Study ofπ−p→Σ−K+at 1170MeVc

We have measured the differential and total cross sections of the reaction ${\pi }^{-}p\to {\Sigma }^{-}{K}^{+}$ with $1170-\frac{\mathrm{MeV}}{c}$ pions incident on the Alvarez 72-in. hydrogen bubble chamber. Using 1338 events, we find the coefficients in the Legendre expansion of the differential cross section $\frac{d\sigma }{d\Omega }=A_0{P}_0+A_1{P}_1+A_2{P}_2$ to be $A_0=18.38\mathrm{}\pm 0.50$ μb/sr, $A_1=7.54\mathrm{}\pm 0.96$ μb/sr, and $A_2=11.10\mathrm{}\pm 1.21$ μb/sr, corresponding to a total cross section $\sigma =231\mathrm{}\pm 6$ μb. No polynomials higher than $P_2$ are needed. The decay asymmetry ${\alpha }_{-}{P}_{-}$ of the decay ${\Sigma }^{-}\to n{\pi }^{-}$ is consistent with zero. Using previously reported results for the differential cross sections of the reactions ${\pi }^{-}p\to {\Sigma }^0{K}^0$ and ${\pi }^{+}p\to {\Sigma }^{+}{K}^{+}$ at $1170-\frac{\mathrm{MeV}}{c}$ incident pion momentum, we have compared the results with the predictions of the hypothesis of charge independence. We have found no significant violations of that hypothesis. We have compared the measured polarization of the ${\Sigma }^0$ with the prediction from the charge-independence hypothesis, using the measured differential cross sections of the three production reactions and the polarization of the ${\Sigma }^{+}$, as determined in the decay ${\Sigma }^{+}\to p{\pi }^0$. The results agree with the prediction.