Neutrino oscillations — evidence for mass
An extension of the topic of elementary particles and nuclear physics. Neutrinos produced in nuclear reactions (e.g. in the Sun) can change their type ("flavour") during flight — the probability of this change oscillates with distance. Such oscillation is possible only if the neutrino has nonzero mass (Nobel 2015).
I will give you a target survival probability — tune the distance L and energy E to reach it.
What just happened?
The neutrino started with a single, pure flavour, and the longer the distance it travelled, the greater the chance it reaches the detector as a different flavour — and not randomly, but periodically, like a wave.
Oscillation formula (two-flavour approximation):
P — the probability that the neutrino keeps its initial flavour; L — distance (km); E — energy (GeV); Δm² — the difference of the squared masses of the neutrino’s two mass states (eV²); θ — the mixing angle.
Why does this prove the neutrino has mass?
If Δm² = 0 (both masses equal, e.g. both zero — as the original Standard Model assumed), the argument of the sine would always be zero and P = 1 at every distance — the flavour would never change. Since we do observe oscillations:
What is conserved and what is not?
The total number of neutrinos does not change — the panel on the right shows that the "N" bar is always full. What oscillates is only the split into flavours (bars "A" and "B"), because the neutrino travels as a mixture of mass states that "drift apart in phase" with distance.
Why this matters for your exam:
In advanced nuclear and particle physics what counts is qualitative reasoning: observation (flavour change) → conclusion (nonzero mass) → contradiction with the original Standard Model. This is the classic exam task of "from an experiment, draw a conclusion about a particle property".
Remember: neutrino flavour oscillations (Nobel 2015, Kajita and McDonald) are possible only when the neutrino has nonzero mass — the number of neutrinos is conserved, only their flavour changes.
Theory & formulas
The phenomenon
A neutrino is born in one of three "flavours" (electron, muon, tau). During flight the probability of detecting a given flavour changes periodically — the neutrino can change its type.
Condition for oscillations
Such oscillation is possible only when the neutrino mass states differ in mass, that is when the difference of squared masses is nonzero (). This means the neutrino has nonzero mass.
Key relationships
- the larger the mass difference , the faster (over a shorter distance) the flavour change occurs,
- the probability of a change grows with the distance and decreases with the energy of the neutrino.
It was precisely the observation of oscillations that was the first proof that neutrinos are not massless (Nobel 2015).
Frequently asked questions
›What are neutrino oscillations?
A periodic change of a neutrino's "flavour" (type) during flight, dependent on the distance travelled.
›Why do oscillations prove that the neutrino has mass?
Because, according to quantum mechanics, a flavour change requires a mass difference between neutrino types (Δm²≠0).
›What is a neutrino "flavour"?
One of three types: electron, muon, tau — associated with the corresponding lepton.
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