The neutrino mass mystery: a floor, a ceiling and three suspects

Experiments on Earth set a minimum weight for the neutrino, a ghostly particle that passes through almost everything. Maps of the universe set a maximum. The minimum comes from detectors, many underground, that watch neutrinos change identity as they travel [Reference 1]. The maximum combines two pictures of the cosmos: a map of more than 14 million galaxies and quasars (the blazing cores of distant galaxies), made by the Dark Energy Spectroscopic Instrument (DESI), which splits each galaxy’s light to gauge its distance, and the oldest light in the universe, the cosmic microwave background [Reference 2,Reference 3].

For years the maximum sat comfortably above the minimum, then crept down toward it [Reference 3]. As of October 2026 the two are pressed against each other, though the newest measurements disagree on exactly how hard. The oscillation experiments say the masses of the three neutrinos, added together, must be at least 0.059 electronvolts (eV), an energy unit that, thanks to E = mc², physicists also use for mass [Reference 3]. That is about 1.05 × 10⁻³⁷ kilograms, nearly nine million times lighter than a single electron [Reference 4,Reference 5]. The galaxy map combined with the microwave background, read in the standard way, says the total is less than 0.064 eV. A second, equally respectable statistical reading of the same data says less than 0.053 eV, below the minimum [Reference 3].

So is somebody lying? Almost certainly not. Each measurement rests on different assumptions, and the real question is which assumption is wrong. Physicists have three main suspects. When the math is allowed to go below zero, the data’s preferred value sits about three standard deviations (σ) below the minimum. Standard deviations count how far a result sits from what was expected, in units of its typical random wobble; physicists usually want five before claiming a discovery [Reference 6]. This one rests on a single data combination, and its size ranges from about two to four depending on the statistical method, so we rate it a hint.

Three ways to weigh a ghost

Neutrinos are electrically neutral cousins of the electron. They come in three types, or “flavors,” named after the electron and its two heavier, short-lived cousins, the muon and the tau [Reference 1,Reference 7]. They are the most abundant particles with mass in the universe, and at least a million times lighter than any other particle of matter [Reference 7]. The Standard Model of particle physics, the theory that describes all the known particles, originally treated them as massless [Reference 1].

That changed with neutrino oscillation: a neutrino created as one flavor can be detected later as another. Each flavor is a different mix of the same three ingredients, called “mass states,” each with one definite mass, and the mix drifts as the states travel slightly out of step, like two tuning forks at slightly different pitches beating against each other. If the masses were equal, there would be no drift; and because both measured gaps (below) are non-zero, at most one of the three can be massless [Reference 1]. The three masses in this story are those of the ingredients; an electron neutrino has no single mass of its own. Oscillations have been seen with neutrinos from the Sun, the atmosphere, nuclear reactors and accelerators, and the discovery won the 2015 Nobel Prize in Physics [Reference 1,Reference 8,Reference 9].

Oscillations measure gaps, not weights. The rate of flavor change depends on the differences between the squares of the masses. It is like knowing the spacing between three rungs of a ladder without knowing how high the bottom rung is [Reference 10]. Two gaps between the squared masses are measured, one about 34 times bigger than the other [Reference 10].

A laboratory scale measures one blurred mass. The KATRIN experiment in Karlsruhe, Germany, watches tritium, a radioactive form of hydrogen, turn into helium while giving off an electron and an antineutrino (the antimatter twin of a neutrino). These two share a fixed energy budget, and the antineutrino’s mass slightly distorts the electron energies near the top end [Reference 7]. KATRIN found that an effective, weighted mass is below 0.45 eV, at 90% confidence: data like KATRIN’s would rarely arise if the true value were higher [Reference 7]. If the lightest neutrino were that heavy, the gaps would hardly matter and the three masses would be nearly equal, totaling about 1.35 eV, more than 20 times the minimum set by oscillations. KATRIN’s result assumes nothing about the universe.

Cosmology weighs the sum, through gravity. The Big Bang left about 340 relic neutrinos and antineutrinos in every cubic centimeter of space [Reference 11]. Their mass adds to the matter in the universe and changes how fast it expands and how matter clumps [Reference 11]. Cosmology measures only the total mass, and only inside a model of the universe, which is where the trouble starts.

The floor

Even without knowing the lightest neutrino’s weight, the two gaps set a minimum: make the lightest weigh nothing at all, and the other two must still be heavy enough to produce the gaps.

There are two ways the masses could be arranged, and nobody yet knows which one nature chose. This is called the neutrino mass ordering. In the “normal” ordering, two mass states are light and close together and the third is much heavier. In the “inverted” ordering, two are heavy and close together and the third is much lighter [Reference 1].

With the lightest set to zero, the normal ordering gives masses of about 0, 0.0087 and 0.050 eV, adding up to 0.0588 eV. The inverted ordering gives about 0, 0.049 and 0.050 eV, adding up to 0.0989 eV [Reference 10,Reference 3].

