Laboratory constraints on peV-scale mass splitting between ordinary and sterile neutron states

Technical Summary: Laboratory Constraints on PeV-Scale Mass Splitting Between Ordinary and Sterile Neutron States

Problem Statement
The existence of a parallel "mirror" sector of matter, proposed as a duplicate of the Standard Model, offers a potential candidate for dark matter. A key mechanism for interaction between ordinary matter and this mirror sector is the oscillation of neutrons ($n$) into sterile mirror neutrons ($n'$). While previous searches focused on the case where $n$ and $n'$ are exactly mass-degenerate, theoretical models suggest a non-zero mass splitting ($\delta m = m_{n'} - m_n$) could exist due to spontaneous mirror parity breaking, environmental factors, or modified gravity. Such a splitting suppresses $n-n'$ oscillations under natural conditions but allows for resonance when an external magnetic field compensates for the energy difference. Previous laboratory constraints on the oscillation time constant ($\tau_{nn'}$) in the finite-mass-splitting scenario were either limited to narrow ranges or weaker than existing astrophysical bounds derived from neutron star cooling (which suggest $\tau_{nn'} > \mathcal{O}(10)$ s).

Methodology
The authors utilized data from a dedicated ultracold neutron (UCN) storage experiment at the Paul Scherrer Institute (PSI). The experimental apparatus consists of a 1.5 m³ stainless-steel storage vessel surrounded by eight rectangular coils capable of generating tunable magnetic fields in the range of $5\,\mu\text{T} < B < 360\,\mu\text{T}$.

The methodology relies on the principle that if $n-n'$ oscillations occur, sterile $n'$ neutrons will escape the material confinement of the storage vessel, leading to a magnetic-field-dependent deficit in the detected UCN count. The experiment employed an asymmetry measurement approach:

1. Resonance Tuning: The magnetic field ($B$) was tuned to create Zeeman energy differences ($V = \pm \mu_n B$) that could compensate for specific mass splitting values ($\delta m$), satisfying the degeneracy condition $\Delta E = 0$ for one spin state.
2. Asymmetry Calculation: The experiment compared neutron counts ($n_i, n_j$) obtained under two different magnetic field settings ($B_i, B_j$). One field was intended to induce degeneracy (resonance), while the other served as a non-degenerate reference. The asymmetry $A_{i,j}$ was calculated as:
   $$A_{i,j} = \frac{n_i - n_j}{n_i + n_j}$$
3. Data Analysis: The analysis involved 832 magnetic-field setting comparisons. To mitigate systematic errors from UCN source drift and environmental fluctuations, data points were paired if taken within one day. A 5$\sigma$-clipping procedure was applied to reject outliers caused by beam interlocks or synchronization issues.
4. Simulation and Limits: Monte Carlo (MC) simulations (using the MCUCN code) were performed to calculate the "resonance functions" $F(B, \delta m)$, representing the cumulated oscillation probability for a unit oscillation time. The experimental asymmetry limits were then converted into exclusion limits for the oscillation time constant $\tau_{nn'}$ using the relation:
   $$\tau_{nn'} = \frac{1}{\sqrt{2|\langle A_{i,j}\rangle|}} \sqrt{|F(B_i, \delta m) - F(B_j, \delta m)|}$$

Key Results

• No Signal Observed: The measured mean asymmetries $\langle A_{i,j}\rangle$ were consistent with the null hypothesis ($H_0$) within standard errors across the entire scanned parameter space. No magnetic-field-dependent loss signal indicative of $n-n'$ oscillation was detected.
• Exclusion Limits: The study derived 95% confidence level (C.L.) exclusion limits for the oscillation time constant $\tau_{nn'}$.
  • The limits reach approximately 20 seconds over the mass-difference range of 0.3 to 22 peV ($3 \times 10^{-13}$ to $1 \times 10^{-11}$ eV).
  • In the range of $\delta m = 6 - 22$ peV, the sensitivity exhibits sharp dips due to the discrete spacing of the magnetic field settings used to cover the broad interval.
• Comparison with Previous Bounds: The new limits exceed those from previous UCN and cold neutron beam experiments [48–53] for the specified mass-splitting range. Crucially, in parts of this parameter space, the laboratory limits are more stringent than the model-dependent astrophysical bound derived from neutron star cooling ($\tau_{nn'} > \mathcal{O}(10)$ s).

Significance and Claims
The paper claims to provide the first experimental constraints on the $n-n'$ oscillation scenario with finite mass splitting that surpass the sensitivity of current astrophysical estimates (neutron star cooling). By extending the experimental coverage into the small mass-splitting region (up to 22 peV) and achieving limits of ~20 s, the work significantly narrows the viable parameter space for mirror neutron dark matter models where the two states are not mass-degenerate. The results demonstrate that laboratory experiments can now probe this specific scenario with greater sensitivity than indirect astrophysical observations, provided the mass splitting falls within the tested range.