Poles and Resonances in the Processπ++p→Σ++K+

Abstract

Several models considered in successively greater degrees of complexity are discussed for the $T=\frac{3}{2}$ process ${\pi }^{+}+p\to {\Sigma }^{+}+K^{+}$. The ingredients of the model are $\Lambda$ and $K^{*}$ poles, the $p_{\frac{3}{2}}$, 1238-MeV resonance and an $f_{\frac{7}{2}}$ resonance at 1925 MeV. Although various combinations of these terms yield generally good results for the total and differential cross sections from threshold (beam momentum of 1021 MeV/c) to 1.76 BeV/c, calculated ${\Sigma }^{+}$ polarizations are too small. Much better agreement is found with the polarization if the pole terms are multiplied by $e^{l\delta }$ where $\delta$ is taken to be a constant of magnitude 40-50°. Such a term may arise from the presence of other open channels. The quantum numbers $f_{\frac{7}{2}}$ for the 1925-MeV resonance are consistent with the notion that this resonance is a Regge recurrence of the $p_{\frac{3}{2}}$, 1238-MeV state.