The floor is solid. It rests on decades of measurements by many experiments, combined in a “global fit,” one joint analysis of all their data [Reference 10]. A new reactor experiment in China, JUNO, started taking data after its completion in August 2025 and within months measured the small gap 1.6 times more precisely than all previous experiments combined [Reference 12]. A 2026 global fit that includes JUNO’s first data leaves the floor unchanged at the precision quoted here [Reference 13].

The ordering is still open. Before JUNO, the global fit favored the normal ordering only mildly, and only with data from one large Japanese detector, Super-Kamiokande [Reference 10]. An exploratory 2026 global fit adding JUNO’s first data favors it with or without those data [Reference 13], and JUNO’s own September 2026 preprint, not yet peer reviewed, finds a one-sided preference of at least 2.1 standard deviations when combined with accelerator experiments [Reference 14].

The ceiling

At the floor, neutrinos make up only about half a percent of all the matter in the universe [Reference 11]. That is small, but it leaves two fingerprints.

The first is in how the universe expands. Mass adds gravity and changes the expansion history, which changes the distances to faraway galaxies. DESI measures those distances with a natural ruler called baryon acoustic oscillations. In the young universe, before atoms formed, ordinary matter and light made a hot, dense soup in which pressure waves rippled outward. When atoms formed and light broke free, the waves froze, leaving a slight preference for galaxies to sit about 150 megaparsecs apart, nearly 500 million light-years [Reference 2,Reference 15]. How big that ruler looks at different distances tells you how the universe has expanded.

The second fingerprint is in how matter clumps. Neutrinos move so fast that they don’t settle into clumps, so their share of the matter doesn’t help pull galaxies and clusters together, and growth is slightly slower [Reference 16,Reference 11]. That shows up in the faint bending of the cosmic microwave background (CMB), the oldest light in the universe, whose pattern of slightly hotter and colder spots gets distorted by all the matter it passes on its way to us, an effect called CMB lensing [Reference 3,Reference 17]. Heavier neutrinos mean a smoother universe, and a smoother universe bends the CMB light less.

The CMB is mapped by the Planck satellite and by the Atacama Cosmology Telescope (ACT) and South Pole Telescope (SPT). On its own, the CMB is only weakly sensitive to neutrino mass, because changing the mass can be offset by changing the amount of matter or the expansion rate. Adding DESI’s distances breaks that ambiguity [Reference 3].

All of this is done within the standard model of cosmology, called ΛCDM (“lambda-C-D-M”). It has ordinary matter, cold dark matter (invisible, slow-moving matter) and dark energy, the unknown cause of the accelerating expansion, in the form of a cosmological constant, labeled Λ, whose strength never changes [Reference 2]. The limits only hold inside that model.

In 2018, Planck plus earlier galaxy maps limited the sum to less than 0.12 eV, with 95% confidence [Reference 18]. In 2025, DESI’s second data release, covering three years of observations and combined with the CMB, brought that down to 0.064 eV, below the inverted-ordering floor and only 0.005 eV above the normal-ordering floor [Reference 3].

Where the floor meets the ceiling

What a “negative mass” really means

What can it mean that the data “prefer negative mass”?

A cosmological analysis asks, for each possible total mass, how well the model fits all the data. Normally only masses of zero or more are allowed. For DESI’s data, the fit keeps improving as the mass goes down, all the way to zero, where the allowed range stops [Reference 3]. Picture a hill of “how well it fits”: we see only its right-hand slope, and its top lies hidden below zero [Reference 3,Reference 2].

That is why there are two ceilings. Imagine a bathroom scale that reads slightly below zero with a feather on it. “How heavy is the feather probably?” and “Which weights would rarely give a reading this low?” have different answers. The 0.064 eV figure comes from a Bayesian analysis, which treats every total between 0 and 5 eV as equally plausible beforehand and asks the first kind of question. The 0.053 eV figure comes from a frequentist analysis, which asks the second; its Feldman–Cousins recipe is built for results next to a boundary like zero [Reference 3,Reference 23]. When the data lean below zero, the second question rules out more masses, so its ceiling is lower.

To see where the data would like to be, cosmologists use an effective neutrino mass: a mathematical stand-in that copies everything a real neutrino mass does to the expansion and the clumping, but can continue below zero [Reference 24]. Real neutrino mass would make the CMB slightly less bent. The combined data show a slightly different expansion history and slightly more bending (Planck’s especially) than the standard cosmology gives even with massless neutrinos, as if the neutrinos weighed less than nothing [Reference 3,Reference 11,Reference 18].

