How We Know Neutrinos Have Mass

Right now, about a hundred trillion neutrinos are streaming through your body every second, and not one of them will touch a single atom of you. They are the second most abundant particle in the universe after the photon, and for most of the twentieth century physicists were certain they weighed exactly nothing. That certainty was wrong. But the proof did not come from weighing one, because nobody has ever managed to. It came from a stranger observation: catch a neutrino changing from one type into another in mid-flight, and you have proven it has mass, because only a massive particle can do that.

Flavour states and mass states are different objects

Neutrinos come in three flavours: electron, muon and tau. The weak interaction defines those labels. A neutrino produced alongside a muon is a muon neutrino, by definition.

Neutrinos also come in three mass states, written ν₁, ν₂ and ν₃. Each has a definite mass and travels through space cleanly. These are the states that propagate.

The two sets do not line up. A muon neutrino is not any one mass state. It is a specific quantum superposition of all three, and the PMNS matrix holds the coefficients. Three mixing angles and one phase fully specify that matrix. This mismatch between how a neutrino is made and how it travels is the entire mechanism.

Oscillation is interference between mass states

Create a muon neutrino and you create three mass states moving together. Each carries a quantum phase that advances as it travels. Because the masses differ, the phases advance at different rates, and the superposition drifts out of step.

Some distance downstream, the same three components now add up to a different flavour mixture. Detect the neutrino there and it may register as an electron or tau neutrino. Nothing transformed along the way. The interference pattern simply moved.

In the simplified two-flavour case the survival probability takes a compact form: P = 1 − sin²(2θ) sin²(1.27 Δm² L / E), with Δm² in eV², baseline L in kilometres and energy E in GeV. The mixing angle θ sets how deep the oscillation dips. The mass-squared difference sets its wavelength.

The formula contains only mass differences

Look again at what appears in that expression. Δm², not m. Oscillation experiments measure the gaps between the squared masses and nothing else.

Add a constant to all three masses and every oscillation prediction stays identical. The absolute scale is invisible to this entire class of experiment, however precise it becomes.

That is why the field splits cleanly in two. Oscillation experiments fix the mixing angles and the splittings. Answering how heavy a neutrino actually is requires completely different apparatus, covered further down.

The solar neutrino problem was the first clue

Ray Davis began counting solar neutrinos in the late 1960s using a tank of dry-cleaning fluid the size of a swimming pool, 100,000 gallons of it, buried nearly a mile underground in the Homestake gold mine to shield it from cosmic rays. Every few weeks a chlorine atom in the fluid would absorb an electron neutrino and turn into argon, and Davis extracted and counted those handful of argon atoms one by one.

He found roughly a third of the flux that solar models predicted. The deficit persisted for three decades.

The result stayed ambiguous the whole time, because two explanations fit equally well. Either the Sun was not behaving as modelled, or the neutrinos were doing something on the way. Gallium experiments at GALLEX and SAGE confirmed a deficit at lower energies too, which narrowed the space for a purely astrophysical fix but did not close it.

Super-Kamiokande settled it with atmospheric neutrinos

Cosmic rays hitting the upper atmosphere produce showers of muon and electron neutrinos in a ratio close to two to one. That ratio comes from particle physics, not from any astrophysical model, which makes it a far cleaner prediction than the solar flux.

Super-Kamiokande exploited geometry. Neutrinos arriving from directly overhead had travelled about 15 kilometres. Neutrinos arriving from below had crossed the entire Earth, roughly 13,000 kilometres. Same detector, same energies, baselines differing by a factor of a thousand.

In 1998 the collaboration reported that downgoing muon neutrinos arrived in the expected numbers while upgoing ones were depleted by about half. The deficit tracked distance. That is the signature of oscillation, and it was the first compelling evidence for neutrino mass.

SNO proved the neutrinos changed rather than vanished

Super-Kamiokande showed muon neutrinos going missing. It could not show where they went. The Sudbury Neutrino Observatory closed that gap with a kilotonne of heavy water.

Deuterium gave SNO two distinct reaction channels. Charged-current interactions on deuterium respond only to electron neutrinos. Neutral-current interactions respond to all three flavours with equal strength. One detector therefore measured both the electron neutrino flux and the total flux at once.

The 2002 result was decisive. The electron neutrino flux came in at about a third of prediction, matching Homestake. The total flux across all flavours matched the Standard Solar Model. The missing neutrinos had become muon and tau neutrinos in transit, and the solar model had been right all along. Takaaki Kajita and Arthur McDonald shared the 2015 Nobel Prize for these two results.

KamLAND reproduced the effect with a man-made source

Solar and atmospheric neutrinos come from sources nobody controls. KamLAND removed that objection by watching antineutrinos from Japanese nuclear reactors, at an average baseline near 180 kilometres.

The experiment did more than confirm a deficit. It resolved the energy spectrum finely enough to see the oscillation dip and partial recovery predicted by the L over E dependence. A generic loss of neutrinos would not produce that shape.

Seeing the actual waveform, from a source with a known power output and a known distance, moved oscillation from strong inference to direct observation.

Accelerators and reactors pinned down the parameters

Once the effect was established, the work shifted to precision. K2K, MINOS, T2K and NOvA fire muon neutrino beams at detectors hundreds of kilometres away, measuring both disappearance of muon neutrinos and appearance of electron neutrinos.

