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Role of the $Δ^*(1940)$ in the $π^+ p \to K^+ Σ^+(1385)$ and $pp \to n K^+ Σ^+(1385)$ reactions

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