Kinematic measurements are closing in on the neutrino mass

The standard model of particle physics has an admirable track record. It accurately describes how, beneath the familiar world of protons, neutrons, electrons, and photons, there lurks a hidden zoo of quarks and gluons, leptons and gauge bosons. It even predicted the existence and behavior of previously unknown particles—the top quark and Higgs boson—decades before they were experimentally observed.

But the model is not perfect. It’s frustratingly silent on many questions, including why particles’ masses and interaction strengths are what they are. It sits in awkward tension with some observations, such as the fact that the universe contains much more matter than antimatter.

And sometimes its predictions are wrong. The model suggests that neutrinos should have zero mass. But we know they do not.

Figure 1.

It’s reasonable to think that at least some of the standard model’s weaknesses may be connected, and that poking at one of the chinks in the model’s armor could yield the insight needed to build a more complete and comprehensive theory of the universe. Toward that end, researchers working on the KATRIN (Karlsruhe Tritium Neutrino) experiment in Germany—part of the apparatus of which is shown in figure 1—have been chipping away at the range of possible masses for the electron neutrino by carefully analyzing the energy spectrum of electrons emitted in beta decay.

The latest KATRIN result, based on a quarter of the data that the experiment will ultimately collect, still provides only an upper bound on the neutrino mass. But that bound has been slashed nearly in half, from 0.8 eV in the previous analysis, ¹ released three years ago, to 0.45 eV in the current one. ²

Other methods of probing the neutrino mass have, at least ostensibly, generated more stringent bounds. But they rely on theoretical assumptions that might not be correct. KATRIN’s kinematic approach, in contrast, assumes nothing beyond the conservation of energy and momentum.

Flavor change

The kinematics of beta decay—in which a neutron emits an electron and transforms into a proton—are what led researchers to learn that neutrinos exist in the first place. If the electron and proton were the only products of the decay, experimental observations would be inconsistent with the law of conservation of energy: The energy imparted to the proton and electron is not always the same, whereas the energy released in the decay should be.

The discrepancy led Wolfgang Pauli to propose in 1930 that beta decay also produced a third, undetected particle that carried the rest of the kinetic energy. The prediction was confirmed in the 1950s by the first direct detection of neutrinos, which was finally honored with a Nobel Prize in 1995 (see Physics Today, December 1995, page 17 ).

According to kinematic analyses of the energy and momentum released in beta decay, the neutrino mass was (and still is) indistinguishable from zero: Its momentum is directly proportional to its kinetic energy, as expected for a massless particle traveling at the speed of light. But the mass must be nonzero because neutrinos undergo the unusual phenomenon of flavor oscillation.

Neutrinos come in three flavors that correspond to the three types of charged lepton: electron, muon, and tau. The particle reactions that create and consume neutrinos all conserve lepton family number. For example, beta decays, which produce electrons, also produce electron antineutrinos. And in the Sun and other stars, nuclear fusion reactions, which convert some protons into neutrons and consume electrons in the process, produce vast numbers of electron neutrinos.

But by the time solar neutrinos reach Earth, they’re not all electron neutrinos anymore: Some have transformed into muon neutrinos or tau neutrinos. Figuring out that that was what was going on—and that there was nothing wrong with models of the Sun or with neutrino-detection experiments—was a multidecade quest that culminated in a 2015 Nobel Prize (see Physics Today, December 2015, page 16 ).

Flavor oscillation is not like other particle transformations. It’s not the result of any of the four fundamental forces; rather, it’s due to the nature of neutrino states. Each flavor state—electron, muon, and tau—is a superposition of three mass states, m₁, m₂, and m₃. As a neutrino propagates through space, the relative phases in the superposition change, which introduces a probability that the neutrino can be detected as a different flavor. Because flavor oscillation requires that the masses all be different, at least two of them must be nonzero.

Measuring mass

Flavor-oscillation measurements reveal relationships between the three masses—specifically, the differences between their squares—but not their absolute values. If m₁ = 0, then m₂ is about 0.01 eV and m₃ is about 0.05 eV. But m₁ could be considerably larger than that, in which case the other masses are significantly larger too.

That’s where KATRIN, which started collecting data in 2019, comes in. In a return to the roots of neutrino physics, the KATRIN researchers strive to learn something about neutrino masses from the distribution of kinetic energies produced when tritium decays into helium-3. The neutrino, which always goes undetected, carries some amount of kinetic energy. Of the rest, the vast majority is carried by the electron, with a small fraction taken by the much heavier ³He nucleus.

The principle of the experiment is illustrated in figure 2. (See also Physics Today, August 2017, page 26 .) If the electron neutrino had no mass, the measured energy distribution would look like the blue curve in the plot, with the maximum kinetic energy exactly equal to the energy released in the beta decay. But because the neutrino does have mass, the distribution must look something like the red curve, with the maximum kinetic energy falling short of the total decay energy.

The analysis, however, is not quite that simple. The blue curve is hypothetical, not something that can actually be measured. So the researchers can’t derive the neutrino mass from the width of the gray shaded region because there’s no gray shaded region to observe. Instead, they aim to infer the mass from the curve’s shape: elongated and concave up for zero mass, or slightly snub and concave down for nonzero mass.

