Neutrino Mass: The Number Physics Still Cannot Pin Down
Physics knows the mass of every fundamental particle it has found, usually to several decimal places. There is one exception. Twenty-five years after it became certain that neutrinos weigh something, nobody can say what any of them weighs. We know one is heavier than another by a specific amount. We do not know where the ladder starts. That gap is not a footnote - it sits at the centre of several open questions about why matter exists in the form it does.
Why Oscillation Cannot Give You a Mass
A neutrino does not have a single well-defined mass. It exists as a superposition of three mass states, and what an experiment detects as an electron, muon or tau neutrino is a particular mixture of those three. As the mixture travels, the components accumulate quantum phase at slightly different rates, and the identity of the whole changes. That is neutrino oscillation.
The rate at which the phases separate depends on the difference between the squared masses of the states involved - not on the masses themselves. An experiment that measures oscillation therefore measures a difference and is completely blind to what you would have to add to both states to get their actual values.
Two such differences have been measured. The smaller, from solar and reactor experiments, is about 7.5 times 10^-5 square electronvolts. The larger, from atmospheric and accelerator experiments, is roughly 2.5 times 10^-3. Both are known to a few percent.
From those you can extract a lower bound. If the lightest state weighed exactly nothing, the heaviest would still have to weigh the square root of the larger difference, around 0.05 electronvolts. So the mass scale has a floor. It has no ceiling from oscillation data at all.
Three Ways to Attack the Scale
The first route is kinematic, and it is the only one that assumes nothing beyond energy conservation. In beta decay the released energy is shared between an electron and an antineutrino, so the electron's maximum possible energy is reduced by the neutrino's rest mass. KATRIN measures that shortfall in tritium decay and has pushed the upper limit below 0.45 electronvolts. It measures an effective combination of the three states weighted by how much electron neutrino each contains.
The second route is neutrinoless double beta decay. If the neutrino is its own antiparticle, a rare nuclear decay becomes possible in which two neutrons convert to two protons and emit two electrons but no neutrinos at all. The rate depends on a different weighted combination of the masses. This route is more sensitive than kinematics, but it only works if the neutrino has a particular character - so a null result is ambiguous.
The third route is cosmological. Neutrinos are the second most abundant particle in the universe, so even a tiny mass affects how cosmic structure formed: massive neutrinos stream out of forming structures and smooth them out. Observations of the cosmic microwave background and galaxy surveys currently constrain the sum of the three masses to roughly 0.12 electronvolts, which is tighter than the laboratory limits. But that number is derived inside a cosmological model, and it moves when the model changes.
The three methods measure three different quantities - an effective kinematic mass, an effective Majorana mass, and a sum. They are not interchangeable, and comparing them is itself a test of the underlying physics.
The Ordering Problem
The two measured differences tell us that two states sit close together and one sits apart. What they do not tell us is whether the lone state is above the pair or below it. The first case is called normal ordering, the second inverted.
This is not a detail. The two arrangements predict measurably different rates for neutrinoless double beta decay, different cosmological signatures, and different prospects for every future experiment. Until it is settled, a whole class of results has to be quoted twice.
Two experiments are attacking it by unrelated methods. DUNE will use the way matter in the Earth distorts oscillation over 1,300 kilometres, and JUNO will read a vacuum interference pattern at 52 kilometres where matter effects vanish. Current data already favour normal ordering, but not yet at a level anyone treats as settled.
The answer matters most for the second measurement route above. In inverted ordering, neutrinoless double beta decay would have a rate that the next generation of experiments can reach. In normal ordering with a very light lightest state, it could be far below anything currently planned.
Why the Smallness Is a Real Puzzle
In the Standard Model as originally written, neutrinos are exactly massless. This was not an accident of fitting data. The model gives mass to particles through their interaction with the Higgs field, and that mechanism requires both a left-handed and a right-handed version of the particle. Every charged fermion has both. The neutrino, as the model was built, has only the left-handed one, so there is nothing for the Higgs field to couple to.
Oscillation broke that. The simplest repair is to add a right-handed neutrino and give it a Higgs coupling like everyone else - but then the coupling strength has to be around 10^-12, roughly a million times smaller than the electron's and with no explanation for why.
The alternative is that neutrino mass comes from a different mechanism altogether, one available only to a particle that is electrically neutral. In that picture the tiny observed mass is the inverse image of an enormous mass scale, far beyond any accelerator, and the smallness stops being arbitrary. This is the reasoning behind the seesaw family of models, and it is one of the main reasons neutrino mass is treated as a window onto physics at energies nobody can reach directly.
Which explanation is right depends on whether the neutrino is its own antiparticle, and that question is currently only answerable through neutrinoless double beta decay.
What the Number Does Not Tell You
The neutrino mass is sometimes invoked in discussions of energy, on the reasoning that mass implies extractable energy through the mass-energy relation. That inference does not survive contact with the numbers.
A neutrino of 0.1 electronvolts carries a rest energy of 0.1 electronvolts, which is about 1.6 times 10^-20 joules. Even the full solar flux of roughly 65 billion neutrinos per square centimetre per second represents a negligible power density, and that is before accounting for the fact that essentially none of them interact. The mass is not a stored resource; it is a parameter in the particle's behaviour.
The relevant constraint remains the interaction probability, which is what every detector on this site exists to overcome. Neutrinovoltaic research addresses a different question entirely - whether ambient radiation and thermal fluctuations at an engineered material surface can drive a measurable current - and the neutrino mass value has no bearing on it either way.
What the mass does determine is cosmology, the structure of the lepton sector, and whether the leading explanations for the matter-antimatter asymmetry can work. Those are the reasons three separate experimental programmes are chasing a number smaller than a millionth of an electron's mass.
Frequently asked questions
Do we know that neutrinos have mass?
Yes. Oscillation requires it, and oscillation has been observed with solar, atmospheric, reactor and accelerator neutrinos by independent experiments. At least two of the three mass states are non-zero.
Why can't oscillation experiments give the actual mass?
Because the oscillation rate depends on differences between squared masses, not on the masses themselves. Adding the same amount to all three states leaves every oscillation prediction unchanged.
What is the current best limit?
Direct kinematic measurement gives below about 0.45 eV, and cosmology gives roughly 0.12 eV for the sum of all three - though the cosmological number depends on the model it is derived within. The floor from oscillation is about 0.05 eV for the heaviest state.
Why is such a small mass considered a problem?
Because the Standard Model's mass mechanism would require a coupling around a million times weaker than the electron's, with nothing explaining why. The alternative explanations tie the smallness to physics at energies far beyond any accelerator.
Does neutrino mass mean neutrinos carry usable energy?
No. A rest mass of 0.1 eV is about 1.6 times 10^-20 joules, and essentially none of the flux interacts with anything. The mass is a parameter of the particle's behaviour, not a stored resource.
