LEGEND: The Germanium Road to Neutrinoless Double Beta Decay

Neutrinoless double beta decay, $0\nu \beta \beta$, would establish that neutrinos are their own antiparticles — Majorana fermions — and constrain the absolute neutrino mass scale through the effective Majorana mass $|m_{\beta \beta }|$. It is the most direct laboratory test of Majorana nature available, and the discovery would rank among the most important results in particle physics. The decade-long parallel campaigns of multiple experiments — KamLAND-Zen, CUORE, EXO-200/nEXO, the Majorana Demonstrator, GERDA — have steadily pushed the sensitivity downward, and the next-generation efforts now in construction are designed to either find the signal or push the limits well into the inverted-mass-ordering parameter space.

This post is about the germanium semiconductor branch of the program. The story runs from the Heidelberg-Moscow and IGEX experiments of the 1990s through the GERDA and Majorana Demonstrator experiments of the 2010s, and into the present generation: LEGEND-200, which began taking data in 2023 at Gran Sasso, and the planned LEGEND-1000, designed for a half-life sensitivity around $10^{28}$ years. The germanium approach offers a combination of features that no other technology delivers — semiconductor-grade energy resolution, the source coincident with the detector, and a path to extreme low backgrounds through active liquid-argon vetoing.

Why germanium

Germanium-76 has properties that make it well-suited to $0\nu \beta \beta$ search.

It undergoes the two-neutrino double beta decay $2\nu \beta \beta$ with a half-life of about $2\times 10^{21}$ years — long enough that backgrounds from the normal mode are manageable but short enough that the source has been calibrated by direct measurement. The $0\nu \beta \beta$ Q-value sits at 2,039 keV, in a relatively clean part of the natural radioactivity spectrum and above most beta decay endpoints.

The isotope can be enriched from its natural 7.8 per cent abundance to over 87 per cent through gas centrifugation of germanium tetrafluoride. The enriched material can then be reduced to elemental germanium and grown into the high-purity single crystals that semiconductor manufacturing routinely produces.

Crucially, germanium is a semiconductor, and high-purity germanium crystals can be operated as solid-state detectors. A charged particle traversing the crystal creates electron-hole pairs at the rate of one pair per 2.96 eV of deposited energy — sixteen orders of magnitude better statistics than the few-photon counting of optical detectors at MeV scales. The resulting energy resolution is around 0.1 per cent at the Q-value, comparable to atomic clocks for relative precision.

The crystal serves as both the source and the detector. Every $0\nu \beta \beta$ candidate event happens inside the active volume, and the energy deposited by the two emitted electrons is recorded directly. There is no need to separate source and detector, no need to deconvolve loss factors for energy escaping into surroundings.

The GERDA legacy

The Germanium Detector Array (GERDA) at Gran Sasso operated from 2011 to 2019 and established the technique that LEGEND continues to develop. Its central innovation was to operate the germanium crystals immersed directly in a 64-cubic-meter tank of liquid argon, dispensing with the traditional copper cryostat. The argon serves two purposes: it cools the crystals to their operating temperature of 90 K, and it functions as an active scintillation veto for events that deposit energy in both the crystal and the surrounding argon — a powerful background discrimination tool.

GERDA’s Phase II configuration deployed 40 kg of enriched germanium and operated continuously for years with background levels around $5\times 10^{-4}$ counts per (kg keV year) in the signal region. This was the lowest background ever achieved in $0\nu \beta \beta$ search, and it pushed the half-life limit to $T_{1/2}^{0\nu }>1.8\times 10^{26}$ years at 90% confidence — a world-leading result that translated into an effective Majorana mass bound around 79-180 meV depending on the nuclear matrix element used.

GERDA’s final analyses also demonstrated background-free operation in the signal region: across the entire Phase II dataset, zero events fell within the 240 keV-wide region of interest after all cuts. Achieving this is essentially the definitional goal of a discovery-class $0\nu \beta \beta$ experiment, because any single event in the signal region would already constitute a candidate.

Majorana Demonstrator

In parallel, the Majorana Demonstrator at the Sanford Underground Research Facility in South Dakota operated 30 kg of enriched germanium between 2015 and 2021. Its complementary approach used a more conventional cryostat with no active argon shield but extreme attention to material radiopurity in the cryostat components themselves. The result was background levels around $4\times 10^{-3}$ counts per (kg keV year) — higher than GERDA’s but achieved with a different technology demonstrating that the conventional copper-cryostat approach was also viable.

Together GERDA and Majorana validated both the active-veto and the passive-shielding approaches to germanium $0\nu \beta \beta$, providing two parallel paths into LEGEND.

LEGEND-200

LEGEND-200 is the merger of the GERDA and Majorana traditions into a single experiment operating at Gran Sasso. It deploys 200 kg of enriched germanium — 40 kg from GERDA’s Phase II detectors, plus newly grown crystals — within an upgraded version of GERDA’s liquid-argon cryostat system. Data-taking began in 2023.

The technical advances over GERDA Phase II are several. The detector array uses a new generation of inverted coaxial point contact (ICPC) germanium crystals, which have larger individual masses (about 2 kg each versus 0.5 kg for GERDA’s BEGe detectors) while retaining excellent energy resolution and pulse-shape discrimination. Fewer crystals are needed to reach the target mass, reducing the surface-to-volume ratio and the corresponding surface-related backgrounds.

