Short-distance scale invariance and the structure of weak transitions

Abstract

The effects of short-distance interactions between hadronic weak currents on the structure of weak transitions are investigated within Wilson's scheme of operator-product expansions and broken scale invariance. It is pointed out that a consistent understanding of these effects can be attained with the hypothesis that the dimensions of nonexotic fields are near-canonical while those of exotic fields are anomalously high. The lack of structure-dependent effects in the ΔI=½ part of ordinary nonleptonic decay, the suppression of the ΔI=3/2 part in the same, and the smallness of the K₁⁰-K₂⁰ mass difference are first explained following Wilson's arguments. The structure of higher-order semileptonic decays disobeying the ΔS=ΔQ role is then discussed. Finally, the important role played by short-distance effects in radiative nonleptonic decays of hadrons is elucidated and a mechanism for the large asymmetry parameter observed in the reaction Σ⁺→p+γ is obtained.