Neutrino Flavor Oscillations

Neutrinos are produced as flavor eigenstates (νe, νμ, ντ) but propagate as mass eigenstates (ν₁, ν₂, ν₃). The mismatch causes quantum oscillations — a νe produced at a reactor will periodically become a νμ. This was the first evidence for non-zero neutrino mass.

Mixing angle θ₁₂ (°): 33.8 Δm²₂₁ (10⁻⁵ eV²): 7.4 Energy E (MeV): 3.0 Matter density ρ (g/cm³): 0

Osc. length L_osc: — km

P(νe→νe) at 50km: —

Effective θ (matter): —°

P(νe→νμ) = sin²(2θ)·sin²(Δm²L/4E)
L in km, E in MeV, Δm² in eV²

MSW matter: θ_eff via
cos(2θ_eff) = (cos2θ-A)/(Δm²)

Solar neutrino problem: solved by MSW effect (matter-enhanced mixing). Reactor experiments: KamLAND measured θ₁₂, Δm²₂₁. Default values are best-fit PDG 2023 parameters. The bottom plot shows P(νe→νe) as a function of L and E.