The liquid argon system is also upgraded with better instrumentation for the scintillation veto and an improved circulation system that maintains argon purity over multi-year operation. The active veto identifies events depositing energy in both the crystal and the surrounding argon, with the inverse-coaxial geometry giving better discrimination between fully-contained and edge events.

The projected sensitivity is a half-life lower limit of about $10^{27}$ years after 5 years of operation — roughly an order of magnitude beyond GERDA’s Phase II result, corresponding to an effective Majorana mass sensitivity around 30-80 meV. This crosses below the cosmologically-allowed degenerate-mass region and starts to probe the inverted-mass-ordering parameter space.

LEGEND-1000

LEGEND-1000 is the next-generation experiment in advanced design, aiming at 1,000 kg of enriched germanium and a half-life sensitivity of $10^{28}$ years. The design is essentially a scaled-up LEGEND-200 with several modifications.

Site selection is between Gran Sasso (LEGEND-200’s current home) and SNOLAB in Canada. SNOLAB offers significantly less muon-induced background from its deeper overburden, while Gran Sasso has the existing infrastructure of LEGEND-200. The choice affects projected background levels by a factor of two or so.

The crystal complement of LEGEND-1000 would deploy roughly 400 ICPC crystals — five times the LEGEND-200 count. Crystal production is the bottleneck for the schedule, as the enrichment process is slow and the crystal growth requires specialised facilities.

The target sensitivity at $10^{28}$ years corresponds to an effective Majorana mass below 15 meV — the lower bound of the inverted-mass-ordering region. A null result at this level, combined with cosmological mass constraints, would essentially rule out the inverted ordering as a Majorana-driven scenario and would either force the normal ordering or place strong constraints on the underlying $0\nu \beta \beta$ mechanism.

If $0\nu \beta \beta$ is detected at this level — by LEGEND-1000 or any of its competitors — the implications would be transformative: Majorana nature confirmed, the absolute mass scale measured, lepton number violation established at low energies, and the seesaw mechanism receiving its first direct experimental support.

Where LEGEND fits in the field

Three major isotope-detector combinations dominate the next-generation 0νββ program:

• Germanium-76 with semiconductor crystals: LEGEND-200, LEGEND-1000. Strengths: 0.1% energy resolution, source-equals-detector, background-free operation demonstrated.
• Xenon-136 in liquid scintillator: KamLAND-Zen. Strengths: very large isotope mass, KamLAND’s existing infrastructure, clean low-background environment.
• Xenon-136 in liquid xenon TPC: nEXO. Strengths: 5-tonne isotope mass, 3D event reconstruction, dual signature from ionisation and scintillation.

A fourth approach, tellurium-130 in cryogenic bolometers, is pursued by CUORE and the proposed CUPID experiments. CUORE has operated at LNGS since 2017; CUPID adds light readout to discriminate alpha-particle backgrounds.

The three or four approaches probe overlapping but distinct parameter regions, with different dominant systematics. LEGEND’s strength is energy resolution and background suppression; nEXO’s is fiducial mass and 3D reconstruction; KamLAND-Zen’s is isotope mass scale. A coherent picture of any positive signal — or a coherent null at the next generation — would benefit from observation in more than one isotope, because the nuclear matrix elements that convert the measured half-life into the effective Majorana mass are independent in each isotope and provide cross-checks on the underlying physics.

The discovery scenario

If LEGEND-1000 detects a signal at the inverted-mass-ordering boundary around $|m_{\beta \beta }|\sim 15$ meV, the implications cascade widely.

The detection would establish that neutrinos are Majorana fermions, confirming the simplest realisation of the seesaw mechanism and showing that lepton number is broken at low energies.

The measured effective mass, combined with cosmological constraints on the mass sum and with the kinematic mass bound from KATRIN, would pin down the absolute neutrino mass scale and the ordering simultaneously.

The result would dramatically tighten the constraints on the underlying seesaw scale: a $|m_{\beta \beta }|\sim 15$ meV signal would be consistent with the high-scale seesaw and disfavoured for low-scale variants in their simplest forms.

A null result at the same sensitivity, by contrast, would essentially force the normal ordering as the Majorana scenario and would require either Dirac neutrinos or strong cancellations in the effective Majorana mass for the inverted ordering case.

Either outcome is transformative. This is why three or four parallel programmes are pursuing the same goal with different technologies: the question is too important for any single result to be the last word.

Summary

LEGEND is the next-generation germanium-semiconductor search for neutrinoless double beta decay, building directly on the GERDA and Majorana Demonstrator experiments. LEGEND-200, operating at Gran Sasso since 2023 with 200 kg of enriched germanium-76 immersed in active liquid argon, aims at a half-life sensitivity of $10^{27}$ years and an effective Majorana mass bound around 30-80 meV. LEGEND-1000, in advanced design, will scale to 1,000 kg of isotope and target $10^{28}$ years half-life sensitivity, reaching the inverted-mass-ordering boundary at $|m_{\beta \beta }|\sim 15$ meV. The germanium approach exploits the unique combination of semiconductor energy resolution (0.1% at Q-value), source-equals-detector geometry, and active liquid-argon vetoing to achieve essentially background-free operation in the signal region. Together with the xenon-based approaches of KamLAND-Zen and nEXO, and the tellurium-based CUORE/CUPID program, LEGEND defines one of three parallel paths into the inverted-mass-ordering parameter space — and into the answer to whether neutrinos are their own antiparticles.