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 $\ensuremath{\Delta}I=\frac{1}{2}$ part of ordinary nonleptonic decay, the suppression of the $\ensuremath{\Delta}I=\frac{3}{2}$ part in the same, and the smallness of the ${K}_{1}^{0}\ensuremath{-}{K}_{2}^{0}$ mass difference are first explained following Wilson's arguments. The structure of higher-order semileptonic decays disobeying the $\ensuremath{\Delta}S=\ensuremath{\Delta}Q$ 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 ${\ensuremath{\Sigma}}^{+}\ensuremath{\rightarrow}p+\ensuremath{\gamma}$ is obtained.