With DESI’s second data release plus the CMB, this effective mass comes out at −0.101 eV, give or take about 0.05 eV [Reference 3]. On our reading, it sits lower than the −0.04 eV top of the hill partly because it lets every effect of mass go negative instead of extending a curve fitted above zero. In this Bayesian analysis only about 0.3% of the probability lies above the normal-ordering floor, which DESI expresses as 3.0 standard deviations; other ways of measuring the same mismatch give 2.7 to 4.0 [Reference 3]. This fits with a 0.064 eV ceiling just above the floor: when negative values are forbidden, all the probability is squeezed between zero and the ceiling; once they are allowed, most of it moves below zero. A frequentist look is milder: on our reading of DESI’s published fit curve, the floor is about two standard deviations from the best fit [Reference 3]. That matches the frequentist ceiling: a 95% limit falling just under the floor means the floor is disfavored at roughly the two-standard-deviation level. The 3.0 comes from the effective-mass analysis, whose center lies lower.

DESI is explicit about how to read this: negative values signal unidentified errors, or new physics that may have nothing to do with neutrinos, not neutrinos with literally negative mass [Reference 3].

Suspect 1: a fluke or a hidden error

Perhaps nothing new is going on; DESI stresses that the statistical significance “is by no means conclusive” [Reference 3].

On its own side, DESI says removing the mismatch would need an unknown error of more than 1% in its distance measurements, well above every known source of error [Reference 3].

On the CMB side there are two candidates. One is a long-standing oddity in Planck’s maps: they look slightly more blurred by gravitational bending than the standard cosmology predicts. Extra blurring mimics extra clumping, the opposite of what neutrino mass does [Reference 3,Reference 18]. The other is the optical depth: think of a thin fog of free electrons, released when the young universe’s atoms were split again into electrons and charged nuclei (ionized, as the hot soup had been before atoms formed), that scattered some CMB light [Reference 25]. Planck measures it as 0.054 ± 0.007, meaning roughly 5% of the light was scattered [Reference 18]. The fog dims the CMB’s pattern of hot and cold spots. If the fog is thicker, the pattern must have started out stronger, which predicts more clumping and more bending than we actually see; heavier neutrinos can then smooth some of it away and still match the measurement [Reference 3].

Fixing the optical depth at 0.067 or 0.074, two to three times Planck’s error bar above its value, shrinks the mismatch to 2.3 or 1.7 standard deviations but doesn’t remove it [Reference 3]. Outside teams mostly blame the CMB side but disagree on which part [Reference 26,Reference 27,Reference 28]. In a 2026 preprint, not yet peer reviewed, one team argued that an optical depth of 0.11, eight times Planck’s error bar above its value and requiring Planck’s own measurement to be set aside, would bring the CMB’s expansion rate into line with DESI’s and give a tentative positive total of about 0.10 eV [Reference 29].

Earlier in 2026, a peer-reviewed combination led by SPT, with ACT, Planck and DESI, put the ceiling at 0.055 eV, below the floor [Reference 20]. The newest result pushes it back up. In August 2026, the SPT collaboration reported, in a preprint not yet peer reviewed, a new measurement of the CMB’s bending that agrees better with DESI; combined with other CMB data and DESI, it gives 0.072 eV. Most of the rise comes from the new map, a little from a different treatment of the optical depth [Reference 22].

Suspect 2: dark energy that changes

The second suspect is dark energy, which ΛCDM treats as constant. DESI’s data combined with the CMB prefer a dark energy whose behavior changes over time, at 3.1 standard deviations. Adding measurements of exploding stars called supernovae, used as distance markers, gave 2.8 to 4.2 depending on the catalog [Reference 2]. Recalibrations have since pulled the catalogs together: a 2026 preprint, not yet peer reviewed, finds 3.2 to 3.4 for all three in DESI’s setup [Reference 30]; the Dark Energy Survey’s own recalibration finds 3.2 using more CMB data [Reference 31]. This is another hint, not a discovery.

Dark energy and neutrino mass both shape the expansion history, so they can partly stand in for each other. If dark energy is allowed to change, DESI plus the CMB give a ceiling of 0.163 eV, comfortably above both floors, and the effective neutrino mass moves to zero, with an uncertainty of about 0.1 eV, wide enough to reach both floors [Reference 3]. The two puzzles may be one: a negative effective mass and some kinds of changing dark energy both break a rule that ordinary matter and energy obey, so DESI suggests they might share a cause [Reference 3,Reference 24]; another team thinks the two are likely separate [Reference 26].

It is not an automatic fix. A simpler variant, in which dark energy thins out or builds up at one steady pace instead of changing its behavior partway through cosmic history, does not help: with supernovae it gives 0.059–0.065 eV, tighter than ΛCDM with the same supernovae, and without them it loosens the limit only to 0.085 eV [Reference 3]. Even the changing kind, once supernova data are added, leaves less room: 0.117–0.139 eV, still above both floors [Reference 3]. In a 2026 preprint, not yet peer reviewed, researchers comparing many dark-energy models found that, with supernovae included, only very specific histories bring back a positive neutrino mass [Reference 32].

