Fermi coupling constant

Fermi wrote his theory of beta decay in 1933 as a four-fermion contact interaction with a single coupling; the journal Nature rejected the paper as too speculative. The coupling has dimensions of inverse energy squared, which is the tell-tale sign of an effective theory hiding a heavy mediator — in this case the W boson, so that G_F/√2 = g²/(8M_W²).

Its numerical value is extracted almost entirely from the muon lifetime, which is why G_F is known to half a part per million while the weak force itself seems so feeble. The weakness is not in the coupling but in the mediator's 80 GeV mass: at energies far below M_W the propagator suppresses everything, giving neutrino cross sections around 10⁻³⁸ cm² and letting a solar neutrino cross a light-year of lead unscathed. At LHC energies the suppression disappears and the weak interaction is comparable in strength to electromagnetism.