First measurement of the absolute branching fractions of $\Sigma^+$ nonleptonic decays and test of the $\Delta I = 1/2$ rule

Based on $(10087 \pm 44) \times 10^6$ $J/\psi$ events collected by the BESIII detector at the center-of-mass energy $\sqrt{s} = 3.097$ GeV, the first absolute measurement of the branching fractions for the decays $\Sigma^+ \to p \pi^0$ and $\Sigma^+ \to n \pi^+$ is performed. The branching fractions are determined to be $B_{\Sigma^+ \to p \pi^0} = (49.79 \pm 0.06 \pm 0.22)\%$ and $B_{\Sigma^+ \to n \pi^+} = (49.87 \pm 0.05 \pm 0.29)\%$, where the first uncertainties are statistical and the second systematic. These results show significant deviations from the PDG values for both decays, with differences of 4.4$\sigma$ for $\Sigma^+ \to p \pi^0$ and 3.4$\sigma$ for $\Sigma^+ \to n \pi^+$. Furthermore, the $\Delta I = 1/2$ rule is tested in nonleptonic $\Sigma^\pm$ decays. The observed results deviate from zero by more than $5\sigma$, indicating the presence of the $\Delta I = 3/2$ transition amplitude in the $\Sigma$ hyperon decays.