Suspect 3: neutrinos that vanish

The third suspect is the neutrinos themselves. Cosmology assumes relic neutrinos are stable. What if they aren’t?

Suppose neutrinos decay over cosmic time into new particles that have no mass and that no detector can see. Their mass energy would be carried off by those fast-moving particles, whose energy thins out faster as space expands, so their gravitational fingerprint would fade and cosmology would underestimate how much they weigh [Reference 16]. In a study posted in January 2026 and published in Physical Review D in June, physicist Guillermo Franco Abellán tested this with DESI and Planck data. With lifetimes of roughly 10 million to 1 billion years, the ceiling rises from 0.062 eV for stable neutrinos to 0.23 eV, at 95% confidence, removing the conflict for both orderings. (His stable value differs slightly from DESI’s 0.064 eV because he uses an older Planck dataset.) [Reference 16]

The caveats matter. The decay must be into new particles: if heavier neutrinos decay into lighter known ones, the limit barely moves or even tightens, because the mass stays in neutrinos that cosmology still weighs [Reference 16]. With newer CMB data the relaxed limit is 0.19 eV. Allowing decays improves the fit only marginally, and the data still fit best with zero mass [Reference 16]. Other proposals, such as neutrinos that cool or change mass over time, likewise lack independent evidence [Reference 25].

Pick your universe

Choose an ordering and a weight for the lightest neutrino, and see where the total lands against each published ceiling.

With the normal ordering and a massless lightest neutrino, the total (0.0588 eV) passes DESI’s Bayesian ceiling but fails its frequentist one, SPT’s published 0.055 eV and a 0.052 eV preprint limit [Reference 21] (SPT’s 0.072 eV preprint would let it through). The inverted ordering lies above every 2025–2026 ΛCDM ceiling, so it is disfavored (odds of roughly 6–10 to 1 in DESI’s analysis) but fits under the dark-energy and decay ceilings [Reference 3].

What happens next

By April 2026, DESI had finished its planned five-year survey, ahead of schedule, with more than 47 million galaxies and quasars. Its first full-survey dark-energy results are expected in 2027, and it will keep observing through 2028 [Reference 33]. Before the survey began, DESI forecast a final sensitivity of about 0.02 eV, which DESI says could allow a significant detection [Reference 3]; because the data already lean below zero, the real test is whether that lean persists. The European Space Agency’s Euclid telescope will release its first large dataset in November 2026, with the measurements of clumping most relevant here following in mid-2027 [Reference 34]. A planned American CMB project, CMB-S4, will not happen: the US Department of Energy and National Science Foundation ended support in July 2025 [Reference 35].

On the lab side, KATRIN reached its planned 1,000 days of data in October 2025 [Reference 36], aiming for a final sensitivity better than 0.3 eV [Reference 7]; as of October 2026 we found no published result from the full dataset.

If ΛCDM is right and neutrinos are ordinary, the Particle Data Group, which publishes the standard reference reviews of particle physics, expects galaxy surveys such as Euclid, combined with new CMB experiments such as the Simons Observatory and LiteBIRD, to detect the total mass, even at the floor, at a significance of at least 3–4 standard deviations [Reference 11]. If DESI’s 2027 data still put the peak below zero, a fluke in DESI’s own data becomes less likely (although the new data include the old), but CMB-side explanations would need new CMB measurements to test; one study expects the below-zero preference to persist [Reference 26].

Open questions

• Is the ceiling real? It depends on how the CMB data are analyzed and which datasets are combined; ΛCDM ceilings from DESI plus CMB data currently range from roughly 0.05 to 0.08 eV [Reference 3,Reference 22,Reference 21].
• What is the optical depth? A higher value would ease the mismatch, but Planck measures 0.054 ± 0.007 [Reference 18]. A 2025 measurement by the CLASS telescope, which calls it the first ground-based attempt, agrees with Planck but is far less precise and not fully independent, since it cross-correlates with Planck’s maps [Reference 37]. A new CMB experiment, LiteBIRD, targets the very large-scale polarization of the CMB (the direction in which its light waves vibrate) that sets this number [Reference 29,Reference 11].
• Which ordering? Cosmology inside ΛCDM, the 2026 global oscillation fit and JUNO’s preprint all lean normal, but none is decisive [Reference 3,Reference 13,Reference 14].
• Do neutrinos decay? Invisible decays fit the data, but nothing else supports them yet [Reference 16].

Five Sigma, “The neutrino mass mystery: a floor, a ceiling and three suspects,” Five Sigma (12 October 2026), https://thefivesigma.com/articles/neutrino-mass-mystery. Version of 12 October 2026.