Theory of the Fermi Interaction

Abstract

The representation of Fermi particles by two-component Pauli spinors satisfying a second order differential equation and the suggestion that in $\ensuremath{\beta}$ decay these spinors act without gradient couplings leads to an essentially unique weak four-fermion coupling. It is equivalent to equal amounts of vector and axial vector coupling with two-component neutrinos and conservation of leptons. (The relative sign is not determined theoretically.) It is taken to be "universal"; the lifetime of the $\ensuremath{\mu}$ agrees to within the experimental errors of 2%. The vector part of the coupling is, by analogy with electric charge, assumed to be not renormalized by virtual mesons. This requires, for example, that pions are also "charged" in the sense that there is a direct interaction in which, say, a ${\ensuremath{\pi}}^{0}$ goes to ${\ensuremath{\pi}}^{\ensuremath{-}}$ and an electron goes to a neutrino. The weak decays of strange particles will result qualitatively if the universality is extended to include a coupling involving a $\ensuremath{\Lambda}$ or $\ensuremath{\Sigma}$ fermion. Parity is then not conserved even for those decays like $K\ensuremath{\rightarrow}2\ensuremath{\pi} or 3\ensuremath{\pi}$ which involve no neutrinos. The theory is at variance with the measured angular correlation of electron and neutrino in ${\mathrm{He}}^{6}$, and with the fact that fewer than ${10}^{\ensuremath{-}4}$ pion decay into electron and neutrino.