Collecting enough data to make that inference is no easy feat. The researchers are reliant on the rare beta decays—fewer than one in a trillion—in which almost all the decay energy is carried by the electron and almost none by the neutrino, and they must catch those rare energetic electrons and measure their energies precisely. And they need to avoid sources of background, such as stray electrons and spurious detector signals, that skew the shape of the observed curve and garble the mass measurement.

Some garbling, however, is inevitable. When the researchers fitted their data for the square of the electron neutrino mass, they got a negative number—a physical and mathematical impossibility but reflective of the fact that, due to background events, the observed energy curve was actually even more elongated than would be expected in the zero-mass case.

The question then becomes: How large can the neutrino mass be and still be consistent with the KATRIN data? Pinning down an answer was a painstaking and time-consuming quest to understand all the sources of background and how they affect the observations. The analysis took years—the new paper, submitted in 2024 and published in 2025, includes data only through 2021. “We need to be very cautious,” says Alexey Lokhov of the Karlsruhe Institute of Technology, “because we’re entering a region of parameter space that no one has measured directly and no one will be able to cross-check for a couple of years at least.” In the end, the researchers concluded at the 90% confidence level that the electron neutrino mass must be less than 0.45 eV.

Not like the other particles

What does it mean that the electron neutrino mass—really, the weighted average of m₁, m₂, and m₃ that creates the electron neutrino flavor state—is less than 0.45 eV? The specific implications are not yet clear, but the first striking feature is how anomalously small the mass is.

Figure 2.

The typical mass scale in particle physics is the gigaelectron volt, or 1 billion eV. Protons and neutrons each weigh in at about 1 GeV, and the Higgs boson at 125 GeV. Even the electron, the next lightest particle after the neutrinos, has a mass of 0.5 MeV—more than a million times that of the neutrino. In other words, the KATRIN researchers point out, the electron neutrino is to the electron as a 1 kg bag of sugar is to five blue whales.

The mass imbalance between neutrinos and other particles has been known for years, even before KATRIN provided any constraints on the specifics. It could have to do with the mechanism or mechanisms that endow particles with their mass. Most particles get their mass through coupling to the Higgs field (see Physics Today, September 2012, page 12 and page 14 ). But the standard model says that the Higgs field shouldn’t couple to neutrinos—which is why it says that neutrino masses should be zero.

Could neutrinos acquire their mass from some other mechanism, and if so, what? The answers are necessarily speculative, but one plausible theory proposes what’s called a seesaw mechanism, which creates both a set of neutrinos with anomalously small masses and a set of counterparts with anomalously large ones. (See the Quick Study by Rabi Mohapatra, Physics Today, April 2010, page 68 .) Although the high-mass particles don’t show up in the universe today, they could have affected the dynamics of the early universe. If so, then knowing just how anomalously small the neutrino masses are is a step toward understanding their massive counterparts.

Neutrinos’ effect on cosmology doesn’t stop there. Because ordinary low-mass neutrinos are so numerous, even in the most remote parts of intergalactic space, they can have a significant effect on the expansion of the universe. Relativistic neutrinos in an expanding universe behave like radiation: Their number density is diluted and their wavelengths are stretched over time. But as the expansion continues, they behave more like matter, which has a cosmologically different effect. When the transition occurs depends on their mass.

And cosmology also offers an alternative route to measuring the neutrino mass. Neutrinos pervade the universe and imbue all space with a background mass density: Not only do they not clump together to form large-scale structures, but their gravitational influence on other matter would have slowed its own clumping. In a sufficiently detailed comparison of structure in the early universe and today, the effect should be measurable.

But last year’s results from the Dark Energy Spectroscopic Instrument (DESI) at the Kitt Peak National Observatory show no sign of such a neutrino-mass effect. ³ The DESI researchers estimated an upper bound on m₁ + m₂ + m₃ of 0.072 eV. That’s at least ostensibly more than an order of magnitude tighter than KATRIN’s result and quite close to the lower bound from flavor oscillation (from which m₁ + m₂ + m₃ > 0.06 eV). “It’s starting to seem worrisome that cosmology doesn’t show any hint of the neutrino mass,” says Christoph Wiesinger, a KATRIN team member from the Technical University of Munich. “It should have seen something by now.”

But DESI’s analysis assumes the standard cosmological model, in which dark energy takes the form of a cosmological constant that doesn’t change over time or space. And DESI’s results this year cast doubt on that assumption. ⁴ If the density of dark energy is allowed to evolve over time, the sum of the neutrino masses could be much larger and still be consistent with the DESI observations.

“A terrestrial mass measurement would be helpful for cosmology,” says Lokhov. “It might help to fix a parameter in their model.” KATRIN’s kinematic data-taking is scheduled to wrap up later this year, for a total of four years’ worth of data not included in the latest analysis. That should be enough to shrink the bound on the neutrino mass by another factor of two.

This article was originally published online on 22 May 2025.