Fermi's Weak Decay Rate Formula

$$\Gamma_{weak} = \frac{G_F^2 m^5}{192\pi^3}$$

Status: Proven — the formula itself. Its application in this paper series was found to be wrong.

This is Enrico Fermi’s real 1934 effective (contact-interaction) theory of beta decay, later understood as the low-energy limit of the full electroweak theory. It correctly gives a particle’s weak-decay rate as a function of its mass $m$ and the Fermi coupling constant $G_F$.

Real, independent confirmation: this exact formula, applied to the muon (using the muon’s actual rest mass), reproduces the real, measured muon lifetime (2.2 μs) almost exactly — a genuine, standard, textbook-verified result. See Symbols & Units for $G_F$’s own real measured value.

Used in: Paper 7 and Paper 10, applied to the neutron using its full rest mass (939 MeV) rather than the small proton-neutron mass difference (the real Q-value, ~0.782 MeV, that actually governs neutron beta decay per Sargent’s rule). This session’s 2026-07-21 audit — verified first against the muon, where the same formula and method reproduce the real value almost exactly, confirming the formula and arithmetic are sound — found this misapplication produces a result about 13 orders of magnitude off the real neutron lifetime (~880 s), the most severe single error found across the whole papers audit. The formula is real and correctly stated; it was applied to the wrong input for this specific decay.