Neutrino Oscillation & Dark Matter Halo Simulator

Neutrino Beam

Baseline L 180 km

Energy E 1.0 GeV

Δm² 2.5 ×10⁻³ eV²

Mixing angle θ 34°

P(νe → νe) at detector

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Oscillation length

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Dominant flavor at detector

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How it works

A neutrino is born in one flavor state (here, electron-flavor νe) but is really a quantum superposition of three mass eigenstates. Because those mass states travel at very slightly different phases, the flavor composition oscillates sinusoidally with distance — a beam that starts pure νe drifts toward νμ and back as it propagates, then reappears as νe further downstream. Each glowing particle in the beam is colored by the survival probability at its current position along the baseline, so the color bands you see moving down the beam are a direct picture of the standing oscillation pattern in space.

P(νe → νe) = 1 − sin²(2θ)·sin²(1.267·Δm²[eV²]·L[km] / E[GeV])
L_osc = π·E / (1.267·Δm²)

Baseline L — distance from source to detector; a longer baseline lets more oscillation cycles fit between them.
Energy E — higher-energy neutrinos oscillate more slowly in space, stretching the oscillation length.
Δm² — the squared mass splitting between eigenstates; a bigger splitting compresses the oscillation length.
Mixing angle θ — sets how deep the oscillation swings; θ = 45° gives full νe ↔ νμ conversion at the peak, θ near 0° gives almost none.

The dim violet cloud drifting around the beam represents the galaxy's dark-matter halo — the unseen mass (≈27% of the universe's energy budget) inferred from flat galactic rotation curves, v² = GM(r)/r, where ordinary visible matter alone predicts velocities should fall off with radius but observations show they stay flat far beyond the visible disk. Leading WIMP and axion candidates interact only through gravity and (weakly) the weak force, which is why the halo here never lights up — only the neutrino beam it surrounds does.

νe (electron flavor) νμ (muon flavor) Dark-matter halo

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