Direct experimental constraints on the spatial extent of a neutrino wavepacket

Abstract

Despite their high relative abundance in our Universe, neutrinos are the least understood fundamental particles of nature. In fact, the quantum properties of neutrinos emitted in experimentally relevant sources are theoretically contested^1-4 and the spatial extent of the neutrino wavepacket is only loosely constrained by reactor neutrino oscillation data with a spread of 13 orders of magnitude^5,6. Here we present a method to directly access this quantity by precisely measuring the energy width of the recoil daughter nucleus emitted in the radioactive decay of beryllium-7. The final state in the decay process contains a recoiling lithium-7 nucleus, which is entangled with an electron neutrino at creation. The lithium-7 energy spectrum is measured to high precision by directly embedding beryllium-7 radioisotopes into a high-resolution superconducting tunnel junction that is operated as a cryogenic sensor. Under this approach, we set a lower limit on the Heisenberg spatial uncertainty of the recoil daughter of 6.2 pm, which implies that the final-state system is localized at a scale more than a thousand times larger than the nucleus itself. From this measurement, the first, to our knowledge, direct lower limit on the spatial extent of a neutrino wavepacket is extracted. These results may have implications in several areas including the theoretical understanding of neutrino properties, the nature of localization in weak nuclear decays and the interpretation of neutrino physics data.

Fig. 1. ⁷Be EC in an STJ.

Schematic of the STJ sensor showing the five layers described in the text. The ⁷Be radioactive source is sparsely implanted into the Ta lattice of the absorber layer. The zoomed-in image (top right) shows the final state after EC decay including ⁷Li recoil and ν_e.

Fig. 2. The STJ array of the BeEST experiment and precision energy measurement.

The measured ⁷Li recoil spectrum with the four peaks described in the text for 20 h of data from the single STJ pixel shown in the inset. The L-ES peak is barely visible because of its weak population probability. The measured uncertainty of the K-GS peak is shown, and is conservatively extracted as the upper limit on the inherent energy width of the recoil, σ_N,E ≤ 2.9 eV, through the procedure described in the text. The comb of the peaks from the calibration laser spectrum (violet) is also shown for comparison. The small bump in the spectrum at 4 eV results from a non-prompt, decay-induced process, the source of which is still under investigation. Scale bar, 1 mm.

Fig. 3. Experimental limits and theoretical predictions for radioactive-decay-based neutrino sources.

a,b, Comparison between experimental limits (horizontal bars) and theoretical estimates (vertical bars) for the spatial extent of a neutrino wavepacket created in EC sources (a) and reactor β⁻ sources (b). This plot encapsulates the current status of the spatial uncertainties of the neutrino wavepacket in both experiment and theory from the literature. For EC sources in a, the theoretical predictions are based on different scales of localization for ν_e. The blue band is based on the conservation of momentum and subatomic localization determined by the momentum uncertainty of the ⁷Li 1s electron orbital. The red and orange bands are from two different predictions for atomic localization in a hot ⁵¹Cr source^,. For the reactor sources in b, the experimental limits are indirectly inferred from various oscillation experiments^,. The blue band from 10 pm to 400 pm is the theoretical estimate based on nucleon-scale/nucleus-scale localization estimates. The orange and red bands are estimates based on localization by atomic interactions in the reactor local environment^,. The bands on the far left spanning both plots correspond to the scenario in which the widths of the neutrino wavepackets are preferred in electronvolt-scale ν_s model fits to data^,, and in the case of reactor sources, would also be the region that wavepacket separation would be visible in JUNO^,.