The third mixing angle held out longest. Many theorists expected θ₁₃ to be zero. In 2012 Daya Bay, RENO and Double Chooz measured it as clearly nonzero using short-baseline reactor antineutrinos. That result mattered beyond bookkeeping: a nonzero θ₁₃ is what makes leptonic CP violation observable at all.

IceCube DeepCore now adds atmospheric measurements at much higher energies, and Borexino has mapped the solar spectrum down to the pp neutrinos that carry most of the Sun’s output.

Where the numbers stand

The NuFIT 6.1 global fit, covering data available in November 2025, combines all of the above. Four parameters are now well determined.

• θ₁₂ ≈ 33.7°, the solar angle, from solar and reactor data.
• θ₁₃ ≈ 8.6°, the smallest angle, from short-baseline reactors.
• Δm²₂₁ ≈ 7.5 × 10⁻⁵ eV², the solar splitting.
• |Δm²₃ℓ| ≈ 2.5 × 10⁻³ eV², the atmospheric splitting, about 30 times larger.

Two quantities remain stubborn. The angle θ₂₃ sits near 45°, and the data cannot yet say which side of it. The CP-violating phase δ is poorly constrained, and its allowed range depends on which mass ordering you assume.

JUNO’s first data reset the precision

JUNO is a 20 kilotonne liquid scintillator detector sitting 52.5 kilometres from several reactor cores. That baseline is chosen so the fine interference structure of reactor antineutrinos falls inside the detector’s energy resolution.

Its first published result used 59.1 days of data and 2,379 candidate events, collected after detector completion in August 2025. From that short exposure the collaboration reported sin²θ₁₂ = 0.3092 ± 0.0087 and Δm²₂₁ = (7.50 ± 0.12) × 10⁻⁵ eV².

Those are precisions of 2.8% and 1.6%, a factor of 1.6 better than every previous measurement combined. Two months of running displaced decades of accumulated data on the solar parameters. We cover what that first result does and does not settle in JUNO’s first result and the neutrino mass ordering.

Direct mass measurement: KATRIN weighs the endpoint

The most model-independent approach ignores oscillation entirely and uses kinematics. In tritium beta decay, an electron and an antineutrino share a fixed energy budget. If the neutrino has mass, creating it costs energy, and the electron spectrum stops fractionally short of where it otherwise would.

KATRIN measures that endpoint with a 70 metre beamline and a high-resolution electrostatic spectrometer. Its 2025 result analysed 36 million electrons collected over 259 measurement days across five campaigns.

The bound is an effective electron antineutrino mass below 0.45 eV at 90% confidence, the tightest direct limit to date. Note the gap: 0.45 eV sits roughly ten times above the minimum the oscillation splittings require. This method is clean but not yet sharp enough to detect the mass it is looking for. The collaboration finished data taking in 2025 after reaching 1,000 days, and the full analysis is expected to approach 0.3 eV.

Cosmology gives the tightest number and the most caveats

Massive neutrinos stream freely out of collapsing regions in the early universe and suppress the growth of structure on small scales. The size of that suppression scales with the summed mass of all three species, written Σmν.

Combining DESI DR2 baryon acoustic oscillation measurements with Planck and ACT data yields Σmν < 0.0642 eV at 95% confidence, assuming ΛCDM. The oscillation splittings set a floor of about 0.059 eV for the normal ordering. Almost no room remains between the two.

Double beta decay would answer a different question

A third experimental line searches for neutrinoless double beta decay, in which two neutrons decay together and emit no neutrinos at all. Nobody has observed it.

The process is only possible if the neutrino is its own antiparticle, a Majorana rather than Dirac fermion. A detection would establish that, would violate lepton number conservation, and would constrain a particular combination of the masses.

KamLAND-Zen, GERDA and LEGEND have pushed the limits steadily without a signal. Half-life limits now exceed 10²⁶ years, and the corresponding bounds on the effective Majorana mass reach down toward the top of the inverted-ordering band, though converting between the two depends on nuclear matrix element calculations that carry their own sizeable uncertainties. This measurement addresses the nature of the neutrino rather than its mass scale, and the two questions are often conflated in coverage.

The mass ordering is the live question

Oscillation fixes the size of the atmospheric splitting but not its sign. Two arrangements remain open. Normal ordering puts ν₃ heaviest, with two light states below it. Inverted ordering puts the close pair on top and the lone state at the bottom.

The choice has measurable consequences. Normal ordering allows a summed mass as low as 0.059 eV. Inverted ordering demands at least about 0.10 eV, which current cosmological data already strains badly.

Oscillation data alone gives only a mild preference for normal ordering, and the significance shifts depending on which datasets enter the fit. JUNO expects roughly six to seven years of exposure to reach three sigma on its own, with faster progress in combination with accelerator results.

Established, contested, unproven

Established. At least two neutrinos carry nonzero mass. Three-flavour mixing describes solar, atmospheric, reactor and accelerator data together. Four of the six oscillation parameters are known to a few percent.

Contested. The cosmological mass bound. It is now tight enough to sit at or below the floor that oscillation requires, which points to either an unrecognised systematic, a wrong assumption about dark energy, or something genuinely new. We follow that standoff in neutrino mass: the sky and the laboratory still disagree.

Unproven. The mass ordering. The value of δ. Which side of 45° θ₂₃ falls on. The absolute mass scale. Whether neutrinos are Majorana particles. Whether a fourth, sterile neutrino exists at all. And the question underneath all of them: why these masses are at least a million times smaller than the electron’s.