page_title: Neutrino oscillation
section_title: Three neutrino probabilities
hierarchical_section_title: Neutrino oscillation / Theory, graphically / Three neutrino probabilities
context_page_description: Neutrino oscillation is a quantum mechanical phenomenon wherein a neutrino created with a specific lepton family number can later be measured to have a different lepton family number. The probability of measuring a particular flavor for a neutrino varies between three known states, as it propagates through space.
  First predicted by Bruno Pontecorvo in 1957, neutrino oscillation has since been observed by a multitude of experiments in several different contexts. Notably, the existence of neutrino oscillation resolved the long-standing solar neutrino problem.
  Neutrino oscillation is of great theoretical and experimental interest, as the precise properties of the process can shed light on several properties of the neutrino. In particular, it implies that the neutrino has a non-zero mass, which requires a modification to the Standard Model of particle physics. The experimental discovery of neutrino oscillation, and thus neutrino mass, by the Super-Kamiokande Observatory and the Sudbury Neutrino Observatories was recognized with the 2015 Nobel Prize for Physics.
context_section_description: If three neutrinos are considered, the probability for each neutrino to appear is somewhat complex. The graphs below show the probabilities for each flavor, with the plots in the left column showing a long range to display the slow "solar" oscillation, and the plots in the right column zoomed in, to display the fast "atmospheric" oscillation. The parameters used to create these graphs (see below) are consistent with current measurements, but since some parameters are still quite uncertain, some aspects of these plots are only qualitatively correct.
  The illustrations were created using the following parameter values:
  sin²(2 θ₁₃) = 0.10 (Determines the size of the small wiggles.)
  sin²(2 θ₂₃) = 0.97
  sin²(2 θ₁₂) = 0.861
  δ = 0 (If the actual value of this phase is large, the probabilities will be somewhat distorted, and will be different for neutrinos and antineutrinos.)
  Normal mass hierarchy: m₁ ≤ m₂ ≤ m₃
  Δm²
  ₁₂ = 7.59×10⁻⁵ eV²
  Δm²
  ₃₂ ≈ Δm²
  ₁₃ = 2.32×10⁻³ eV²
caption: Electron neutrino oscillations, long range. Here and in the following diagrams black means electron neutrino, blue means muon neutrino and red means tau neutrino.[23]