Interference Effects in Leptonic Decays

Abstract

It is proven that in any leptonic decay experiment in which the lepton masses and charges may be neglected, and in which no pseudoscalar correlations are measured, all $V·A$ interference terms will be antisymmetric under exchange of the two leptons, while the pure $V$ and $A$ terms will be symmetric. If the experiment measures a pseudoscalar correlation, these conclusions are reversed. Even if the lepton masses cannot be ignored (e.g., for ${\Lambda }^0\to {\mu }^{-}+\overline{\nu }+p$, or low-energy $\beta$ decay) it is still true that no $V·A$ interference may appear when scalars are measured, and only $V·A$ interference may contribute when pseudoscalars are measured, providing that the lepton spins and momenta are not directly observed. Thus experiments can be devised that involve no interference effects, or only interference effects. This theorem holds independently of the strangeness change, spin change, energy transfer, or of any particular assumptions about the form of the $V$ and $A$ currents. It proves most useful when it is difficult or tedious to calculate transition rates directly. Applications are discussed, including possible tests of the Feynman-Gell-Mann theory in nonunique forbidden $\beta$ decay, of the nature of the leptonic ${\Lambda }^0$ and $K^0$ decay interaction, and of the charge symmetry properties of weak interactions.