Neutrino Oscillation Probability Calculator

Neutrino oscillation is the quantum mechanical phenomenon where a neutrino created in one flavor (electron, muon, or tau) has a probability of being detected as a different flavor after traveling some distance, caused by neutrinos having mass and their flavor and mass eigenstates being different (mixed) quantum states.

P(νa→νb) = sin²(2θ)sin²(1.267Δm²L/E), where θ is the mixing angle, Δm² is the mass-squared splitting in eV², L is the baseline distance in kilometres, and E is the neutrino energy in GeV. The constant 1.267 makes these specific units work directly.

The mixing angle describes how much the flavor eigenstates (electron, muon, tau neutrino) overlap with the mass eigenstates. θ=45° gives 'maximal mixing' (the largest possible oscillation amplitude, sin²(2θ)=1), while θ=0° or θ=90° means no mixing (no oscillation) between those two states.

Δm² is the difference of the squares of two neutrino mass eigenstates (in eV²). Because oscillation only depends on this squared mass difference (not the individual absolute masses), oscillation experiments cannot directly measure absolute neutrino masses, only mass-squared splittings.

The T2K long-baseline experiment uses a baseline of about 295 km and a muon neutrino beam energy around 0.6 GeV, probing the atmospheric mass-squared splitting Δm²≈2.5×10⁻³ eV², producing a large, near-maximal oscillation probability at that baseline and energy.

The oscillation phase 1.267Δm²L/E depends only on the ratio L/E (for fixed Δm²), because a neutrino accumulates oscillation phase proportionally to how long it travels relative to its energy (inversely related to its de Broglie wavelength), this is why experiments are often designed around a specific L/E to probe a particular Δm².

No, real neutrino oscillation involves three flavors and three mixing angles (the PMNS matrix) plus two independent mass-squared splittings and a CP-violating phase. The two-flavor formula used here is an excellent approximation when one splitting and one angle dominate a given experiment's sensitivity, the standard simplification used in most introductory treatments.

The survival probability, 1−P(νa→νb), is the probability that a neutrino created in flavor a is still detected in flavor a (has not oscillated away) after traveling the given baseline, this calculator reports it directly alongside the oscillation (flavor-change) probability.

The Super-Kamiokande experiment's 1998 measurement of atmospheric neutrino flavor ratios, and the Sudbury Neutrino Observatory's measurement of solar neutrino flavors, both provided decisive evidence for oscillation, work recognized with the 2015 Nobel Prize in Physics (Takaaki Kajita and Arthur B. McDonald).

Yes, oscillation can only occur if Δm²≠0, meaning at least two neutrino mass eigenstates have different (and therefore nonzero) masses, direct proof that neutrinos are not massless as originally assumed in the Standard Model.