$\pi^+$ Emission from Hypernuclei and the Weak $\Delta I=3/2$ Transitions

Abstract

Low energy $\pi^+$ emission in hypernuclear weak decays is studied in the soft pion limit. It is found that the $\pi^+$ decay amplitude is dominated by the $\Delta I=3/2$ part of nonmesonic weak decays according to the soft pion theorem. The ratios, $R(\pi^+/soft \pi^-) $, for light hypernuclei are estimated in the direct quark mechanism, which predicts violation of the $\Delta I=1/2$ rule, and found to be about 1/3 for $^4_{\Lambda}He$.