On the structure and parity of weak interaction currents

Abstract

The formulation of weak interactions by means of a current interacting with itself is generalized to the case in which T = 3 2 currents also exist, assuming the ΔT = 1 2 rule to be valid. Furthermore, generalizing the Feynman-Gell-Mann theory, it is postulated that all the currents entering the weak interactions are conserved in the limit of meson masses and baryon mass differences being neglected. This restriction limits the isotopic spin of the currents to T = 1 2 , 1, and 3 2 if S = 2 currents are excluded. Another consequence of the same hypothesis is that parity mixtures are allowed for the T = 1 2 and T = 1 currents, but not for the T = 3 2 current. The five types of currents thus obtained ( V and A currents with T = 1 2 , 1 and only V or A with T = 3 2 ) can be combined into a 4 × 4 matrix current | J χ . It is shown that a weak Lagrangian proportional to the trace of |J λ †|J λ satisfies the ΔT = 1 2 rule. In the absence of neutral lepton currents the charged lepton current is necessarily incorporated in a rather unsymmetrical manner, but in conformity with the ΔT = 1 2 rule in strangeness changing leptonic decays. The scheme is applied to the decay of Σ hyperons. In the pionic decay of Σ +, and in the lowest order in strong interactions, parity is conserved in the channel Σ + → n + π + and violated in the channel Σ + → ϱ + π 0 if all the five types of current are present. The phenomenological Lagrangian of Bludman for Σ decay is obtained as a direct interaction from the terms of the weak Lagrangian. Finally, a model of a baryonmeson nonlinear interaction generalizing a previous model is given in which all the five types of conserved currents are shown to exist.