Five-parameter fit formula: N(t) = N₀ · exp(-t/γτ) · [1 + A · cos(ω_a · t + φ)]
Honoring multi-decade contributions from CERN, Brookhaven (E821), and Fermilab (E989)
Five-parameter fit formula: N(t) = N₀ · exp(-t/γτ) · [1 + A · cos(ω_a · t + φ)]
| Scenario / Baseline | Value a_μ | Method / Source | Tension |
|---|---|---|---|
| Fermilab E989 (Combined) | 0.00116592061 |
Final Run 1-6 Storage Ring | Reference |
| Theory Initiative (2020) | 0.00116591810 |
e⁺e⁻ → Hadrons (Dispersive) | 5.1 σ Tension |
| BMW Collaboration (2021) | 0.00116591954 |
Ab-Initio Lattice QCD | 1.5 σ (Consistent) |
| Dirac Baseline (Tree-Level) | 0.00000000000 |
g = 2 exact (No QFT loops) | > 1000 σ |
1. Relativistic Magic Momentum: Muons are injected into a 1.4513 Tesla uniform dipole ring at p = 3.09 GeV/c (γ = 29.3). At this "magic momentum," the electric field focusing term (a_μ - 1/(γ² - 1)) vanishes completely, isolating purely magnetic spin precession.
2. Spin vs. Momentum: If muons were ideal Dirac fermions (g = 2), their spin would rotate at the exact same rate as their momentum (ω_s = ω_c), meaning the spin vector would always point in the direction of flight. Because virtual quantum loops (QED, Electroweak, and Hadronic Vacuum Polarization) add an anomaly a_μ = (g-2)/2 ≈ 0.0011659, the spin rotates faster at ω_a = ω_s - ω_c = a_μ (eB/m).
3. Parity-Violating Decay: In weak muon decay (μ⁺ → e⁺ + ν_e + anti-ν_μ), high-energy positrons are emitted preferentially in the direction of the muon's spin vector. As the spin sweeps past the ring's 24 lead-fluoride calorimeters, the count of detected positrons oscillates, generating the iconic wiggle plot.