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

TL;DR

This paper investigates the role of the $ ext{Δ}^*(1940)$ resonance in $ ext{π}^+ p$ and $pp$ reactions producing $ ext{K}^+ ext{Σ}^+(1385)$, showing its significant contribution to experimental cross sections and providing predictions for future measurements.

Contribution

It introduces the $ ext{Δ}^*(1940)$ resonance into the effective Lagrangian model for these reactions, offering a better fit to data and new insights into its properties.

Findings

The $ ext{Δ}^*(1940)$ resonance significantly improves the description of low-energy cross sections.

Experimental data support the resonance's mass around 1940 MeV and width near 200 MeV.

Invariant mass and Dalitz plot analyses can reveal details of $ ext{Σ}^+(1385)$ production.

Abstract

The $p p \to n K^+ \Sigma^+(1385)$ reaction is a very good isospin $3/2$ filter for studying $\Delta^{++*}$ 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 $p p \to n K^+ \Sigma^+(1385)$ reactions. For $\pi^+ p \to K^+ \Sigma^+(1385)$ reaction, in addition to the "background" contributions from $t$-channel $K^{*0}$ exchange, $u$-channel $\Lambda(1115)$ and $\Sigma^0(1193)$ exchange, we also consider the contribution from the $s$-channel $\Delta^*(1940)$ resonance, which has significant coupling to $K\Sigma(1385)$ channel. We show that the inclusion of the $\Delta^*(1940)$ 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 $\Delta^*(1940)$ resonance dominant the $pp \to n K^+ \Sigma^+(1385)$ reaction, we calculate the total and differential cross sections of $p p \to n K^+ \Sigma^+(1385)$ reaction. It is shown that the new experimental data support the important role played by the $\Delta^*(1940)$ 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.