BeEST: Weighing a Neutrino From a Recoiling Lithium Atom

The absolute mass of the neutrino has three principal experimental routes, each with its own physics and its own systematics. The first is kinematic measurement at a beta-decay endpoint, currently dominated by KATRIN’s tritium-beta-decay spectrometer with a 0.45 eV upper limit and a roadmap to 0.2 eV. The second is cosmological inference from large-scale structure and the cosmic microwave background, currently around $\sum m_{\nu }<0.12$ eV depending on assumptions, with much tighter limits expected from CMB-S4 and the Simons Observatory. The third is the search for neutrinoless double beta decay, sensitive to the effective Majorana mass under the assumption that neutrinos are their own antiparticles, with the strongest current bound from KamLAND-Zen and a vigorous program of next-generation experiments.

A fourth, less heralded route has matured into a credible competitor. BeEST — the Beryllium Electron capture in Superconducting Tunnel junctions — measures the neutrino mass by detecting the recoil of a single lithium-7 atom produced when an implanted beryllium-7 atom undergoes electron capture. The technique uses cryogenic quantum sensors developed for X-ray astronomy and avoids all of KATRIN’s molecular-final-state and spectrometer systematics. Phase II results published in 2022 set an upper limit of about 0.8 keV. Phase III, with much larger sensor arrays, aims at sub-10-eV sensitivity, and the long-term roadmap targets below 0.1 eV. The technique would not on its own surpass KATRIN’s current bound for several years, but as an independent third measurement of the same physical quantity with completely different systematics, BeEST is one of the more interesting bets in the absolute-neutrino-mass game.

This post is about how electron-capture kinematics encodes the neutrino mass, how BeEST exploits superconducting tunnel junctions as ultra-sensitive calorimeters, and where the technique sits relative to its competitors.

Electron capture as a recoil thermometer

Beryllium-7 is one of the simplest unstable nuclei. It decays by electron capture:

${}^7\mathrm{Be}+e^{-}\to {}^7\mathrm{Li}+{\nu }_e$

with a half-life of about 53 days. The nucleus captures an inner-shell electron — usually from the K shell — and converts a proton into a neutron, emitting a monoenergetic neutrino. The total energy release, the Q-value, is 862 keV, with about 90% going to the ground state of lithium-7 and about 10% to the first excited state at 478 keV.

By energy and momentum conservation, the lithium-7 nucleus recoils. In the rest frame of the parent atom, energy conservation gives

$Q=T_{\nu }+T_{\mathrm{Li}}$

and momentum conservation requires the lithium-7 nucleus to balance the neutrino’s momentum exactly:

$p_{\nu }=p_{\mathrm{Li}}$

Working through the kinematics with $T_{\mathrm{Li}}=p_{\mathrm{Li}}^2/(2m_{\mathrm{Li}})$ and $T_{\nu }=\sqrt{p_{\nu }^2{c}^2+m_{\nu }^2{c}^4}-m_{\nu }{c}^2$, and substituting numerical values, the lithium recoil energy comes out to approximately

$T_{\mathrm{Li}}^{\max }\approx \frac{Q^2}{2m_{\mathrm{Li}}{c}^2}\left(1-\frac{m_{\nu }^2{c}^4}{Q^2}\right)\approx 56.8\mathrm{eV}-\text{(neutrino-mass correction)}$

The neutrino-mass correction shifts the endpoint of the recoil-energy spectrum downward. Measuring that shift gives a kinematic bound on the neutrino mass — completely analogous to the endpoint shift of a tritium beta spectrum, but using a different decay topology with very different systematics.

The unique feature of electron capture for this purpose is that only one particle escapes. There is no electron in the final state because the electron was absorbed; only the neutrino and the recoiling daughter atom remain. If the recoil energy can be measured precisely, then the rest of the energy is unambiguously the neutrino. There is no molecular spectrum to deconvolve, no continuous beta spectrum to fit, no shape-fitting near the endpoint to disentangle from backgrounds.

The superconducting tunnel junction as calorimeter

Measuring a 57 eV recoil to sub-eV precision requires a detector with an energy resolution of perhaps 1 eV at full width at half maximum and a fast response time. Conventional silicon ionization detectors cannot do this; the eV scale is below their bandgap. The technology that can is the superconducting tunnel junction (STJ), originally developed for X-ray astronomy and adapted for BeEST.

An STJ is a sandwich of two superconducting tantalum thin films separated by an insulating barrier. At cryogenic temperatures the films are in the superconducting state. When a particle deposits energy in the tantalum, the energy breaks Cooper pairs, producing quasiparticles that tunnel across the barrier and produce a measurable current pulse. The number of quasiparticles is proportional to the deposited energy, with the proportionality set by the superconducting gap energy of about 0.7 meV in tantalum. Because the gap is so small, each eV of deposited energy produces roughly a thousand quasiparticles — a much larger signal than the few-eV-per-electron-hole pair statistics of a semiconductor.

