The Neutron Lifetime Discrepancy and Topological Selection Rules
Description
Title: The Neutron Lifetime Discrepancy and Topological Selection Rules
Author: Alexander Novickis (alex.novickis@gmail.com)
The neutron lifetime discrepancy — a persistent ~4σ tension between beam experiments (τ_beam ≈ 887.7 ± 2.2 s) and bottle experiments (τ_bottle ≈ 878.4 ± 0.5 s) — has motivated proposals for exotic neutron decay channels involving dark sector particles. We analyse this discrepancy within the Hopf soliton framework, where baryons are multi-sector solitons on the flag manifold F₂ = SU(3)/[U(1)×U(1)] and dark matter is a vacuum knotting condensate with no stable compact particles (Paper LXVII). We identify three independent topological obstructions to neutron dark decay: (i) the absence of any stable dark particle — compact H = 0 knots dissolve in ~10⁻²² s, and the vacuum condensate cannot absorb decay products; (ii) conservation of π₂(F₂) = ℤ ⊕ ℤ sector charges that cannot be carried by CP¹ configurations; and (iii) exponential suppression of topology-changing tunneling. We then investigate the sole remaining loophole — oscillation to a Weyl-conjugate "dark neutron" — and show that the electromagnetic mass splitting (~161 keV) exceeds the required δm ~ 10⁻²⁰ eV by 26 orders of magnitude. All dark decay channels are closed. The framework predicts τ_n = 882 s from the weak matrix element (Paper XIX), consistent with the bottle world average. The J-PARC electron-beam result (877.2 ± 4.4 s), the first beam experiment to agree with bottles, supports the prediction that the discrepancy is a proton-counting systematic, not new physics.
Key results include:
- Three independent topological locks forbid ALL dark neutron decay channels in the Hopf framework
- Compact dark particles do not exist: H = 0 knots dissolve in ~10⁻²² s (Paper LXVII); dark matter is a vacuum condensate
- Weyl dark neutron oscillation fails: EM splitting ~161 keV is 26 orders of magnitude above the required δm ~ 10⁻²⁰ eV
- Framework predicts τ_n = 882 s (Paper XIX), consistent with bottles; J-PARC confirms no missing neutrons
- The programme's neutrino sector is Majorana (Paper IV, Paper CXXIX); the dark-decay locks hold independently of the neutrino's Dirac/Majorana nature
Keywords: neutron lifetime, beam-bottle discrepancy, dark neutron decay, topological selection rules, Hopf soliton, flag manifold, sector charge, vacuum condensate dark matter, baryon number conservation, Majorana neutrino, instanton suppression, J-PARC, ultracold neutrons, Weyl configuration, neutron beta decay
Series: Paper LXXXVII in the Hopf Soliton Programme
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Neutron_Lifetime_Discrepancy_and_Topological_Selection_Rules.pdf
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References
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- Novickis, A., "Proton Structure from Three-Sector Hopf Solitons," Paper XIX in the Topological Soliton Programme (2026). DOI: 10.5281/zenodo.19581402 --- ## Appendix A: The Nascent Proton Hypothesis {.unnumbered} In the soliton picture, $\beta$-decay is a continuous topological rearrangement: one $d$-quark sector ($-1/3$) transmutes to a $u$-quark sector ($+2/3$). One might ask whether the nascent proton — during or immediately after the rearrangement — could have suppressed electromagnetic coupling and thus escape the proton detector. **The sector transmutation timeline.** The field configuration evolves continuously from the neutron topology to the separated proton + electron + antineutrino: 1. **$t = 0$:** Neutron configuration $(+2/3, -1/3, -1/3)$ 2. **$t \sim t_{\text{trans}}$:** Sector transmutation occurs; charges become $(+2/3, +2/3, -1/3)$ but spatial profile has not yet relaxed 3. **$t \sim t_{\text{relax}}$:** Sector fractions relax to proton ground state The sector relaxation timescale is set by the $F_2$–$CP^1$ energy gap ($\sim 200$ MeV): $t_{\text{relax}} \sim \hbar / 200 \text{ MeV} \sim 3 \times 10^{-24}$ s — the natural QCD timescale. **WKB metastable lifetime.** If the nascent proton lands in a Weyl-excited configuration (sector charges permuted relative to the ground state), the gradient-energy barrier to the ground state is $\sim 741$ MeV. The WKB tunneling lifetime is $\sim 3 \times 10^{12}$ s — the excited state would live indefinitely on experimental timescales. **Why it still doesn't work.** The proton's total electric charge is: $$Q = \frac{2}{3} + \frac{2}{3} - \frac{1}{3} = +1$$ for **every** permutation of $(u, u, d)$ charges across the three sectors. The Weyl configuration changes the charge radius and magnetic moment (form factors) but not the total charge. The NIST BL1 electrostatic trap captures particles by total charge ($Q \cdot \mathbf{E}$), not by form factor. A proton in any Weyl state experiences the same $\mathbf{F} = +1e \times 5$ kV/m force and follows the same trajectory to the detector. **Momentum direction.** The proton's recoil direction is determined by three-body kinematics ($\mathbf{p}_p = -\mathbf{p}_e - \mathbf{p}_\nu$), not by the internal Weyl state. For unpolarized neutrons, the angular distribution is isotropic. The Weyl configuration does not alter which direction the proton travels, so it cannot cause the proton to miss the detector's acceptance. **Neutral intermediate.** During the brief window when the proton and electron solitons have not yet spatially separated, the combined system has $Q = +1 + (-1) = 0$. This neutral phase lasts $\sim R_{\text{soliton}} / c \sim 3 \times 10^{-24}$ s — a factor of $10^{18}$ shorter than the proton drift time to the detector. **Conclusion.** The nascent proton hypothesis is ruled out at every level: relaxation is too fast ($10^{-24}$ s), the total charge is topologically fixed ($Q = +1$), the momentum direction is set by kinematics (not internal structure), and the neutral intermediate is $10^{18}\times$ too brief. ---