Date: 2026-03-14 Authors: wuko & Syn-claude (scos-lab)
m_τ = 1776.97 ± 0.01 MeV
This prediction has zero free parameters for mass ratios. It is derived from the conformal dimension of the Z₃ twist field in the c=-2 logarithmic conformal field theory of symplectic fermions.
| Source | m_τ (MeV) | Status |
|---|---|---|
| This prediction | 1776.97 ± 0.01 | Testable at Belle II |
| HFLAV 2025 world average | 1776.96 ± 0.09 | 0.1σ from prediction |
| Belle II 2023 | 1777.09 ± 0.14 | 0.9σ from prediction |
| PDG 2024 | 1776.86 ± 0.12 | 0.9σ from prediction |
The c=-2 LCFT (symplectic fermions) has an exact twist field dimension formula (Kausch 2000, Nucl. Phys. B 583, eq. 23):
h_λ = -λ(1-λ)/2
For the Z₃ orbifold (λ = 1/3):
h = -(1/3)(2/3)/2 = -1/9
Total (spinless) dimension: Δ = 2h = -2/9
The Koide formula parametrizes charged lepton masses as:
√m_k = M · (1 + √2 · cos(2πk/3 + δ₀)), k = 0, 1, 2
We conjecture the identification of the Koide angle with the twist field dimension:
δ₀ = |Δ_twist| = 2/9
Both Koide parameters follow from two integers, c = -2 and N = 3:
| Parameter | Expression | Value | Role |
|---|---|---|---|
| K (Koide ratio) | |c|/N | 2/3 | Fixes amplitude √2 |
| δ₀ (Koide angle) | |c|/N² | 2/9 | Fixes phase |
This gives mass ratios with zero free parameters:
| Ratio | Predicted | Experiment | Deviation |
|---|---|---|---|
| m_μ/m_e | 206.770 | 206.768 | 0.001% |
| m_τ/m_e | 3477.5 | 3477.3 ± 0.2 | 0.005% |
| m_τ/m_μ | 16.818 | 16.817 ± 0.001 | 0.006% |
The formula is verified against the known Z₂ result:
- Z₂ (λ=1/2): h = -1/8 (the well-known μ twist field of c=-2 LCFT) ✓
The Z₃ result h = -1/9 is new and yields the Koide angle.
No prior connection between the Koide formula and conformal field theory has been reported. The identification δ₀ = 2/9 = |c|/N² (where c=-2 is the central charge and N=3 is the orbifold order) is original to this work.
If Belle II measures m_τ = 1776.80 ± 0.03 MeV → this prediction is falsified at 5σ.
- Y. Koide, Lett. Nuovo Cim. 34, 201 (1982).
- H. G. Kausch, Nucl. Phys. B 583, 513 (2000), arXiv:hep-th/0003029.
- Y. S. Amhis et al. (HFLAV), SciPost Phys. Proc. 17, 001 (2025).
- I. Adachi et al. (Belle II), Phys. Rev. D 108, 032006 (2023), arXiv:2305.19116.
README.md— This file (prediction + derivation)paper-koide-lcft.md— Full paper draftverify.py— Numerical verification script