Role of the ${\Delta }^{\ast }(1940)$ in the ${\pi }^{+}p\to K^{+}{\Sigma }^{+}(1385)$ and $pp\to n{K}^{+}{\Sigma }^{+}(1385)$ reactions

Abstract

The $pp\to n{K}^{+}{\Sigma }^{+}(1385)$ reaction is a very good isospin $3/2$ filter for studying ${\Delta }^{++\ast }$ resonance decaying to $K^{+}{\Sigma }^{+}(1385)$. Within the effective Lagrangian method, we investigate the $\Sigma (1385)$ (spin-parity $J^P=3/2^{+}$) hadronic production in the ${\pi }^{+}p\to K^{+}{\Sigma }^{+}(1385)$ and $pp\to n{K}^{+}{\Sigma }^{+}(1385)$ reactions. For ${\pi }^{+}p\to K^{+}{\Sigma }^{+}(1385)$ reaction, in addition to the "background" contributions from $t$-channel $K^{\ast 0}$ exchange, $u$-channel $\Lambda (1115)$ and ${\Sigma }^0(1193)$ exchange, we also consider the contribution from the $s$-channel ${\Delta }^{\ast }(1940)$ resonance, which has significant coupling to $K\Sigma (1385)$ channel. We show that the inclusion of the ${\Delta }^{\ast }(1940)$ resonance leads to a fairly good description of the low energy experimental total cross section data of ${\pi }^{+}p\to K^{+}{\Sigma }^{+}(1385)$ reaction. Basing on the study of ${\pi }^{+}p\to K^{+}{\Sigma }^{+}(1385)$ reaction and with the assumption that the excitation of ${\Delta }^{\ast }(1940)$ resonance dominant the $pp\to n{K}^{+}{\Sigma }^{+}(1385)$ reaction, we calculate the total and differential cross sections of $pp\to n{K}^{+}{\Sigma }^{+}(1385)$ reaction. It is shown that the new experimental data support the important role played by the ${\Delta }^{\ast }(1940)$ resonance with a mass in the region of $1940$ MeV and a width of around $200$ MeV. We also demonstrate that the invariant mass distribution and the Dalitz Plot provide direct information of the ${\Sigma }^{+}(1385)$ production, which can be tested by future experiments.

arXiv commentPublished in Phys. Rev. C. arXiv admin note: substantial text overlap with arXiv:1302.0468

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