KamLAND-Zen 2024: Pushing the Inverted-Ordering Bound on Neutrinoless Double Beta Decay

If neutrinos are Majorana particles — their own antiparticles, in the sense that the neutrino field is identical to the antineutrino field — then a particular kind of nuclear decay should occur. Neutrinoless double beta decay ($0\nu \beta \beta$): a nucleus simultaneously emits two electrons, with no accompanying neutrinos. The total energy carried by the electrons would equal the nuclear Q-value (1-3 MeV depending on the isotope), unlike the familiar two-neutrino double beta decay which has a continuous electron spectrum.

The process violates lepton number by two units. It is forbidden in the Standard Model. It is allowed only if neutrinos have a Majorana mass term — meaning the two-component spinor field for the left-handed neutrino has mass coupling that mixes the field with its complex conjugate, in a way that does not distinguish particle from antiparticle.

The question of whether neutrinos are Majorana or Dirac is one of the deepest open questions in particle physics. It connects to the seesaw mechanism (the standard explanation for why neutrinos are so light), to leptogenesis (the standard explanation for the matter-antimatter asymmetry of the universe), and to the broader structure of beyond-Standard-Model physics. A direct detection of $0\nu \beta \beta$ would settle the question.

For three decades, experimental searches for $0\nu \beta \beta$ have been underway. The most sensitive approach uses isotopes that can undergo two-neutrino double beta decay (the Standard-Model-allowed background process) and looks for the rare neutrinoless mode at the spectrum’s endpoint. The leading isotopes are ${}^{76}$Ge (used by GERDA, MAJORANA, and now LEGEND), ${}^{136}$Xe (KamLAND-Zen, EXO-200, nEXO planned), ${}^{130}$Te (CUORE, SNO+), and a handful of others.

In 2024, the KamLAND-Zen collaboration published its most stringent limit yet. The half-life lower bound for ${}^{136}$Xe $0\nu \beta \beta$ has been pushed past $3.8\times 10^{26}$ years — corresponding to an upper bound on the effective Majorana neutrino mass of $⟨m_{\beta \beta }⟩<28$–$122$ meV (the range reflects nuclear matrix element uncertainties). For the first time, an experiment has begun to probe the inverted-ordering parameter space directly.

This post is about how the experiment works, what the result means, and what the next several years of running are expected to show.

Why xenon-136

${}^{136}$Xe has several properties that make it an ideal $0\nu \beta \beta$ target:

• Q-value of 2.458 MeV — high enough that the endpoint is well above most natural radioactive backgrounds (which are below 2.6 MeV with very few exceptions)
• Naturally abundant — about 8.9% of natural xenon, allowing economical isotopic enrichment to ~90% purity
• Two-neutrino double beta decay half-life of approximately $2\times 10^{21}$ years, which is the standard background process and is well-measured
• Noble gas — chemically inert, easy to purify, easy to load into liquid scintillators or operate as a TPC working medium

KamLAND-Zen uses a clever approach: the ${}^{136}$Xe is dissolved in liquid scintillator (specifically, isooctane and PPO at low concentration) inside a transparent nylon balloon, which is then suspended in the center of the much larger KamLAND scintillator volume. The xenon serves as both the source isotope and the active medium; the surrounding scintillator provides shielding and additional event reconstruction.

When a ${}^{136}$Xe nucleus undergoes double beta decay (with or without neutrinos), the two emitted electrons deposit their energy in the loaded scintillator and produce a localised burst of light. The total energy is reconstructed by the surrounding photomultiplier tubes (1,879 of them, around the original KamLAND detector). The two-neutrino events have a continuous energy spectrum extending up to $Q$ minus the neutrino energies; the neutrinoless events would appear as a sharp peak at $Q=2.458$ MeV.

Three phases of running

Phase 1 (KamLAND-Zen 400): Operated 2011-2015 with approximately 410 kg of ${}^{136}$Xe. Total exposure approximately 504 kg·yr. Reported half-life lower bound of $T_{1/2}>1.9\times 10^{25}$ years.

