---
title: "Double-beta searches: why use several nuclei? | Sandbox Physics"
description: "Searches in germanium, xenon and tellurium face different backgrounds. A half-life limit, its expected sensitivity and an inferred mass are separate results."
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  zh-CN: "https://sandboxphysics.com/zh/stories/neutrinos/global-neutrinoless-double-beta-searches/"
last_modified: "2026-10-13"
---

[2026 Nobel Prize in Physics](https://sandboxphysics.com/nobel/2026/physics/)

# Double-beta searches: why use several nuclei?

Germanium, xenon and tellurium searches differ in isotope exposure, energy resolution and backgrounds. Turning a half-life limit into a neutrino mass is a further step.

Sandbox Physics · 2026-10-11 · Updated 2026-10-13 · Interpreting evidence

## The signal is a peak at the decay energy

Ordinary double-beta decay emits two electrons and two antineutrinos. The invisible antineutrinos carry off a different share of energy each time, so the summed electron energy forms a continuous spectrum. In a neutrinoless decay, the summed energy would instead pile up near the nuclear energy release, broadened by the detector and by any energy that escapes.

A peak there could also come from ordinary radioactivity. Gamma rays, surface contamination and coincident deposits can land in the same energy region. Experiments fit the signal shape together with the background components, and use calibration data to fix where a real decay peak should appear.

The nucleus under study is also part of the apparatus. Its decay energy, abundance and chemistry decide how much source an experiment can use, what the detector is made of and which backgrounds compete. That is why several isotopes are valuable checks on one another, even when their headline half-life limits differ.

Sources: [1] · [2] · [3]

## Three ways to build the source into a detector

LEGEND uses enriched germanium crystals that are both the source and a semiconductor detector. Their sharp energy response keeps the signal window narrow. The surrounding liquid argon does more than shield the crystals: light from an energy deposit outside them can veto a candidate event.

KamLAND-Zen dissolves enriched xenon in scintillator held in a balloon, which puts a large mass of isotope inside an existing optical detector. To separate a possible decay from surrounding activity, it relies on where events occur, the energy response and an understanding of the backgrounds that muons create in the xenon.

CUORE runs tellurium-oxide crystals as very cold calorimeters and measures deposited energy from the rise in temperature. Its 2022 Nature paper is cited here to illustrate the cryogenic method, not as its latest exposure. Each design balances energy resolution, room to scale up the isotope mass and background rejection in its own way.

Sources: [2] · [3] · [1]

1. 01 **Isotope exposure**

   Count the candidate nuclei and the usable running time

2. 02 **Signal window**

   Calibrate the energy scale and estimate backgrounds

3. 03 **Interpretation**

   Keep lifetime limits, sensitivity and mass apart

Schematic of the method, not a measured spectrum. Each isotope needs its own nuclear calculation.

## The signal grows with nuclei, efficiency and live time

A tonne of compound contains less than a tonne of the candidate isotope. Enrichment, chemical composition and the part of the detector volume used in the analysis set how many nuclei can contribute. How many real decays survive also depends on whether their energy is fully contained, on quality cuts and on any veto used against backgrounds.

When the lifetime is vastly longer than the measurement, the expected number of accepted decays is proportional to the number of isotope nuclei, the efficiency and the live time, and inversely proportional to the half-life. This predicts a rate; setting a limit from data needs a separate statistical procedure.

With negligible background, the half-life reach grows roughly in proportion to exposure. With a large, steady background, fluctuations often slow the gain to something closer to the square root of exposure. A narrower energy window helps only if the calibration, signal efficiency and background model stay reliable.

$$
s=\frac{\ln 2\,N_{\mathrm{iso}}\,\varepsilon t}{T_{1/2}}
$$

Expected number of accepted decays when the live time is much shorter than the half-life. Live time and half-life must use the same time unit; efficiency has no unit.

Sources: [2] · [1] · [4]

## Observed limits and sensitivity are different numbers

KamLAND-Zen's complete result combines its newer xenon-136 data with the earlier phase and puts the half-life above 3.8 times ten to the power of 26 years at 90 percent confidence. Read as exchange of a light Majorana neutrino, this gives a range of upper limits on the mass, not one measured mass.

The first LEGEND-200 paper uses 61.0 kilogram-years of its own data. Combined with GERDA and the MAJORANA DEMONSTRATOR, it gives an observed germanium-76 limit of 1.9 times ten to the power of 26 years at 90 percent confidence. The reported exclusion sensitivity is 2.8 times ten to the power of 26 years.

Those two germanium numbers answer different questions. The sensitivity is the limit expected under a stated procedure if only background were present; the observed limit depends on how the actual data fluctuated. A fair comparison keeps track of the isotope, the data combined, how the interval was built and which version of the paper is used, and does not just pick the stronger-looking number.

Sources: [3] · [2] · [4]

## Turning a half-life into a mass needs nuclear theory

If the decay goes through light-neutrino exchange, converting a half-life into an effective Majorana mass requires a phase-space factor, a nuclear matrix element and a convention for the axial coupling. Different many-body calculations of the nucleus turn the same measured limit into different masses.

A different interaction that violates lepton number could change both the rate and how it varies between isotopes. A future signal seen in several nuclei would therefore test the detector backgrounds and the proposed mechanism at once. Judging whether such signals agree means including correlated theoretical uncertainties; no single mass conversion is exact.

A search that finds nothing rules out a range of lifetimes and model parameters; it does not show that neutrinos are Dirac particles. A confirmed signal would mean lepton number is violated and would need an explanation, but on its own it would not show which exchange process dominates. Keeping these steps apart makes the worldwide search scientifically stronger.

Sources: [5] · [6] · [1]

## What we learned

Different nuclei ask the same question about lepton number, with different backgrounds and nuclear calculations. The observed half-life limit, the expected sensitivity and the inferred mass range are separate results and must be reported separately.

## Try it in the Lab

[Double Beta Decay Observatory](https://sandboxphysics.com/labs/neutrinoless-double-beta/)

## Primary sources & revision

1. [CUORE Collaboration · Search using millikelvin cryogenics (2022)](https://www.nature.com/articles/s41586-022-04497-4)
2. [LEGEND Collaboration · First LEGEND-200 results (2025, v4)](https://arxiv.org/abs/2505.10440v4)
3. [KamLAND-Zen · Complete dataset search for Majorana neutrinos (2024–2026)](https://arxiv.org/abs/2406.11438)
4. [Particle Data Group · Statistics (2025)](https://pdg.lbl.gov/2025/reviews/rpp2025-rev-statistics.pdf)
5. [Dvali, Maiezza, Senjanović & Tello · Neutrino mass versus new physics (2023)](https://arxiv.org/abs/2303.17261)
6. [Schechter & Valle · Neutrinoless double-beta decay in gauge theories (1982)](https://doi.org/10.1103/PhysRevD.25.2951)

First published 2026-10-11; last revised 2026-10-13. Original explanatory text and diagrams by Sandbox Physics. Illustrations are schematic; no experimental event records are reproduced here. This is an independent educational publication, not an official Nobel or experiment collaboration publication.

[← Previous: Dirac or Majorana: is the neutrino its own antiparticle?](https://sandboxphysics.com/stories/neutrinos/dirac-majorana-neutrino-nature/) [Next: Weigh neutrinos with the universe: what is assumed? →](https://sandboxphysics.com/stories/neutrinos/cosmology-neutrino-mass-inference/)

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