Effective Neutrino Number N_eff
Effective Neutrino Number N_eff: τ-value 3.000, observed 2.99 ± 0.17, deviation –.
Prediction
τ-Formula
| **N_eff = | gen | = 3.000 (not 3.044, no QED correction)** |
Derivation
The bottom quark mass as a standalone $τ$-prediction:
m_b = m_t(τ) · ι_τ^45/13 = W_3(3)|lobes|^2 · W_3(4) · ι_τ^-20/13 · m_n = 1720\,ι_τ^-20/13\,m_n = 4,174.4\;MeV
at $-1,351$ ppm from PDG $m_b(MS, m_b) = 4,180 ± 7$ MeV (within $0.8σ$).
Combined exponent. The exponent $-20/13 = -5 + 45/13 = (-65+45)/13$ decomposes as: [ -2013 = -|lobes|^2 · W_3(4)a_3 = -4 × 513, ] the negative of the denominator prefactor of the top mass divided by $a_3$. Equivalently, $m_b/m_n = (17/20)\,ι_τ^-20/13 = 4.443$, a dimensionless ratio governed entirely by CF arithmetic.
Source
This prediction is derived in the Physics Ledger (Chapter 36 — koide-mass-hierarChapter ies), Books IV–V of Panta Rhei.