Phase 2 (KamLAND-Zen 800): Operated 2018-2024 with the xenon mass increased to approximately 745 kg. Total exposure of approximately 970 kg·yr. The inner balloon was redesigned to reduce backgrounds from the polymer material itself. Reported half-life lower bound of $T_{1/2}>2.3\times 10^{26}$ years (Phase 2 alone, 2022).

Combined Phase 1 + Phase 2 (2024 result): Reported half-life lower bound of $T_{1/2}>3.8\times 10^{26}$ years (90% C.L.), corresponding to: $⟨m_{\beta \beta }⟩<28-122\text{ meV}$ (the range reflects different nuclear-matrix-element calculations).

This represents the most stringent direct $0\nu \beta \beta$ bound from any isotope to date, comparable in sensitivity to GERDA’s ${}^{76}$Ge result and slightly tighter on the upper end of the matrix-element range.

What 28-122 meV means

The effective Majorana mass parameter, $⟨m_{\beta \beta }⟩$, is a coherent sum over the three neutrino mass eigenstates weighted by the leptonic mixing matrix elements: $⟨m_{\beta \beta }⟩=\left|{\sum }_i{U}_{ei}^2{m}_i\right|$

where $U_{ei}$ are the first-row elements of the PMNS matrix and $m_i$ are the absolute mass eigenvalues. The cancellations or constructive additions among the three terms depend on the unknown CP-violating phases.

If neutrinos are normal-ordered (m_1 < m_2 < m_3), the predicted $⟨m_{\beta \beta }⟩$ has a complex parameter-space structure. There is a “funnel” region where the three terms can cancel almost completely, allowing $⟨m_{\beta \beta }⟩$ to be effectively zero even with finite neutrino masses. This funnel is centered around $m_{\text{lightest}}\sim 5$ meV and is approximately 5-30 meV wide depending on phases.

If neutrinos are inverted-ordered (m_3 < m_1 < m_2), the funnel does not exist. The two heavier mass eigenstates carry most of the contribution to $⟨m_{\beta \beta }⟩$, and the prediction is bounded from below at approximately 15-50 meV (depending on the phases).

KamLAND-Zen’s 2024 bound — 28-122 meV upper limit — is just on the edge of the inverted-ordering parameter space. If the upper-end of the matrix-element range is correct (122 meV), the bound is well above all of inverted ordering. If the lower end (28 meV) is correct, the bound has begun to enter the inverted-ordering region.

The matrix-element uncertainty is the dominant source of ambiguity. Different theoretical calculations (interacting shell model, quasiparticle random phase approximation, self-consistent Green’s functions) give different values for the same nuclear isotope. The current spread is approximately a factor of 4. Improvement in matrix-element calculations is one of the field’s active research areas.

Implications

What KamLAND-Zen 2024 establishes:

• $0\nu \beta \beta$ does not occur at half-lives shorter than $3.8\times 10^{26}$ years for ${}^{136}$Xe. This excludes a significant region of Majorana-neutrino parameter space.
• The effective Majorana mass is below approximately 122 meV at the optimistic matrix-element extreme, or below 28 meV at the pessimistic extreme.
• The inverted-ordering parameter space has begun to be tested, but is not yet excluded.

What KamLAND-Zen 2024 does NOT establish:

• It does not detect $0\nu \beta \beta$. The experiment sees only the Standard-Model two-neutrino background, which is consistent with calculations.
• It does not exclude Majorana neutrinos with small effective masses (in the funnel region of normal ordering, or at the lower edge of inverted ordering).
• It does not exclude Dirac neutrinos.

The result is therefore a tightening of an existing bound rather than a discovery. But the bound is now close enough to interesting parameter space that the next several years of running could potentially detect $0\nu \beta \beta$ if it exists at the inverted-ordering rate.

What’s next

Several next-generation experiments are designed to probe the inverted-ordering parameter space and beyond:

KamLAND-Zen 800 continued running — the existing detector will continue accumulating exposure through the late 2020s. By 2027 the cumulative exposure should reach approximately 1500 kg·yr, pushing the half-life bound toward $5\times 10^{26}$ years.

