Imagine you have a room full of very shy, slow-moving guests called neutrons. These guests are usually very predictable: they hang out, bounce off walls, and eventually fade away (decay) on their own. But physicists have a wild theory: what if some of these neutrons aren't just fading away? What if they are secretly slipping through a hidden door into a parallel universe, only to return a moment later?

This paper is the report card from a massive experiment designed to catch these "neutron spies" in the act.

The Theory: The Mirror Universe

Scientists suspect there might be a "Mirror Universe" right next to ours. In this mirror world, there are "mirror neutrons" that look exactly like our neutrons but are invisible to us. They can't talk to our world (they don't feel our light or electricity), but they might be able to swap places with our neutrons for a split second.

If a neutron swaps places with its mirror twin, it effectively disappears from our detectors. If it swaps back, it reappears. The scientists wanted to see if they could make this swapping happen more often by using a magnetic field as a tuning fork.

The Setup: A Magnetic Slide

The experiment took place at a giant particle lab in France (the ILL). Here's how they set the trap:

1. The Slower the Better: They used Ultra-Cold Neutrons (UCNs). Think of these not as high-speed bullets, but as slow-motion bowling balls rolling down a lane. Because they are so slow, they can be guided easily.
2. The Magnetic Slide: The neutrons were sent through a long, hollow tube (a solenoid) that acted like a giant magnet. The scientists could adjust the strength of this magnet, like turning a dimmer switch on a light.
3. The Tuning Fork: The theory says that if the magnetic field is set to a very specific strength, it creates a "resonance." Imagine pushing a child on a swing. If you push at the exact right rhythm, the swing goes higher. Similarly, if the magnetic field matches the "mass difference" between the real neutron and the mirror neutron, the neutron is much more likely to slip into the mirror world.

The Strategy: The "A-B-C" Dance

The scientists didn't just turn the magnet on and hope for the best. They played a game of "A-B-C":

• Phase A: They set the magnet to a specific strength and counted how many neutrons arrived at the detector.
• Phase B: They tweaked the magnet slightly (the "sweet spot" they were testing) and counted again.
• Phase C: They went back to the original strength (or a mirror image of it) and counted a third time.

They calculated a ratio: Did fewer neutrons show up during Phase B?

If the neutrons were disappearing into the mirror world, the count in Phase B would drop. It's like if you had a bucket of water and, every time you turned on a specific faucet, the water level mysteriously dropped because some water was leaking into a hidden pipe.

The Results: No Spies Found

After running this experiment for months, collecting millions of data points, and filtering out "noise" (like background radiation or random electronic glitches), the answer was clear:

The neutrons did not disappear.

The number of neutrons arriving at the detector was exactly the same, regardless of how they tweaked the magnetic field. The "hidden door" remained closed.

What Does This Mean?

Since they didn't find the disappearing act, they had to set a new rulebook. They said:

• "If these mirror neutrons exist, they must be very hard to catch."
• They established that the time it takes for a neutron to swap with a mirror twin must be longer than 100 to 200 milliseconds.

Think of it like this: If you were looking for a ghost that only appears for a blink of an eye, and you didn't see it, you can't say the ghost doesn't exist. But you can say, "If the ghost is real, it must be hiding for longer than a blink."

The Takeaway

This experiment is like a very thorough search for a needle in a haystack. They didn't find the needle, but by searching so carefully, they proved that if the needle is there, it's much harder to find than we thought.

This helps physicists rule out certain theories about the universe and tells them they need to look in different places or with different tools to solve the mystery of Dark Matter and the missing pieces of our universe. For now, the neutrons are staying right where they belong: in our world.

Technical Summary

1. Problem and Scientific Context

The paper addresses the search for neutron-hidden-neutron ($n-n'$) oscillations, a phenomenon predicted by various extensions of the Standard Model (SM), including "mirror matter" and extra-dimensional brane models.

• Theoretical Basis: These models propose a "hidden sector" of particles that interact with SM particles primarily via gravity and mixing portals. A specific hypothesis suggests that neutrons ($n$) can oscillate into hidden neutrons ($n'$), effectively causing the ordinary neutron to "disappear" from the observable sector.
• The Mechanism: The oscillation probability depends on the mass splitting ($\delta m$) between the two states and a mixing parameter ($\epsilon_{nn'}$). The transition is resonantly enhanced when the energy difference induced by an external magnetic field ($\Delta E = \mu_n B$) matches the mass splitting ($\delta m$).
• Objective: The experiment aims to detect the anomalous disappearance of ultra-cold neutrons (UCNs) as a function of an applied magnetic field, specifically exploring the poorly constrained mass splitting regime of 60–1550 peV (pico-electronvolts).

2. Methodology and Experimental Setup

The experiment was conducted at the PF2 facility of the Institut Laue-Langevin (ILL) in Grenoble, France, between May and July 2024.

