Radiative corrections to the nonleptonicΞdecays and theΔI=12selection rule

Abstract

The effects of radiative corrections on the $\Delta I=\frac{1}{2}$ rule predictions for the nonleptonic $\Xi$ decays are studied. The radiative corrections are estimated using standard perturbation theory, assuming that all particles are structureless. Two different Lagrangian models are considered and it is found that the radiative corrections are sensitive to the choice of the Lagrangian. Most of the results have the usual divergence difficulties which are overcome with the aid of a cutoff. The results for the branching ratio $\frac{\Gamma ({\Xi }^{-}\to {\Lambda }^0{\pi }^{-})}{\Gamma ({\Xi }^0\to {\Lambda }^0{\pi }^0)}$ give a corrected value in disagreement with the latest experimental data by as much as 5.3 standard deviations. The corrections to the asymmetry parameters lead to good agreement between $\Delta I=\frac{1}{2}$ and experiment.