The resulting energy resolution at the few-tens-of-eV scale is around 1 eV FWHM, sufficient to resolve the recoil endpoint structure. The response time is microseconds, fast enough to handle decay rates without pileup at the relevant source activities.

The beryllium-7 source is implanted directly into the tantalum film at a depth of a few nanometers, so that the lithium-7 daughter is born inside the sensor and its full kinetic energy is captured. Every electron capture produces a recoil event in the local sensor, with the deposited energy reading out as a clean pulse.

Phase II and what was measured

The BeEST collaboration’s phase II result, published in 2022, used a single beryllium-7-implanted tantalum STJ with a source activity of about $10^{10}$ atoms. Over a run of months, several million electron-capture events were recorded. The energy spectrum showed the expected structure: a dominant peak near 57 eV from ground-state-to-ground-state transitions, plus a smaller peak from transitions to the 478-keV excited state in lithium-7, plus a continuum from atomic-excitation final states that arise when the recoil deposits energy into electronic shells along with the kinetic energy.

The atomic-excitation continuum is, surprisingly, the dominant physics systematic. The recoiling lithium can leave inner-shell vacancies or excited atomic states that decay by emitting Auger electrons or photons, depositing additional energy in the sensor. The measured pulse-height distribution near the endpoint is therefore not a simple recoil spectrum but a convolution of the recoil and the atomic deexcitation. Modeling this requires careful atomic-physics input and is the main thing that distinguishes BeEST’s systematic budget from KATRIN’s molecular-final-state budget — different physics, comparable challenge.

The phase-II analysis extracted an upper limit of approximately $m_{{\nu }_e}<0.8$ keV at 90% confidence, with the limit set mainly by the statistical precision near the endpoint and by the modeling of the atomic-excitation continuum. This is far above KATRIN’s current 0.45 eV, but the goal of phase II was always to demonstrate the technique and characterize the atomic-excitation systematic, not to set a competitive limit.

Phase III and beyond

The reach of the technique scales with the number of sensors. A single STJ has a fixed source activity set by the implantable beryllium-7 density; gains come from arraying many sensors in parallel. Phase III, currently in construction, scales up from a single STJ to an array of several hundred. Combined with improved atomic-physics modeling, the projected sensitivity reaches a few electron-volts.

Phase IV planning targets arrays of thousands of sensors, multi-year exposures, and refined atomic-excitation deconvolution. The projected sensitivity is below 0.1 eV — within range of the cosmologically-allowed mass region and, more importantly, in territory where the absolute mass scale could realistically be measured rather than just upper-bounded.

Achieving this requires several improvements. The energy resolution at the endpoint has to be pushed below 1 eV. The atomic-excitation modeling has to be cross-validated against direct measurements of beryllium-7 implant excitation states. And the source-implantation uniformity has to be controlled so that the deposited recoil energy is consistent across the sensor area. Each is a tractable engineering and physics problem.

Why a third measurement matters

Even if BeEST eventually reaches the same sensitivity as KATRIN — say 0.1 eV — its scientific value goes beyond the limit itself. The two measurements address the same physical quantity through completely different processes:

• KATRIN measures the beta-decay endpoint shift of tritium with a magnetic spectrometer. Its dominant systematics involve molecular final-state effects, the source column density, and the spectrometer transmission function.
• BeEST measures the recoil endpoint shift of lithium-7 from beryllium-7 electron capture with a cryogenic calorimeter. Its dominant systematics involve atomic-excitation final states and the calorimeter energy response.

A consistent result from both would be a powerful cross-check on the absolute neutrino-mass scale. A discrepancy would point to either a misunderstood systematic or a genuinely surprising physical effect. Neither outcome is currently available with KATRIN alone.

The mass scale matters because it sits at a junction of several major lines of inquiry. The cosmological mass sum constrains structure formation and is now approaching the 0.06 eV scale where it would test the mass-ordering hypothesis directly. The kinematic measurement is independent of cosmology and of the Majorana-versus-Dirac question. The neutrinoless double beta decay measurement is conditional on Majorana nature and depends on the lightest mass eigenstate. Three independent measurements with very different systematics would put the absolute neutrino mass on a footing comparable to the way three different measurements once pinned down the Hubble constant — and would either confirm consistency among all three or reveal tensions that point toward new physics.

Summary

BeEST measures the absolute neutrino mass through the recoil endpoint of lithium-7 atoms after beryllium-7 electron capture, using superconducting tunnel junctions as ultra-sensitive cryogenic calorimeters. The technique exploits the kinematic simplicity of two-body decay — only the recoil atom and a single escaping neutrino — to give a clean endpoint structure shifted by the neutrino mass. Phase II demonstrated the principle with a single sensor and an upper limit of 0.8 keV; phase III aims at few-eV sensitivity with several hundred sensors; longer-term plans target below 0.1 eV with sensor arrays of thousands. The systematics are completely different from KATRIN’s tritium beta-decay endpoint approach, providing an independent third route to the same physical quantity. A consistent measurement at the relevant scale would cross-check the absolute neutrino mass with confidence beyond what any single technique can provide.