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

Based on $(10087\pm 44)\times {10}^6$ $J\mathrm{/}\psi$ 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 ${\mathrm{\Sigma }}^{+}\to p{\pi }^0$ and ${\mathrm{\Sigma }}^{+}\to n{\pi }^{+}$ is performed. The branching fractions are determined to be $B_{{\mathrm{\Sigma }}^{+}\to p{\pi }^0}=(49.79\pm 0.06\pm 0.22)\mathrm{\%}$ and $B_{{\mathrm{\Sigma }}^{+}\to n{\pi }^{+}}=(49.87\pm 0.05\pm 0.29)\mathrm{\%}$, 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 ${\mathrm{\Sigma }}^{+}\to p{\pi }^0$ and 3.4$\sigma$ for ${\mathrm{\Sigma }}^{+}\to n{\pi }^{+}$. Furthermore, the $\mathrm{\Delta }I=1\mathrm{/}2$ rule is tested in nonleptonic ${\mathrm{\Sigma }}^{\pm }$ decays. The observed results deviate from zero by more than $5\sigma$, indicating the presence of the $\mathrm{\Delta }I=3\mathrm{/}2$ transition amplitude in the $\mathrm{\Sigma }$ hyperon decays.