Proton–Neutron Mass Splitting

τ-Formula

Δm / mₙ = (3/16)√3 · ι_τ⁵ − (3/20)α · ι_τ²

Derivation

The proton–neutron mass splitting is given by the two-sector formula:

where $α ≈ 1/137.036$ is the fine-structure constant and $ι_τ = 2/(π + e)$. The first term is the strong-sector (C-sector) contribution; the second is the electromagnetic correction (B-sector). Numerically:

in agreement with the measured value at $+33$ ppm. (Registry: IV.T142, Wave 1.)

Structural anatomy. The two-sector formula (eq:ch60-pn-formula) has a transparent structure:

Source

This prediction is derived in the Numerical Physics Ledger (Chapter 60 — mass-spectrum), Books IV–V of Panta Rhei.