• Apparatus:
  • Source: UCNs were extracted from the PF2 cold source (liquid D2) and transported via a 15 cm diameter stainless-steel guide.
  • Magnetic Field: A 1.2 m long solenoid (re-purposed from another experiment) generated a homogeneous magnetic field up to 30 mT. To cover a wider range of $\delta m$ values within time constraints, a magnetic gradient was intentionally created using correction coils, widening the resonance width at the cost of peak sensitivity.
  • Detector: The GADGET detector, a fast-response neutron counter based on a $^3$He/CF4 gas mixture. Neutrons captured on $^3$He produce a proton and triton, which scintillate the CF4. The light is detected by three photomultiplier tubes (PMTs) arranged orthogonally.
• Data Acquisition Strategy:
  • Cycles: The experiment operated in 200-second cycles, alternating with another experiment at an adjacent beam port.
  • Field Scanning: Within each cycle, the solenoid current was stepped through three phases (A, B, C) to create a self-normalizing ratio. The B-period field was the "test" field, while A and C served as baselines.
  • Scanning Regimes: Two phases were executed:
    1. Low Energy: 0.28–2.12 A (60–500 peV).
    2. High Energy: 1.999–6.6 A (470–1550 peV).
  • Polarity: The current direction was periodically reversed to test both positive and negative polarities.
• Event Selection:
  • A dedicated background sample (beam-off) was used to characterize environmental and activation backgrounds (e.g., $^{28}$Al, $^{56}$Mn).
  • Pulse-Shape Discrimination (PSD): Cuts were applied based on charge ($Q$), amplitude ($A$), and relative charge distribution ($D_i$) across the three PMTs to distinguish UCN capture events (Gaussian-like distribution) from background (Cherenkov radiation, pile-up, or activation).
  • Efficiency: The cuts retained ~74.2% of beam-on events while reducing background to <2% of the signal.

3. Analysis and Computation

• Probability Calculation: The disappearance probability $P_{nn'}$ was computed by numerically solving the Schrödinger equation for the $n-n'$ system.
  • Simulation: Neutron trajectories were simulated using STARucn Monte Carlo software, incorporating the specific magnetic field map of the solenoid (modeled as 4092 current loops).
  • Integration: The probability was integrated over the neutron flight path and averaged over 50 trajectories.
  • Interpolation: Due to computational intensity, probabilities were pre-calculated for 55 $\delta m$ values and interpolated across the parameter space.
• Statistical Analysis:
  • A self-normalizing ratio $R_{ABC} = N_B / (N_A + N_C)$ was used to cancel long-term flux variations.
  • A $\chi^2$ function was constructed to fit the data, profiling over nuisance parameters related to magnetic field fluctuations ($\delta B$).
  • Systematics: The dominant systematic uncertainty arose from non-statistical fluctuations in the UCN rate (likely due to reactor power or cold source temperature), requiring an error inflation factor of 2.53.

4. Key Results

• Observation: No evidence for neutron disappearance was observed.
• Significance: A local excess was found at $\delta m = 838$ peV with a significance of $3.7\sigma$ (corresponding to $\tau_{nn'} = 117$ ms). However, after applying the Look-Elsewhere Effect (LEE) correction (Bonferroni factor of ~100 due to the wide scan range), this result was deemed statistically insignificant.
• Exclusion Limits: The experiment set conservative 95% Confidence Level (CL) limits on the oscillation period $\tau_{nn'}$:
  • $\tau_{nn'} > 200$ ms for $|\delta m| \in [60, 400]$ peV.
  • $\tau_{nn'} > 100$ ms for $|\delta m| \in [400, 1550]$ peV.
• Comparison: These limits cover a significant portion of the previously unconstrained parameter space, extending the search range significantly compared to previous trapped UCN experiments.

5. Significance and Conclusion

• Parameter Space Coverage: This work is the first to probe the 60–1550 peV mass splitting regime using a beam-based disappearance method, filling a gap left by previous experiments that were limited to lower mass splittings or different methodologies (e.g., wall-passing regeneration).
• Methodological Trade-off: The use of a magnetic gradient allowed for a broader scan of $\delta m$ values within the available beam time, though it reduced sensitivity compared to a perfectly homogeneous field.
• Future Outlook: The authors note that this direct disappearance method has likely reached its practical limits for higher mass splittings. Further exploration of higher $\delta m$ values would require significantly stronger magnetic fields, necessitating complex superconducting coils or room-temperature magnets with advanced cooling systems.
• Impact: The results provide stringent constraints on mirror matter models and other hidden sector theories, ruling out specific regions of the mixing parameter space ($\tau_{nn'}$ vs. $\delta m$) and guiding future theoretical and experimental efforts in fundamental physics.