Muon g-2: Anomalous Magnetic Moment

Storage Ring

Magnetic field B 1.45 T

Anomaly a = (g−2)/2 0.00116

Visual amplification ×1

Time speed 1.0×

Live Readouts

Cyclotron freq ω_c

0 rad/s

Spin freq ω_s

0 rad/s

Anomalous freq ω_a

0 rad/s

g-2 period T_a

0 µs

Spin–momentum angle

0.0°

Laps completed

How it works

A charged particle circling in a uniform magnetic field B turns at the cyclotron frequency ω_c = qB/(γm). If its magnetic moment were exactly the Dirac value g = 2, its spin would precess at exactly the same rate as its momentum vector, and the angle between spin and momentum would never change lap to lap.

ω_c = qB / (γm)               cyclotron (momentum) rotation
ω_s = g/2 · qB / (γm) − ...   spin precession (Thomas–BMT)
ω_a = ω_s − ω_c = a·qB/m      anomalous precession, a = (g−2)/2

QED loop corrections (the muon briefly emitting and reabsorbing virtual photons) make g slightly larger than 2, so a ≈ 0.00116 for the muon. The spin vector then drifts slowly relative to the momentum direction as the particle laps the ring — exactly the "wiggle" signal (decay-positron rate vs time) that real g-2 storage-ring experiments at Fermilab and CERN measure to pin down a to 10 significant figures, the most precise confrontation between theory and experiment in physics.

Magnetic field B — sets the cyclotron frequency of the orbit.
Anomaly a — the (g−2)/2 value; drag to 0 to see spin and momentum stay perfectly locked, or crank it up to exaggerate the drift.
Visual amplification — the real a is far too small to see directly in one lap, so this multiplies the spin-lag angle for display only (readouts stay physically accurate).
Wiggle plot (top-right of the canvas) — the spin–momentum angle traced over time, mirroring the oscillating decay-positron count of a real g-2 measurement.

Momentum (cyclotron) Spin (Thomas–BMT)

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Muon g-2: Anomalous Magnetic Moment in a Storage Ring