Theory of Neutral Leptonic Currents

D'Espagnat's theory of weak interactions is extended to include neutral leptonic currents. It is found possible to obtain agreement with the experimental absence of neutral lepton currents in all processes involving hadrons in a natural way, but only by introducing $i\equiv \surd \mathrm{}(-1\mathrm{})\mathrm{}$ multiplying the entire leptonic Lagrangian. It is also found natural to couple the $\mu$ leptons and the $e$ leptons in symmetrical, but different, ways. The consequences of the coupling scheme, in addition to the sought-for absence of most neutral currents, are: (1) separate conservation of $\mu$ and $e$ leptons, (2) a mechanism for the $\mu -e$ mass difference, (3) production of $\mu$ pairs in $e$-type neutrino scattering and in $\mu$ scattering. If, in addition, the decoupling of hadronic and leptonic neutral currents which we have set up is broken by any small perturbation, $\mathrm{CP}$ violation results. The experimental consequences of two such possible symmetry-breaking mechanisms are discussed.