LEGEND-200 at Gran Sasso uses 200 kg of enriched germanium-76 in a liquid-argon shielding tank. It is currently running and is expected to reach half-life sensitivity of approximately $10^{27}$ years — comparable to KamLAND-Zen — within the next 3-5 years.

LEGEND-1000 is the planned tonne-scale germanium successor. Approximately 1,000 kg of enriched ${}^{76}$Ge in liquid argon, with ultra-low background. Sensitivity goal of half-life $>10^{28}$ years, which would probe deep into the inverted-ordering parameter space and reach the upper edge of normal-ordering parameter space. Construction is in advanced design; first data expected late 2020s.

nEXO is the planned tonne-scale xenon successor. Approximately 5,000 kg of liquid xenon enriched to 90% in ${}^{136}$Xe, in a TPC configuration. Similar sensitivity to LEGEND-1000.

CUPID (CUORE Upgrade with Particle ID) — the next-generation tellurium-130 experiment at Gran Sasso, with bolometric scintillating crystals to discriminate background from signal at the event level.

By approximately 2032, all four next-generation experiments are expected to be running. Their combined sensitivity should cover most of the inverted-ordering parameter space. If $0\nu \beta \beta$ is discovered within the next decade, it will most likely be in this experimental round.

What if 0νββ is detected?

If $0\nu \beta \beta$ is observed, the implications are profound:

1. Lepton number is violated, contradicting the original Standard Model prediction of conserved lepton number.
2. Neutrinos are Majorana particles, with mass terms that mix the neutrino field with itself rather than with a separate right-handed partner.
3. The effective Majorana mass would be measured with precision determined by the nuclear matrix elements.
4. The seesaw mechanism becomes much more strongly motivated as the natural explanation for small neutrino masses.
5. Leptogenesis becomes a very strong candidate for the origin of the matter-antimatter asymmetry, as the same Majorana mass that drives $0\nu \beta \beta$ also drives the leptogenesis CP-violating decays.

A discovery of $0\nu \beta \beta$ would be the clearest beyond-Standard-Model signal in particle physics in decades, comparable to the original discovery of neutrino oscillation in terms of scope and impact.

What if 0νββ is not detected?

If next-generation experiments cover the inverted-ordering parameter space and find nothing, the implications are equally significant:

1. Inverted ordering is excluded as the neutrino mass hierarchy (or rather, the combination of inverted ordering plus Majorana character is excluded).
2. Either neutrinos are Dirac, or they are Majorana with normal ordering and a small effective Majorana mass that escapes detection in the funnel region.
3. Probing the normal-ordering funnel would require even more sensitive successor experiments — perhaps multi-tonne arrays operating for decades.

A null result would not close the question of Majorana versus Dirac, but it would significantly constrain the parameter space and force a longer-term experimental program.

A central frontier of neutrino physics

The $0\nu \beta \beta$ search is one of the highest-priority open questions in neutrino physics. Unlike the oscillation parameters (which are now mostly measured), the Majorana-versus-Dirac question is still completely open at the experimental level. KamLAND-Zen’s 2024 result is one entry in an active program with multiple experiments approaching the inverted-ordering boundary.

The next 5-10 years are likely to be decisive. Whether through a positive detection (with all the dramatic implications) or through a null result that closes the inverted-ordering window, the field will know substantially more about the fundamental nature of neutrinos by approximately 2032.

KamLAND-Zen has now done its part. The torch passes to LEGEND-1000, nEXO, CUPID, and the continuing KamLAND-Zen runs. The answer to one of particle physics’ deepest open questions may come within this decade.

Whatever the outcome, the result will reshape the field. Majorana neutrinos in inverted ordering with appreciable effective mass would be a discovery. Their absence would force us to reconsider the structure of beyond-Standard-Model physics. Either way, the bounds we have today — set by KamLAND-Zen and the previous generation of experiments — are the foundation on which the coming era of measurements is being built.