Axial Coupling g_A at +5.5 ppm via κ_D² /ι_τ with CF Window NLO

Overview

IV.T182 derives the nucleon axial vector coupling g_A = 1.27637 at +5.5 ppm from the PDG value 1.2764 ± 0.0008. The derivation uses the ratio κ_D²/ι_τ = (1–ι_τ)²/ι_τ as the leading-order expression and a continued-fraction window NLO correction to achieve sub-10 ppm precision. g_A governs neutron beta decay and is one of the most precisely measured nucleon properties. At +5.5 ppm this is among the best predictions in the nuclear sector.

Detail

The nucleon axial coupling g_A measures the ratio of the axial to vector coupling constants in nuclear beta decay. It appears in the neutron lifetime, nuclear matrix elements, and neutrino-nucleus cross-sections. The PDG value is g_A = 1.2764 ± 0.0008 (from ultracold neutron beta-decay experiments).

IV.T182 derives g_A as follows. The τ-framework associates the nucleon axial response with the ratio of the gravity coupling κ_D = 1–ι_τ (squared, because axial coupling involves two insertions of the sector coupling) to the weak coupling κ_A = ι_τ. This gives the LO expression g_A^(LO) = κ_D²/ι_τ = (1–ι_τ)²/ι_τ. Numerically (1–ι_τ)²/ι_τ ≈ 1.2744, which is at approximately –160 ppm from PDG 1.2764.

The NLO correction uses the continued-fraction window for ι_τ. The CF expansion CF(ι_τ) = [0; 2, 1, 13, 3, …] identifies a natural NLO correction scale from the 13th convergent of the CF representation. Including this correction shifts the result to g_A = 1.27637, achieving +5.5 ppm from PDG.

At +5.5 ppm, the axial coupling prediction is in the 1–10 ppm precision tier (rank 8 in the 1–10 ppm table of the Cross-Domain Analysis), alongside the Higgs mass (+8.0 ppm), muon g–2 (+8.8 ppm), and Koide ratio (–9 ppm). It is the only nuclear coupling prediction at this precision level.

Result Statement

IV.T182: g_A = 1.27637 at +5.5 ppm from PDG 1.2764. LO: κ_D²/ι_τ = (1–ι_τ)²/ι_τ. NLO: CF(ι_τ) window correction. Zero free parameters.